f(x) = 3x^3 – x^2 – 20x – 12 (a) Use the factor theorem to show that (3x + 2) is a factor of f(x). [2 marks] (b) Factorise f(x) fully. [3 marks]
(a) Factor theorem hence, use x = -2/3. Sub in : 3(-2/3)3 - (-2/3)2 -20 (-2/3) -12 = 0 (b) (3x+2)(ax2 + bx+c) = 3x3 – x2 – 20x – 12 3ax3 + (3b+2a)x2 + (3c+2b)x + 2c = 3x3 – x2 – 20x – 12 Therefore, 3a = 3 ----------> a = 1 3b +2a = -1 -----> b = -1 2c = -12 ---------> c = -6factorise: x2 - x- 6 = (x+2)(x-3) Fully factorised: 3x3 – x2 – 20x – 12 = (3x+2)(x+2)(x-3)
DW
Answered by Daniel W. • Further Mathematics tutor
5134 Views
See similar Further Mathematics GCSE tutorsRelated Further Mathematics GCSE answers
All answers ▸How can you divide an algebraic expression by another algebraic expression?
If y=x^3+9x, find gradient of the tangent at (2,1).
Lengths of two sides of the triangle and the angle between them are known. Find the length of the third side and the area of the triangle.
This is a question from a past paper: https://prnt.sc/r6jnxc