Unit 7: Polynomials & Factoring Review

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What is a polynomial?

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A polynomial is a mathematical expression consisting of variables (also called indeterminates) raised to whole number powers and coefficients. For example, 3x^2 + 2x + 1 is a polynomial.

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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. For example, factoring 2x^2 + 4x gives 2x(x + 2).

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What is the Greatest Common Factor (GCF)?

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The GCF of a set of terms is the largest factor that divides each of the terms. For example, the GCF of 6x^2 and 9x is 3x.

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How do you factor by grouping?

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To factor by grouping, you group terms in pairs, factor out the GCF from each pair, and then factor out the common binomial factor.

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What is the difference of squares?

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The difference of squares is a special factoring pattern that states a^2 - b^2 = (a + b)(a - b). For example, x^2 - 9 = (x + 3)(x - 3).

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What is the standard form of a polynomial?

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The standard form of a polynomial is written in descending order of the degree of its terms. For example, 4x^3 + 2x^2 - x + 7 is in standard form.

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What is a quadratic polynomial?

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A quadratic polynomial is a polynomial of degree 2, which can be expressed in the form ax^2 + bx + c, where a, b, and c are constants and a ≠ 0.

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How do you factor a quadratic polynomial?

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To factor a quadratic polynomial ax^2 + bx + c, find two numbers that multiply to ac and add to b, then rewrite the polynomial and factor by grouping.

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What is a binomial?

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A binomial is a polynomial with exactly two terms, such as x + 5 or 3x^2 - 2.

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What is a trinomial?

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A trinomial is a polynomial with exactly three terms, such as x^2 + 5x + 6.