How do you factor the expression $4 r^{2} - 40 r + 96$ $4r^2-40r+96$ ?

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How do you factor the expression $4 r^{2} - 40 r + 96$ $4r^2-40r+96$ ?

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Answer 1 · 2017-05-29T13:05:33

$4 r^{2} - 40 r + 96 = 4 (r - 6) (r - 4)$ $4r^2-40r+96 = 4(r-6)(r-4)$

Explanation:

Note that all of the given terms are divisible by $4$ $4$ , so separate that out as a factor first then complete the square:

$4 r^{2} - 40 r + 96 = 4 (r^{2} - 10 r + 24)$ $4r^2-40r+96 = 4(r^2-10r+24)$

$4 r^{2} - 40 r + 96 = 4 (r^{2} - 10 r + 25 - 1)$ $color(white)(4r^2-40r+96) = 4(r^2-10r+25-1)$

$4 r^{2} - 40 r + 96 = 4 ({(r - 5)}^{2} - 1^{2})$ $color(white)(4r^2-40r+96) = 4((r-5)^2-1^2)$

$4 r^{2} - 40 r + 96 = 4 ((r - 5) - 1) ((r - 5) + 1)$ $color(white)(4r^2-40r+96) = 4((r-5)-1)((r-5)+1)$

$4 r^{2} - 40 r + 96 = 4 (r - 6) (r - 4)$ $color(white)(4r^2-40r+96) = 4(r-6)(r-4)$

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How do you factor the expression $4 r^{2} - 40 r + 96$ $4r^2-40r+96$ ?

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Explanation:

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How do you factor the expression $4 r^{2} - 40 r + 96$ $4r^2-40r+96$ ?