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) and (x + 3) are factors of x3 + ax + b, find the values of ‘a’ and ‘b’.
Using the Factor Theorem, show that (x + 5) is a factor of 2x3 + 5x2 – 28x – 15. Hence, factorise the expression 2x3 + 5x2 – 28x – 15 completely.
Prove that ( p-q) is a factor of (q - r)3 + (r - p) 3
Prove that (x-3) is a factor of x3 - x2 - 9x +9 and hence factorize it completely.
Find the value of the constant a and b, if (x – 2) and (x + 3) are both factors of expression x3 + ax2 + bx - 12.
If x – 2 is a factor of 2x3 - x2 - px - 2.
with the value of p, factorize the above expression completely.
Using the Remainder and Factor Theorem, factorise the following polynomial: x3 + 10x2 – 37x + 26.
Factors of 3x3 – 2x2 – 8x are ______.
Factors of 4 + 4x – x2 – x3 are ______.
Is (x – 2) a factor of x3 – 4x2 – 11x + 30?
