Polynomials and Factoring

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What is a polynomial?

Back

A polynomial is a mathematical expression that consists of variables, coefficients, and exponents, combined using addition, subtraction, and multiplication. For example, 3x^2 + 2x - 5 is a polynomial.

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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. For example, in the polynomial 4x^3 + 2x^2 - x, the degree is 3.

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What is a monomial?

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A monomial is a polynomial with only one term. For example, 5x^2 is a monomial.

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What is a binomial?

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A binomial is a polynomial with two terms. For example, 3x + 4 is a binomial.

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What is a trinomial?

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A trinomial is a polynomial with three terms. For example, x^2 + 5x + 6 is a trinomial.

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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. For example, factoring x^2 - 9 gives (x + 3)(x - 3).

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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 - 16 = (x + 4)(x - 4).

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How do you factor a trinomial of the form x^2 + bx + c?

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To factor a trinomial of the form x^2 + bx + c, find two numbers that multiply to c and add to b. For example, x^2 + 5x + 6 factors to (x + 2)(x + 3).

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What is the greatest common factor (GCF)?

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The GCF is the largest factor that divides two or more numbers or terms. For example, the GCF of 12 and 16 is 4.

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How do you factor by grouping?

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To factor by grouping, group terms with common factors, factor them out, and then factor the remaining polynomial. For example, in 2x^2 + 4x + 3x + 6, group as (2x^2 + 4x) + (3x + 6) = 2x(x + 2) + 3(x + 2) = (2x + 3)(x + 2).