Factor Quadratics to Find Zeros - Algebra 2
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What is the factored form of $2x^2+7x+3$?
What is the factored form of $2x^2+7x+3$?
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$(2x+1)(x+3)$. Use AC method: $2 \cdot 3 = 6$, factors $1$ and $6$ add to $7$.
$(2x+1)(x+3)$. Use AC method: $2 \cdot 3 = 6$, factors $1$ and $6$ add to $7$.
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What are the zeros of $f(x)=(x-4)(x-5)$?
What are the zeros of $f(x)=(x-4)(x-5)$?
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$x=4,5$. Set each factor equal to zero: $x-4=0$ or $x-5=0$.
$x=4,5$. Set each factor equal to zero: $x-4=0$ or $x-5=0$.
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What is the factored form of $x^2+6x+9$?
What is the factored form of $x^2+6x+9$?
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$(x+3)^2$. Perfect square trinomial: $x^2+6x+9=(x+3)^2$.
$(x+3)^2$. Perfect square trinomial: $x^2+6x+9=(x+3)^2$.
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What are the zeros of $f(x)=x^2-16$?
What are the zeros of $f(x)=x^2-16$?
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$x=4,-4$. From factored form $x^2-16=(x-4)(x+4)$.
$x=4,-4$. From factored form $x^2-16=(x-4)(x+4)$.
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What are the zeros of $f(x)=3x^2-10x-8$?
What are the zeros of $f(x)=3x^2-10x-8$?
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$x=-\frac{2}{3},4$. From factored form $3x^2-10x-8=(3x+2)(x-4)$.
$x=-\frac{2}{3},4$. From factored form $3x^2-10x-8=(3x+2)(x-4)$.
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What is the factored form of $x^2+x-12$?
What is the factored form of $x^2+x-12$?
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$(x+4)(x-3)$. Find two numbers that multiply to $-12$ and add to $1$: $4$ and $-3$.
$(x+4)(x-3)$. Find two numbers that multiply to $-12$ and add to $1$: $4$ and $-3$.
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What is the factored form of $x^2+7x+12$?
What is the factored form of $x^2+7x+12$?
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$(x+3)(x+4)$. Find two numbers that multiply to $12$ and add to $7$: $3$ and $4$.
$(x+3)(x+4)$. Find two numbers that multiply to $12$ and add to $7$: $3$ and $4$.
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What are the zeros of $f(x)=(x-5)(x+2)$?
What are the zeros of $f(x)=(x-5)(x+2)$?
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$x=5,-2$. Set each factor equal to zero: $x-5=0$ or $x+2=0$.
$x=5,-2$. Set each factor equal to zero: $x-5=0$ or $x+2=0$.
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What is the relationship between factors and zeros for $f(x)=(x-r)(x-s)$?
What is the relationship between factors and zeros for $f(x)=(x-r)(x-s)$?
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Zeros are $x=r$ and $x=s$. When $(x-r)=0$ then $x=r$, and when $(x-s)=0$ then $x=s$.
Zeros are $x=r$ and $x=s$. When $(x-r)=0$ then $x=r$, and when $(x-s)=0$ then $x=s$.
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What is the factored form of $x^2-9$?
What is the factored form of $x^2-9$?
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$(x-3)(x+3)$. Difference of squares: $a^2-b^2=(a-b)(a+b)$.
$(x-3)(x+3)$. Difference of squares: $a^2-b^2=(a-b)(a+b)$.
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What are the zeros of $f(x)=x^2-9$?
What are the zeros of $f(x)=x^2-9$?
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$x=3,-3$. Set each factor equal to zero: $x=3$ or $x=-3$.
$x=3,-3$. Set each factor equal to zero: $x=3$ or $x=-3$.
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What is the factored form of $x^2-5x+6$?
What is the factored form of $x^2-5x+6$?
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$(x-2)(x-3)$. Find two numbers that multiply to $6$ and add to $-5$: $-2$ and $-3$.
$(x-2)(x-3)$. Find two numbers that multiply to $6$ and add to $-5$: $-2$ and $-3$.
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What are the zeros of $f(x)=x^2-5x+6$?
What are the zeros of $f(x)=x^2-5x+6$?
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$x=2,3$. From factored form $x^2-5x+6=(x-2)(x-3)$.
$x=2,3$. From factored form $x^2-5x+6=(x-2)(x-3)$.
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What is the factored form of $x^2+2x-15$?
What is the factored form of $x^2+2x-15$?
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$(x+5)(x-3)$. Find two numbers that multiply to $-15$ and add to $2$: $5$ and $-3$.
$(x+5)(x-3)$. Find two numbers that multiply to $-15$ and add to $2$: $5$ and $-3$.
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What are the zeros of $f(x)=(x+5)(x-3)$?
What are the zeros of $f(x)=(x+5)(x-3)$?
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$x=-5,3$. Set each factor equal to zero: $x+5=0$ or $x-3=0$.
$x=-5,3$. Set each factor equal to zero: $x+5=0$ or $x-3=0$.
