Factor as the product of two binomials. x^(2)-x-42=

Identify Quadratic Expression: Identify the quadratic expression to be factored. The given quadratic expression is x^2 - x - 42.Determine Factors: Determine the factors of the constant term that add up to the coefficient of the x term. The constant term is -42, and the coefficient of the x term is -1. We need to find two numbers that multiply to -42 and add up to -1.List Factor Pairs: List the pairs of factors of -42. The pairs of factors of -42 are (1, -42), (-1, 42), (2, -21), (-2, 21), (3, -14), (-3, 14), (6, -7), (-6, 7).Find Correct Pair: Find the correct pair of factors that add up to -1. By checking the pairs, we find that 6 and -7 add up to -1.Write as Binomials: Write the quadratic expression as the product of two binomials using the found factors. The quadratic expression x^2 - x - 42 can be factored as (x - 7)(x + 6).

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Q. Factor as the product of two binomials.

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x^{2}-x-42=

Identify Quadratic Expression: Identify the quadratic expression to be factored. $\newline$ The given quadratic expression is $x^2 - x - 42$ .
Determine Factors: Determine the factors of the constant term that add up to the coefficient of the $x$ term. $\newline$ The constant term is $-42$ , and the coefficient of the $x$ term is $-1$ . We need to find two numbers that multiply to $-42$ and add up to $-1$ .
List Factor Pairs: List the pairs of factors of $-42$ . The pairs of factors of $-42$ are $(1, -42)$ , $(-1, 42)$ , $(2, -21)$ , $(-2, 21)$ , $(3, -14)$ , $(-3, 14)$ , $(6, -7)$ , $(-6, 7)$ .
Find Correct Pair: Find the correct pair of factors that add up to $-1$ . By checking the pairs, we find that $6$ and $-7$ add up to $-1$ .
Write as Binomials: Write the quadratic expression as the product of two binomials using the found factors. $\newline$ The quadratic expression $x^2 - x - 42$ can be factored as $(x - 7)(x + 6)$ .