Factor Quadratics to Find Zeros - Algebra
Card 1 of 30
What is the factored form of $2x^2+5x+3$?
What is the factored form of $2x^2+5x+3$?
Tap to reveal answer
$(2x+3)(x+1)$. Use AC method or trial factoring with leading coefficient 2.
$(2x+3)(x+1)$. Use AC method or trial factoring with leading coefficient 2.
← Didn't Know|Knew It →
What is the factored form of $x^2-6x$?
What is the factored form of $x^2-6x$?
Tap to reveal answer
$x(x-6)$. Factor out GCF of $x$ from both terms.
$x(x-6)$. Factor out GCF of $x$ from both terms.
← Didn't Know|Knew It →
What are the zeros of $f(x)=3x(2x+3)$?
What are the zeros of $f(x)=3x(2x+3)$?
Tap to reveal answer
$x=0$ and $x=-\frac{3}{2}$. Set each factor to zero: $3x=0$ and $(2x+3)=0$.
$x=0$ and $x=-\frac{3}{2}$. Set each factor to zero: $3x=0$ and $(2x+3)=0$.
← Didn't Know|Knew It →
What is the first step to factor $6x^2+9x$ to reveal zeros?
What is the first step to factor $6x^2+9x$ to reveal zeros?
Tap to reveal answer
Factor out the GCF: $3x(2x+3)$. Factor out the greatest common factor before finding zeros.
Factor out the GCF: $3x(2x+3)$. Factor out the greatest common factor before finding zeros.
← Didn't Know|Knew It →
What is the factored form of $3x^2+2x-8$?
What is the factored form of $3x^2+2x-8$?
Tap to reveal answer
$(3x-4)(x+2)$. Use AC method or trial factoring with leading coefficient 3.
$(3x-4)(x+2)$. Use AC method or trial factoring with leading coefficient 3.
← Didn't Know|Knew It →
What are the zeros of $f(x)=2x^2-x-3$ after factoring?
What are the zeros of $f(x)=2x^2-x-3$ after factoring?
Tap to reveal answer
$x=\frac{3}{2}$ and $x=-1$. From $(2x-3)(x+1)=0$, set each factor to zero.
$x=\frac{3}{2}$ and $x=-1$. From $(2x-3)(x+1)=0$, set each factor to zero.
← Didn't Know|Knew It →
What is the factored form of $2x^2-x-3$?
What is the factored form of $2x^2-x-3$?
Tap to reveal answer
$(2x-3)(x+1)$. Use AC method or trial factoring with leading coefficient 2.
$(2x-3)(x+1)$. Use AC method or trial factoring with leading coefficient 2.
← Didn't Know|Knew It →
What are the zeros of $f(x)=x^2+12x+35$ after factoring?
What are the zeros of $f(x)=x^2+12x+35$ after factoring?
Tap to reveal answer
$x=-5$ and $x=-7$. From $(x+5)(x+7)=0$, set each factor to zero.
$x=-5$ and $x=-7$. From $(x+5)(x+7)=0$, set each factor to zero.
← Didn't Know|Knew It →
What are the zeros of $f(x)=3x^2+2x-8$ after factoring?
What are the zeros of $f(x)=3x^2+2x-8$ after factoring?
Tap to reveal answer
$x=\frac{4}{3}$ and $x=-2$. From $(3x-4)(x+2)=0$, set each factor to zero.
$x=\frac{4}{3}$ and $x=-2$. From $(3x-4)(x+2)=0$, set each factor to zero.
← Didn't Know|Knew It →
What are the zeros of $f(x)$ if $f(x)=(5x-10)(2x+1)$?
What are the zeros of $f(x)$ if $f(x)=(5x-10)(2x+1)$?
Tap to reveal answer
$x=2$ and $x=-\frac{1}{2}$. Set each factor equal to zero: $(5x-10)=0$ gives $x=2$.
$x=2$ and $x=-\frac{1}{2}$. Set each factor equal to zero: $(5x-10)=0$ gives $x=2$.
← Didn't Know|Knew It →
What are the zeros of $f(x)=2x^2+5x+3$ after factoring?
What are the zeros of $f(x)=2x^2+5x+3$ after factoring?
Tap to reveal answer
$x=-\frac{3}{2}$ and $x=-1$. From $(2x+3)(x+1)=0$, set each factor to zero.
$x=-\frac{3}{2}$ and $x=-1$. From $(2x+3)(x+1)=0$, set each factor to zero.
← Didn't Know|Knew It →
What are the zeros of $f(x)=3x^2-12$ using the factored form?
What are the zeros of $f(x)=3x^2-12$ using the factored form?
Tap to reveal answer
$x=2$ and $x=-2$. From $3(x-2)(x+2)=0$, only the linear factors give zeros.
$x=2$ and $x=-2$. From $3(x-2)(x+2)=0$, only the linear factors give zeros.
← Didn't Know|Knew It →
What is the factored form of $3x^2-12$?
What is the factored form of $3x^2-12$?
Tap to reveal answer
$3(x-2)(x+2)$. Factor out 3, then use difference of squares.
$3(x-2)(x+2)$. Factor out 3, then use difference of squares.
← Didn't Know|Knew It →
What are the zeros of $f(x)=x^2-6x$ after factoring?
What are the zeros of $f(x)=x^2-6x$ after factoring?
Tap to reveal answer
$x=0$ and $x=6$. From $x(x-6)=0$, set each factor to zero.
$x=0$ and $x=6$. From $x(x-6)=0$, set each factor to zero.
← Didn't Know|Knew It →
What are the zeros of $f(x)=2x^2+8x$ using its factored form?
