4.3-4.5 Review Solve Polynomials by Factoring

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What is synthetic division?

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Synthetic division is a simplified form of polynomial long division that is used to divide a polynomial by a linear factor of the form (x - c). It is faster and more efficient than traditional long division.

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CCSS.HSA.APR.D.6

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How do you evaluate a polynomial function at a specific value?

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To evaluate a polynomial function f(x) at a specific value x = a, substitute a into the polynomial and simplify. For example, for f(x) = 2x^4 - 5x^2 + 8x - 7, to find f(6), substitute 6 for x.

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CCSS.HSF.IF.A.2

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What does it mean for a polynomial to be in fully factored form?

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CCSS.HSF-IF.C.7C

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What is the Factor Theorem?

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The Factor Theorem states that if a polynomial f(x) has a factor (x - c), then f(c) = 0. This means that c is a root of the polynomial.

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CCSS.HSA.APR.B.2

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How do you factor a polynomial of the form x^n - a^n?

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CCSS.HSA.APR.C.4

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What is the first step in solving a polynomial equation by factoring?

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The first step in solving a polynomial equation by factoring is to set the equation equal to zero and then factor the polynomial completely.

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CCSS.HSA-REI.B.4B

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What are the roots of a polynomial?

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The roots of a polynomial are the values of x that make the polynomial equal to zero. They can be found by solving the factored form of the polynomial.

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What is the significance of the degree of a polynomial?

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The degree of a polynomial indicates the highest power of the variable in the polynomial. It determines the number of roots (real and complex) the polynomial can have.

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How do you find the roots of a polynomial using factoring?

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To find the roots of a polynomial using factoring, factor the polynomial into linear factors, set each factor equal to zero, and solve for x.

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What is a linear factor?

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A linear factor is a polynomial of degree one, typically in the form (x - c), where c is a constant. Linear factors are used to express polynomials in factored form.

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CCSS.HSA.APR.B.2