Factoring Trinomials

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What is factoring in algebra?

Back

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.

Front

What is a trinomial?

Back

A trinomial is a polynomial that consists of three terms, typically in the form ax² + bx + c.

Front

What does GCF stand for in factoring?

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GCF stands for Greatest Common Factor, which is the largest factor that divides all terms in a polynomial.

Front

How do you factor a trinomial of the form x² + bx + c?

Back

To factor a trinomial of the form x² + bx + c, find two numbers that multiply to c and add to b, then express the trinomial as (x + m)(x + n), where m and n are those two numbers.

Front

What is the first step in factoring a polynomial completely?

Back

The first step in factoring a polynomial completely is to factor out the Greatest Common Factor (GCF) from all the terms.

Front

How do you factor the trinomial a² - a - 12?

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To factor a² - a - 12, find two numbers that multiply to -12 and add to -1. The factors are -4 and 3, so it can be factored as (a - 4)(a + 3).

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What is the factored form of 3x² + 18x + 15?

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The factored form is 3(x + 5)(x + 1), after factoring out the GCF of 3.

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What is the factored form of 5x² - 15x + 10?

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The factored form is 5(x - 2)(x - 1), after factoring out the GCF of 5.

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What is the process to factor a polynomial completely?

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The process includes finding the GCF, factoring out the GCF, and then factoring any remaining polynomial, often by grouping or using special factoring techniques.

Front

What is the factored form of 3n² - 15n + 18?

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The factored form is 3(n - 3)(n - 2), after factoring out the GCF of 3.