Question

If (x+1) is factor of f(x) =aoxn+a1xn-1.....+an then ​

Answer 1

Answer:

Value of a + b is -7

Step-by-step explanation:

Given:

( x + 2 ) and ( x - 2 ) are factors of polynomial say

To find: Value of a + b

We use the factor theorem of polynomials.

Factor Theorem states that is x - a is factor of a polynomial p(x) then p(a) = 0.

Here, x + 2  is factor of p(x)

then p(-2) = 0

8a - b = 16 ................(1)

Now, x - 2 is factor of p(x)

then p(2) = 0

8a + b = 0 ................(2)

Add (1) and (2),

8a + 8a = 16

16a = 16

a = 1

put in (2), we get

8(1) + b = 0

b = -8

So, a + b = 1  + (-8) = 1 - 8 = -7

Therefore, Value of a + b is -7

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