Question

1. Divide the polynomial x^4 + 3x^3 - 2x^2 + x + 10 by (x + 2) and verify remainder by using remainder theorem.
2. Using Factor theorem , find the value of 'a' if 2x^4 - ax^3 + 4x^2 - x + 2 is divisible by 2x + 1.
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Answer 1

Answer:

f(x)=2x^4-ax^3+4×^2-×+2

we will consider 2x+1 as g(x)

now g(x)=0

2×+1 =0

×=-1/2

now 2(-1/2)^4-a(-1/2)^3+4(-1/2)^2-(-1/2)+2

=-1^4-a3/8+4-1/2+2

=4-a3/8+4-1/2+2

=4+4+2-1/2+a3/8

=10-1×4/2×4+a3/8

=10-4/8+a3/8

=10-1/2+a3/8

=20-1+a3/8

=19+a3+8