Factor. f^2 - 20f + 19 ______

Identify coefficients: Identify the coefficients a, b, and c in the quadratic expression f^2 - 20f + 19. The quadratic expression is in the form af^2 + bf + c, where a = 1, b = -20, and c = 19.Find numbers for ac: Find two numbers that multiply to give ac (which is 19, since a = 1) and add up to b (which is -20). The numbers that satisfy these conditions are -1 and -19 because: -1 * -19 = 19 -1 + (-19) = -20Write quadratic expression: Write the quadratic expression using the two numbers found in the previous step to split the middle term. The expression becomes f^2 - f - 19f + 19.Factor by grouping: Factor by grouping. Group the first two terms together and the last two terms together. (f^2 - f) + (-19f + 19)Factor out common factor: Factor out the greatest common factor from each group. f(f - 1) - 19(f - 1)Since both groups contain the common factor (f - 1), factor this out. The factored form is (f - 1)(f - 19).

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Factor. $\newline$ $f^2 - 20f + 19$

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Q. Factor.

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f^2 - 20f + 19

Identify coefficients: Identify the coefficients $a$ , $b$ , and $c$ in the quadratic expression $f^2 - 20f + 19$ . The quadratic expression is in the form $af^2 + bf + c$ , where $a = 1$ , $b = -20$ , and $c = 19$ .
Find numbers for $\newline$ $ac$ : Find two numbers that multiply to give $\newline$ $ac$ (which is $\newline$ $19$ , since $\newline$ $a = 1$ ) and add up to $\newline$ $b$ (which is $\newline$ $-20$ ). $\newline$ The numbers that satisfy these conditions are $\newline$ $-1$ and $\newline$ $-19$ because: $\newline$ $\newline$ $-1 \times -19 = 19$ $\newline$ $\newline$ $-1 + (-19) = -20$
Write quadratic expression: Write the quadratic expression using the two numbers found in the previous step to split the middle term. The expression becomes $f^2 - f - 19f + 19$ .
Factor by grouping: Factor by grouping. Group the first two terms together and the last two terms together. $f^2 - f$ + $-19f + 19$
Factor out common factor: Factor out the greatest common factor from each group. $\newline$ $f(f - 1) - 19(f - 1)$
Factor out common factor: Factor out the greatest common factor from each group. $\newline$ $f(f - 1) - 19(f - 1)$ Since both groups contain the common factor $(f - 1)$ , factor this out. $\newline$ The factored form is $(f - 1)(f - 19)$ .