Advertisements
Advertisements
Question
Using the Remainder Theorem, factorise the following completely:
4x3 + 7x2 – 36x – 63
Advertisements
Solution
f(x) = 4x3 + 7x2 – 36x – 63
For x = 3,
f(x) = f(3)
= 4(3)3 + 7(3)2 – 36(3) – 63
= 108 + 63 – 108 – 63
= 0
Hence, (x – 3) is a factor of f(x).
4x2 + 19x + 21
`x – 3")"overline(4x^3 + 7x^2 – 36x - 63)`
4x3 – 12x2
– +
19x2 – 36x – 63
19x2 – 57x
– +
21x – 63
21x – 63
– +
0
∴ 4x3 + 7x2 – 36x – 63 = (x – 3)(4x2 + 19x + 21)
= (x – 3)(4x2 + 12x + 7x + 21)
= (x – 3)[4x(x + 3) + 7(x + 3)]
= (x – 3)(4x + 7)(x + 3)
APPEARS IN
RELATED QUESTIONS
Find the remainder when x3 + 3x2 + 3x + 1 is divided by x + π.
Use the Remainder Theorem to find which of the following is a factor of 2x3 + 3x2 – 5x – 6.
x + 2
Divide the first polynomial by the second polynomial and find the remainder using remainder theorem.
(2x3 − 2x2 + ax − a) ; (x − a)
If ( x31 + 31) is divided by (x + 1) then find the remainder.
Find the remainder when the polynomial f(x) = 2x4 - 6x3 + 2x2 - x + 2 is divided by x + 2.
(x – 2) is a factor of the expression x3 + ax2 + bx + 6. When this expression is divided by (x – 3), it leaves the remainder 3. Find the values of a and b.
Given f(x) = ax2 + bx + 2 and g(x) = bx2 + ax + 1. If x – 2 is a factor of f(x) but leaves the remainder – 15 when it divides g(x), find the values of a and b. With these values of a and b, factorise the expression. f(x) + g(x) + 4x2 + 7x.
If on dividing 4x2 – 3kx + 5 by x + 2, the remainder is – 3 then the value of k is
If x3 + 6x2 + kx + 6 is exactly divisible by (x + 2), then k = ?
The remainder, when x3 – x2 + x – 1 is divided by x + 1, is ______.
