Factoring (a=1, a=/1)

Front

What is the process of factoring in algebra?

Back

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

Front

What is the factored form of a quadratic expression?

Back

The factored form of a quadratic expression is typically written as (ax + b)(cx + d), where a, b, c, and d are constants.

Front

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

Back

To factor a quadratic expression of the form x² + 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.

Front

What is the significance of the leading coefficient in factoring?

Back

The leading coefficient (the coefficient of the highest degree term) affects the methods used for factoring, especially in quadratics where it is not equal to 1.

Front

What is the difference between factoring completely and factoring partially?

Back

Factoring completely means breaking down an expression into its simplest factors, while factoring partially means finding some factors but not all.

Front

What is the first step in factoring a trinomial?

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The first step in factoring a trinomial is to identify the coefficients of the quadratic term, linear term, and constant term.

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How do you factor the expression (x - 1)(x - 9)?

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To factor the expression (x - 1)(x - 9), you can expand it to get x² - 10x + 9.

Front

What is the factored form of 6x² + 7x - 3?

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The factored form of 6x² + 7x - 3 is (2x + 3)(3x - 1).

Front

What method can be used to factor the expression 2x² - 3x - 2?

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To factor 2x² - 3x - 2, you can use the grouping method or trial and error to find factors that work.

Front

What is the factored form of 3a² + 4a + 1?

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The factored form of 3a² + 4a + 1 is (3a + 1)(a + 1).