Advertisements
Advertisements
Question
Using the Factor Theorem, show that (3x + 2) is a factor of 3x3 + 2x2 – 3x – 2. Hence, factorise the expression 3x3 + 2x2 – 3x – 2 completely.
Advertisements
Solution
Let f(x) = 3x3 + 2x2 – 3x – 2
3x + 2 = 0 `\implies x = (-2)/3`
∴ Remainder = `f ((-2)/3)`
= `3((-2)/3)^3 + 2((-2)/3)^2 - 3((-2)/3) - 2`
= `(-8)/9 + 8/9 + 2 - 2`
= 0
Hence, (3x + 2) is a factor of f(x).
Now, we have:
x2 – 1
`3x + 2")"overline(3x^3 + 2x^2 - 3x - 2)`
3x3 + 2x2
– –
– 3x – 2
– 3x – 2
+ +
0
∴ 3x3 + 2x2 – 3x – 2 = (3x + 2)(x2 – 1)
= (3x + 2)(x + 1)(x – 1)
APPEARS IN
RELATED QUESTIONS
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.
Using the Remainder Theorem, factorise each of the following completely.
3x3 + 2x2 – 23x – 30
Find the value of k, if 2x + 1 is a factor of (3k + 2)x3 + (k − 1).
Prove by factor theorem that
(2x - 1) is a factor of 6x3 - x2 - 5x +2
Find the value of m ·when x3 + 3x2 -m x +4 is exactly divisible by (x-2)
Prove that ( p-q) is a factor of (q - r)3 + (r - p) 3
Prove that (x+ 1) is a factor of x3 - 6x2 + 5x + 12 and hence factorize it completely.
Show that (2x + 1) is a factor of 4x3 + 12x2 + 11 x + 3 .Hence factorise 4x3 + 12x2 + 11x + 3.
Using the Remainder and Factor Theorem, factorise the following polynomial: x3 + 10x2 – 37x + 26.
If p(a) = 0 then (x – a) is a ___________ of p(x)
