Have some Math questions?

Question

Let f(x) =2x^3 -x^2 - 5x -2 and g(x)=x^3 -4x^2+x+6
(a) Show that x+1 is a common factor of f(x) and g(x)
(b) Factorize f(x) and g(x) completely
(c)(i) It is given that h(x) =3x^3 -5x^2 -4x +4 . Express h(x) in terms of f(x) and g(x).
(ii) Hence or otherwise , solve the equation 3x^3 -5x^2 -4x +4 =0 .

Answer 1

a) let x = -1. and substitute - using the factor theorem. Answer should be zero in each case
b) use algebraic long division to do that, starting by dividing x+1 through
c) I can see that h(x) = f(x) + g(x) so I imagine that by adding them together in their factorised form, you will see some common factors - we already know (x+1) is in common.

Hope this helps

Answer 2

A,B) F(x)= 2x^3-x^2-5x-2

2 -1 -5 -2
-1 /__ -2 _3__2____
2 -3 -2 0
=( x+1) (2x^2 -3x-2)
= (x+1) (2x+1) (x-2)

G(x)= x^3-4X^2+x+6

1 -4 1 6
-1 /__-1_ 5_-6__
1 -5 6 0

= (x+1)(x^2 -5x+6)
= (x+1) (x-3) (x-2)

C) h(x)= 3x^3-5x^2-4x+4
= ( 3x^2-8x+4 ) ( x+1)

G(x)+ F(x) = (2x^2 - 3x-2)(x+1) +(x^2-5x+6)(x+1)
= (3x^2 -8x+4 ) (x+1) = H(x)

H( x)= (3x-2) (x-2) (x+1)

Answer 3

maan u really gotta practice maths ..these sums are really easy.

Answer 4

is the answer leona off x-factor??