Question

If x ^ 3 - 3x ^ 2 + 3x + 7 = (x + 1)(a * x ^ 2 + bx + c) , then find the value of a + b + c .
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Answer 1

QUESTION:-

If x³-3x²+3x+7=(x+1)(ax²+bx+c) , then find the value of a+b+c.

SOLUTION:-

We have

• x³-3x²+3x+7=(x+1)(ax²+bx+c)
• (x³-3x²+3x+7)/(x+1)=ax²+bx+c

Now Dividing x³-3x²+3x+7 by (x+1)

x+1)x³-3x²+3x+7(x²-4x+1

x³+ x²

__________

× -4x²+3x+7

-4x²-4x

______________

7x+7

7x+7

______________

×

Thus Dividing x³-3x²+3x+7 by (x+1) we get :-

x²-4x+1= ax²+bx +c

On seeing above clearly we get a=1, b=-4 and c=1

So now we have a+b+c=1+(-4)+1=-2

Thus -2 is the required answer

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