Question

If remander is same when polynomial p(x)=x^3+8x^2+17x+ax is divided by (x+2)&(x+1),find the value of a​

Answer 1

HeyMate❤...

i hope it helps you...

Answer 2

HeYa❤️...

Answer:

→Given,

[x + 2 = 0]

[x = -2]

=> Let (x= -2) is a factor of p(x).

So, put value of x in p(x).

$p(x) = x {}^{3} + 8x {}^{2} + 17x + ax \\ 0= ( - 2) {}^{3} + 8( - 2) {}^{2} + 17( - 2) + a( - 2) \\ 0= - 8 + 32 - 34 - 2a \\ 0 = - 10 - 2a \\ a = -5$

___________________________

→And,

[x + 1 = 0]

[x = -1]

=> Let (x= -1) is a factor of p(x).

Let's put the value of x in p(x).

$p(x) = x {}^{3} + 8x {}^{2} + 17x + ax \\ 0 = ( - 1) {}^{3} + 8( - 1) {}^{2} + 17( - 1) + a( - 1) \\ 0 = - 1 + 8 - 17 + a( - 1) \\ 0 = 8 - 18 + a( - 1) \\ 0 = - 10 - a \\ a = -10$

Hence, Value of a is (-5) and (-10).

I hOpe It HeLpS Ya!

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