Question

Find k if x power 4 + 10x cube + 25 x square + 15 + k is exactly divisible by x + 7

Answer 1

(x4 + 10 x3 + 25x2 + 15x + k) is exactly divisible by (x + 7) Zero of (x + 7) = -7 ⇒ f(x) = (x4 + 10 x3 + 25x2 + 15x + k) ⇒ f(-7) = (-7)4 + 10 (-7)3 + 25 (-7)2 + 15(-7) + k = 0 ⇒ 2401 - 3430 + 1225 - 105 + k = 0 ⇒ k + 91 = 0 ⇒ k = -91

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Answer 2

Answer:

Step-by-step explanation:

By factor theorem

f(-7)=(-7)^4+10*-7^3+25*-7^2+15+k=0

f(-7)=2401+10*-343+25*49+15+k=0

f(-7)=2401-3430+1225+15+k=0

f(-7)=211+k=0

=k=-211

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