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What is the factored form of $x^2-2x-8$?
What is the factored form of $x^2-2x-8$?
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$(x-4)(x+2)$. Find two numbers that multiply to $-8$ and add to $-2$: $-4$ and $2$.
$(x-4)(x+2)$. Find two numbers that multiply to $-8$ and add to $-2$: $-4$ and $2$.
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What is the factored form of $x^2+11x+24$?
What is the factored form of $x^2+11x+24$?
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$(x+3)(x+8)$. Find two numbers that multiply to $24$ and add to $11$: $3$ and $8$.
$(x+3)(x+8)$. Find two numbers that multiply to $24$ and add to $11$: $3$ and $8$.
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What are the zeros of $f(x)=(x+3)(x+8)$?
What are the zeros of $f(x)=(x+3)(x+8)$?
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$x=-3,-8$. Set each factor equal to zero: $x+3=0$ or $x+8=0$.
$x=-3,-8$. Set each factor equal to zero: $x+3=0$ or $x+8=0$.
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What is the factored form of $x^2-11x+24$?
What is the factored form of $x^2-11x+24$?
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$(x-3)(x-8)$. Find two numbers that multiply to $24$ and add to $-11$: $-3$ and $-8$.
$(x-3)(x-8)$. Find two numbers that multiply to $24$ and add to $-11$: $-3$ and $-8$.
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What are the zeros of $f(x)=x^2-11x+24$?
What are the zeros of $f(x)=x^2-11x+24$?
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$x=3,8$. From factored form $x^2-11x+24=(x-3)(x-8)$.
$x=3,8$. From factored form $x^2-11x+24=(x-3)(x-8)$.
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What is the factored form of $x^2+9x+20$?
What is the factored form of $x^2+9x+20$?
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$(x+4)(x+5)$. Find two numbers that multiply to $20$ and add to $9$: $4$ and $5$.
$(x+4)(x+5)$. Find two numbers that multiply to $20$ and add to $9$: $4$ and $5$.
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What is the factored form of $x^2-9x+20$?
What is the factored form of $x^2-9x+20$?
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$(x-4)(x-5)$. Find two numbers that multiply to $20$ and add to $-9$: $-4$ and $-5$.
$(x-4)(x-5)$. Find two numbers that multiply to $20$ and add to $-9$: $-4$ and $-5$.
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What is the factored form of $x^2-13x+36$?
What is the factored form of $x^2-13x+36$?
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$(x-4)(x-9)$. Find two numbers that multiply to $36$ and add to $-13$: $-4$ and $-9$.
$(x-4)(x-9)$. Find two numbers that multiply to $36$ and add to $-13$: $-4$ and $-9$.
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What are the zeros of $f(x)=x^2-13x+36$?
What are the zeros of $f(x)=x^2-13x+36$?
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$x=4,9$. From factored form $x^2-13x+36=(x-4)(x-9)$.
$x=4,9$. From factored form $x^2-13x+36=(x-4)(x-9)$.
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What is the factored form of $x^2+13x+36$?
What is the factored form of $x^2+13x+36$?
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$(x+4)(x+9)$. Find two numbers that multiply to $36$ and add to $13$: $4$ and $9$.
$(x+4)(x+9)$. Find two numbers that multiply to $36$ and add to $13$: $4$ and $9$.
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What is the factored form of $x^2-4x-21$?
What is the factored form of $x^2-4x-21$?
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$(x-7)(x+3)$. Find two numbers that multiply to $-21$ and add to $-4$: $-7$ and $3$.
$(x-7)(x+3)$. Find two numbers that multiply to $-21$ and add to $-4$: $-7$ and $3$.
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What are the zeros of $f(x)=(x-7)(x+3)$?
What are the zeros of $f(x)=(x-7)(x+3)$?
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$x=7,-3$. Set each factor equal to zero: $x-7=0$ or $x+3=0$.
$x=7,-3$. Set each factor equal to zero: $x-7=0$ or $x+3=0$.
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What is the factored form of $x^2+4x-21$?
What is the factored form of $x^2+4x-21$?
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$(x+7)(x-3)$. Find two numbers that multiply to $-21$ and add to $4$: $7$ and $-3$.
$(x+7)(x-3)$. Find two numbers that multiply to $-21$ and add to $4$: $7$ and $-3$.
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What is the factored form of $x^2-6x+9$?
What is the factored form of $x^2-6x+9$?
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$(x-3)^2$. Perfect square trinomial: $x^2-6x+9=(x-3)^2$.
$(x-3)^2$. Perfect square trinomial: $x^2-6x+9=(x-3)^2$.
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What is the zero (with multiplicity) of $f(x)=(x-3)^2$?
What is the zero (with multiplicity) of $f(x)=(x-3)^2$?
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$x=3$ with multiplicity $2$. A repeated factor gives a zero with multiplicity equal to the exponent.
$x=3$ with multiplicity $2$. A repeated factor gives a zero with multiplicity equal to the exponent.
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