Advertisements
Advertisements
Question
Factorise:
3x3 – x2 – 3x + 1
Advertisements
Solution
Let p(x) = 3x3 – x2 – 3x + 1
Constant term of p(x) = 1
Factor of 1 are ±1
By trial, we find that p(1) = 0, so (x – 1) is a factor of p(x)
Now, we see that 3x3 – x2 – 3x + 1
= 3x3 – 3x2 + 2x2 – 2x – x + 1
= 3x2(x – 1) + 2x(x – 1) – 1(x – 1)
= (x – 1)(3x2 + 2x – 1)
Now, (3x2 + 2x – 1) = 3x2 + 3x – x – 1 ...[By splitting middle term]
= 3x(x + 1) – 1(x + 1)
= (x + 1)(3x – 1)
∴ 3x3 – x2 – 3x + 1 = (x – 1)(x + 1)(3x – 1)
APPEARS IN
RELATED QUESTIONS
Identify polynomials in the following:
`g(x)=2x^3-3x^2+sqrtx-1`
Show that (x − 2), (x + 3) and (x − 4) are factors of x3 − 3x2 − 10x + 24.
Find α and β, if x + 1 and x + 2 are factors of x3 + 3x2 − 2αx + β.
If \[x = \frac{1}{2}\] is a zero of the polynomial f(x) = 8x3 + ax2 − 4x + 2, find the value of a.
If x + 1 is a factor of the polynomial 2x2 + kx, then k =
One factor of x4 + x2 − 20 is x2 + 5. The other factor is
If x2 + x + 1 is a factor of the polynomial 3x3 + 8x2 + 8x + 3 + 5k, then the value of k is
If x2 − 1 is a factor of ax4 + bx3 + cx2 + dx + e, then
Factorise the following:
5x2 – 29xy – 42y2
(a + b – c)2 is equal to __________