What are the zeros of $f(x)=2x^2+8x$ using its factored form?
Tap to reveal answer
$x=0$ and $x=-4$. From $2x(x+4)=0$, set each factor to zero.
$x=0$ and $x=-4$. From $2x(x+4)=0$, set each factor to zero.
← Didn't Know|Knew It →
What is the factored form of $2x^2+8x$?
What is the factored form of $2x^2+8x$?
Tap to reveal answer
$2x(x+4)$. Factor out GCF of $2x$ from both terms.
$2x(x+4)$. Factor out GCF of $2x$ from both terms.
← Didn't Know|Knew It →
What are the zeros of $f(x)=x^2+10x+25$ after factoring?
What are the zeros of $f(x)=x^2+10x+25$ after factoring?
Tap to reveal answer
$x=-5$ (double root). From $(x+5)^2=0$, the repeated factor gives one zero.
$x=-5$ (double root). From $(x+5)^2=0$, the repeated factor gives one zero.
← Didn't Know|Knew It →
What are the zeros of $f(x)=x^2-16$ after factoring?
What are the zeros of $f(x)=x^2-16$ after factoring?
Tap to reveal answer
$x=4$ and $x=-4$. From $(x-4)(x+4)=0$, set each factor to zero.
$x=4$ and $x=-4$. From $(x-4)(x+4)=0$, set each factor to zero.
← Didn't Know|Knew It →
What are the zeros of $f(x)=x^2-9x+20$ after factoring?
What are the zeros of $f(x)=x^2-9x+20$ after factoring?
Tap to reveal answer
$x=5$ and $x=4$. From $(x-5)(x-4)=0$, set each factor to zero.
$x=5$ and $x=4$. From $(x-5)(x-4)=0$, set each factor to zero.
← Didn't Know|Knew It →
What are the zeros of $f(x)=x^2+7x+12$ after factoring?
What are the zeros of $f(x)=x^2+7x+12$ after factoring?
Tap to reveal answer
$x=-3$ and $x=-4$. From $(x+3)(x+4)=0$, set each factor to zero.
$x=-3$ and $x=-4$. From $(x+3)(x+4)=0$, set each factor to zero.
← Didn't Know|Knew It →
What is the factored form of $x^2+10x+25$?
What is the factored form of $x^2+10x+25$?
Tap to reveal answer
$(x+5)^2$. Perfect square trinomial: $a^2+2ab+b^2=(a+b)^2$.
$(x+5)^2$. Perfect square trinomial: $a^2+2ab+b^2=(a+b)^2$.
← Didn't Know|Knew It →
What is the factored form of $x^2-25$?
What is the factored form of $x^2-25$?
Tap to reveal answer
$(x-5)(x+5)$. Difference of squares pattern: $a^2-b^2=(a-b)(a+b)$.
$(x-5)(x+5)$. Difference of squares pattern: $a^2-b^2=(a-b)(a+b)$.
← Didn't Know|Knew It →
What are the zeros of $f(x)=x^2+3x-10$ after factoring?
What are the zeros of $f(x)=x^2+3x-10$ after factoring?
Tap to reveal answer
$x=-5$ and $x=2$. From $(x+5)(x-2)=0$, set each factor to zero.
$x=-5$ and $x=2$. From $(x+5)(x-2)=0$, set each factor to zero.
← Didn't Know|Knew It →
What is the factored form of $x^2+3x-10$?
What is the factored form of $x^2+3x-10$?
Tap to reveal answer
$(x+5)(x-2)$. Find two numbers that multiply to $-10$ and add to 3: 5 and $-2$.
$(x+5)(x-2)$. Find two numbers that multiply to $-10$ and add to 3: 5 and $-2$.
← Didn't Know|Knew It →
What are the zeros of $f(x)$ if $f(x)=(2x+3)^2$?
What are the zeros of $f(x)$ if $f(x)=(2x+3)^2$?
Tap to reveal answer
$x=-\frac{3}{2}$ (double root). Square factor gives one zero with multiplicity 2.
$x=-\frac{3}{2}$ (double root). Square factor gives one zero with multiplicity 2.
← Didn't Know|Knew It →
What is the factored form of $x^2-16$?
What is the factored form of $x^2-16$?
Tap to reveal answer
$(x-4)(x+4)$. Difference of squares pattern: $a^2-b^2=(a-b)(a+b)$.
$(x-4)(x+4)$. Difference of squares pattern: $a^2-b^2=(a-b)(a+b)$.
← Didn't Know|Knew It →
What is the factored form of $x^2+2x-24$?
What is the factored form of $x^2+2x-24$?
Tap to reveal answer
$(x+6)(x-4)$. Find two numbers that multiply to $-24$ and add to 2: 6 and $-4$.
$(x+6)(x-4)$. Find two numbers that multiply to $-24$ and add to 2: 6 and $-4$.
← Didn't Know|Knew It →
What is the factored form of $x^2-13x+36$?
What is the factored form of $x^2-13x+36$?
Tap to reveal answer
$(x-9)(x-4)$. Find two numbers that multiply to 36 and add to $-13$: $-9$ and $-4$.
$(x-9)(x-4)$. Find two numbers that multiply to 36 and add to $-13$: $-9$ and $-4$.
← Didn't Know|Knew It →
What is the factored form of $x^2+x-12$?
What is the factored form of $x^2+x-12$?
Tap to reveal answer
$(x+4)(x-3)$. 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 $-3$.
← Didn't Know|Knew It →
What is the factored form of $x^2-2x-15$?
What is the factored form of $x^2-2x-15$?
Tap to reveal answer
$(x-5)(x+3)$. 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.
← Didn't Know|Knew It →