Solving polynomials by factoring

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What is a polynomial?

Back

A polynomial is a mathematical expression consisting of variables, coefficients, and non-negative integer exponents, combined using addition, subtraction, and multiplication.

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What does it mean to factor a polynomial?

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Factoring a polynomial means expressing it as a product of its factors, which are polynomials of lower degrees.

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What is the degree of a polynomial?

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The degree of a polynomial is the highest power of the variable in the expression.

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What are the zeros of a polynomial?

Back

The zeros of a polynomial are the values of the variable that make the polynomial equal to zero.

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How do you find the zeros of a polynomial?

Back

To find the zeros of a polynomial, set the polynomial equal to zero and solve for the variable.

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What is the Factor Theorem?

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The Factor Theorem states that if a polynomial P(x) has a zero at x = a, then (x - a) is a factor of P(x).

Tags

CCSS.HSA.APR.B.2

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What is the Remainder Theorem?

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The Remainder Theorem states that when a polynomial P(x) is divided by (x - a), the remainder is P(a).

Tags

CCSS.HSA.APR.B.2

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What is synthetic division?

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Synthetic division is a simplified method of dividing a polynomial by a linear factor of the form (x - a).

Tags

CCSS.HSA.APR.D.6

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What is the relationship between the degree of a polynomial and the number of zeros?

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A polynomial of degree n can have at most n zeros, counting multiplicities.

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What is a quadratic polynomial?

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A quadratic polynomial is a polynomial of degree 2, typically in the form P(x) = ax^2 + bx + c.