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)
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.
Find the value of k, if 3x – 4 is a factor of expression 3x2 + 2x − k.
Using the Remainder Theorem, factorise each of the following completely.
3x3 + 2x2 – 23x – 30
If x + a is a common factor of expressions f(x) = x2 + px + q and g(x) = x2 + mx + n; show that : `a = (n - q)/(m - p)`
Use the factor theorem to factorise completely x3 + x2 - 4x - 4.
In the following problems use the factor theorem to find if g(x) is a factor of p(x):
p(x) = x3 - 3x2 + 4x - 4 and g(x) = x - 2
Use factor theorem to factorise the following polynominals completely. x3 – 13x – 12.
Determine whether (x – 1) is a factor of the following polynomials:
x3 + 5x2 – 10x + 4
If x – 3 is a factor of p(x), then the remainder is
If mx2 – nx + 8 has x – 2 as a factor, then ______.
