Advertisements
Advertisements
Question
Given that x + 2 and x + 3 are factors of 2x3 + ax2 + 7x - b. Determine the values of a and b.
Advertisements
Solution
If x + 2 is a factor is 2x3 + ax2 + 7x - b then x + 2 = 0, x = -2 in equation
2(-2)3 + a (-2)2 + 7(-2) - b = 0
2(-8) + a(4) + 7(-2) - b = 0
-16 + 4a - 14 - b = 0
4a - b = 30 ...(1)
Also given that x + 3 is a factor of
2x3 + ax2 + 7x - b, then x + 3 = 0
x = -3 in equation
2(-3)3 + a(-3)2 + 7(-3) - b = 0
2(-27) + a(9) + 7(-3) - b = 0
-54 + 9a - 21 - b = 0
9a - b = 75 ...(2)
Solving (1) and (2) we get
a = 9, b = 6.
RELATED QUESTIONS
Find the value of k, if 3x – 4 is a factor of expression 3x2 + 2x − k.
What should be subtracted from 3x3 – 8x2 + 4x – 3, so that the resulting expression has x + 2 as a factor?
Prove by factor theorem that
(2x+1) is a factor of 4x3 + 12x2 + 7x +1
Prove that (x-3) is a factor of x3 - x2 - 9x +9 and hence factorize it completely.
Using factor theorem, show that (x - 3) is a factor of x3 - 7x2 + 15x - 9, Hence, factorise the given expression completely.
Use factor theorem to factorise the following polynominals completely.
x3 + 2x2 – 5x – 6
If (x + 2) and (x – 3) are factors of x3 + ax + b, find the values of a and b. With these values of a and b, factorise the given expression.
If p(a) = 0 then (x – a) is a ___________ of p(x)
Is (x – 2) a factor of x3 – 4x2 – 11x + 30?
If mx2 – nx + 8 has x – 2 as a factor, then ______.
