Factoring completely

Front

What is factoring in algebra?

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Factoring is the process of breaking down an expression into a product of simpler expressions, or factors, that when multiplied together give the original expression.

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What is the first step in factoring polynomials?

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The first step is to find the Greatest Common Factor (GCF) of the terms in the polynomial.

Front

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

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To factor a quadratic expression of the form x^2 + bx + c, find two numbers that multiply to c and add to b, then express the quadratic as (x + m)(x + n), where m and n are the two numbers.

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What is the factored form of x^2 - 5x - 36?

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(x + 4)(x - 9) is the factored form of x^2 - 5x - 36.

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What does it mean to factor by grouping?

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Factoring by grouping involves rearranging and grouping terms in a polynomial to factor out common factors from each group.

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What is the factored form of 3x^2 - 15x + 18?

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3(x - 2)(x - 3) is the factored form of 3x^2 - 15x + 18.

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What is the factored form of k^2 + 7k + 10?

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(k + 2)(k + 5) is the factored form of k^2 + 7k + 10.

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What is the significance of the GCF in factoring?

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The GCF is significant because it simplifies the polynomial and makes it easier to factor the remaining terms.

Front

What is the process of factoring a polynomial with four terms?

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To factor a polynomial with four terms, you can use factoring by grouping, where you group the first two terms and the last two terms, factor out the GCF from each group, and then factor out the common binomial.

Front

What is a binomial?

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A binomial is a polynomial that consists of exactly two terms, such as (x + 3) or (2y - 5).