Question

If x 3 – 9x 2 + (k + 1)x – 7 has a factor x – 7, find the
value of x.
1. If the polynomials x 3 – ax 2 + 8x +11 and 2x 3 – ax 2 +
7ax +13 leaves the same remainder when divided by
x – 1, find the value of a.
2. Find the values of a and b so that polynomial x 3 +
10x 2 + ax + b is exactly divisible by x – 1 and x + 2.
3. What must be subtracted from the polynomial 2x 3 +
x 2 – 2x + 4 so that it is exactly divisible by x +1.

Answer 1

Answer:

1.Let the given polynomials be f(x) and g(x).

ATQ, 

When f(x) and g(x) are divided by (x-2) they leave the same remainder.

I.e (x-2) is a factor of f(x) and g(x). It means 2 is the zero of f(x) and g(x)

So that,

f(2) = g(2)

2x³+ax²+3x-5 = x³+x²-4x+a

2(2)³+a(2)²+3(2)-5 = 2³+2²-4(2)+a

2(8)+a(4)+6-5 = 8+4-8+a

16+4a+1 = 4+a

17+4a = 4+a

4a-a = 4-17

3a = -13

a = -13/3.

Step-by-step explanation: