Polynomial Equations - SAT Math
Card 0 of 17
End behavior of even-degree polynomials when $a_n < 0$.
End behavior of even-degree polynomials when $a_n < 0$.
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Both ends go down as $x \to \pm\infty$.
Both ends go down as $x \to \pm\infty$.
End behavior of even-degree polynomials when $a_n > 0$.
End behavior of even-degree polynomials when $a_n > 0$.
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Both ends go up as $x \to \pm\infty$.
Both ends go up as $x \to \pm\infty$.
End behavior of odd-degree polynomials when $a_n < 0$.
End behavior of odd-degree polynomials when $a_n < 0$.
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Rises left, falls right.
Rises left, falls right.
End behavior of odd-degree polynomials when $a_n > 0$.
End behavior of odd-degree polynomials when $a_n > 0$.
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Falls left, rises right.
Falls left, rises right.
Factor $x^2 - 2x - 15$.
Factor $x^2 - 2x - 15$.
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$(x - 5)(x + 3)$.
$(x - 5)(x + 3)$.
Factor $x^2 - 49$.
Factor $x^2 - 49$.
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$(x - 7)(x + 7)$.
$(x - 7)(x + 7)$.
Factor $x^2 + 5x + 6$.
Factor $x^2 + 5x + 6$.
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$(x + 2)(x + 3)$.
$(x + 2)(x + 3)$.
Factoring rule for $x^2 - 6x + 9$.
Factoring rule for $x^2 - 6x + 9$.
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$(x - 3)^2$.
$(x - 3)^2$.
Factoring rule for $x^2 - 9$.
Factoring rule for $x^2 - 9$.
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$(x - 3)(x + 3)$.
$(x - 3)(x + 3)$.
Factoring rule for $x^2 + 6x + 9$.
Factoring rule for $x^2 + 6x + 9$.
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$(x + 3)^2$.
$(x + 3)^2$.
Sum and product of roots of $ax^2 + bx + c = 0$.
Sum and product of roots of $ax^2 + bx + c = 0$.
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Sum $= -\frac{b}{a}$, Product $= \frac{c}{a}$.
Sum $= -\frac{b}{a}$, Product $= \frac{c}{a}$.
What is a polynomial?
What is a polynomial?
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An expression made up of terms in the form $a_nx^n + a_{n-1}x^{n-1} + \dots + a_1x + a_0$, where coefficients $a_i$ are constants and exponents are nonnegative integers.
An expression made up of terms in the form $a_nx^n + a_{n-1}x^{n-1} + \dots + a_1x + a_0$, where coefficients $a_i$ are constants and exponents are nonnegative integers.
What is a zero of a polynomial?
What is a zero of a polynomial?
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A value of $x$ that makes the polynomial equal to 0.
A value of $x$ that makes the polynomial equal to 0.
What is the constant term in a polynomial?
What is the constant term in a polynomial?
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The term with no variable, usually $a_0$.
The term with no variable, usually $a_0$.
What is the degree of a polynomial?
What is the degree of a polynomial?
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The highest exponent of $x$ with a nonzero coefficient.
The highest exponent of $x$ with a nonzero coefficient.
What is the leading coefficient in a polynomial?
What is the leading coefficient in a polynomial?
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The coefficient of the term with the highest power of $x$.
The coefficient of the term with the highest power of $x$.
What is the relationship between zeros and factors?
What is the relationship between zeros and factors?
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If $x = r$ is a zero, then $(x - r)$ is a factor of the polynomial.
If $x = r$ is a zero, then $(x - r)$ is a factor of the polynomial.