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.
Use the Remainder Theorem to find which of the following is a factor of 2x3 + 3x2 – 5x – 6.
2x – 1
The expression 2x3 + ax2 + bx – 2 leaves remainder 7 and 0 when divided by 2x – 3 and x + 2 respectively. Calculate the values of a and b.
When x3 + 3x2 – mx + 4 is divided by x – 2, the remainder is m + 3. Find the value of m.
Find without division, the remainder in the following:
5x3 - 7x2 +3 is divided by (x-1)
What number should be added to 2x3 - 3x2 + 7x -8 so that the resulting polynomial is exactly divisible by (x-1) ?
A polynomial f(x) when divided by (x - 1) leaves a remainder 3 and when divided by (x - 2) leaves a remainder of 1. Show that when its divided by (x - i)(x - 2), the remainder is (-2x + 5).
Use the Remainder Theorem to factorise the following expression:
2x3 + x2 – 13x + 6
Find the remainder when 3x3 – 4x2 + 7x – 5 is divided by (x + 3)
Determine which of the following polynomials has x – 2 a factor:
4x2 + x – 2
