Question

if (x+p) is a factor of both x^2+16x+64 and 4x^2+37x+k, where p and k are nonzero integer constants, what could be the value of k?

A)9
B)24
C)40
D)63

Answer 1

Answer:

I don't know

Step-by-step explanation:

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Answer 2

Answer:

Concept - Algebric expression.

Given -  (x+p) is a factor of both $x^{2} +16x+64$ and $4x^{2} +37x+k$, where p and k are nonzero integer constants.

To find - value of k.

Step-by-step explanation:

As we know that $x^{2} +16x+64$ factor is $(x+p)$

$=x^{2} +16x+64\\=x^{2} +8x+8x+64\\=x(x+8)+8(x+8)\\= (x+8)(x+8)\\= (x+8)^{2}$

Hence $x^{2} +16x+64=(x+8)^{2}$

Now , Factor of $x^{2} +16x+64=(x+8)^{2}$

$= > (x+8) = (x+p)\\= > p = 8$

Now if (x+p) =(x+8) is factor of $4x^{2} +37x+k$ then putting x = -p = -8

we get,

$= > 4x^{2}+ 37x+k =0$ where x = -8

$= > 4(-8^{2}) + 37(-8)+k = 0\\= > 4(64)+37(-8) +k =0\\= > 256-236+k =0\\= > k = 40$

Hence value of k is 40.

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