Advertisements
Advertisements
Question
Using the Remainder Theorem, factorise the following completely:
4x3 + 7x2 – 36x – 63
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
What must be subtracted from 16x3 – 8x2 + 4x + 7 so that the resulting expression has 2x + 1 as a factor?
Using the Remainder Theorem, factorise the expression 3x3 + 10x2 + x – 6. Hence, solve the equation 3x3 + 10x2 + x – 6 = 0
Find without division, the remainder in the following:
5x3 - 7x2 +3 is divided by (x-1)
Find without division, the remainder in the following:
8x2 - 2x + 1 is divided by (2x+ 1)
Using remainder theorem, find the value of m if the polynomial f(x)= x3 + 5x2 -mx +6 leaves a remainder 2m when divided by (x-1),
What number should be added to polynomial f(x)= 12x3 + 16x2 - 5x - 8 so that the resulting polynomial is exactly divisible by (2x - 1) ?
Find the remainder (without division) on dividing f(x) by (2x + 1) where f(x) = 3x3 – 7x2 + 4x + 11
If (x – 2) is a factor of the expression 2x3 + ax2 + bx – 14 and when the expression is divided by (x – 3), it leaves a remainder 52, find the values of a and b.
If x + 1 is a factor of 3x3 + kx2 + 7x + 4, then the value of k is
Find the remainder when 2x3 – 3x2 + 4x + 7 is divided by x – 2
