Question

a) Find the remainder when 2x3 - 2x2 + 5x - 1 is divided by

(i) x+1

(ii) x- ½

(b) Find the value of each of the following polynomials at the indicated value

of variables:

(i) p(x) = 5x3 – 3x2 +4x -7

at x= 1

(ii) q(y) = 3y3 -4√2 y +13 at y= 2
​

Answer 1

Step-by-step explanation:

p(x) = 2x3 - 2x2 + 5x - 1

(i)

remainder = p(-1) = 2 X (-1)^3-2(-1)^2+ 5 X (-1)-1

= -2 -2-5-1

=-10

(ii)

remainder = p(1/2) = 2 X (1/2)^3-2(1/2)^2+ 5 X (1/2)-1

= 1/4- 1/2 + 5/2 -1

= 5/4

b)

(I)

p(x) = 5x3 – 3x2 +4x -7

at x= 1

p(1) = 5(1)3 – 3(1)2 +4(1) -7

= 5-3+4-7

=-1

(ii)

q(y) = 3y3 -4√2 y +13

at y= 2

q(2) = 3(2)3 -4√2 (2)+13

=24-8√2+13

=37-8√2