Advertisements
Advertisements
Question
Factorise the following:
a4 – 3a2 + 2
Advertisements
Solution
Let a2 = x
a4 – 3a2 + 2 = (a2)2 – 3a2 + 2
= x2 – 3x + 2
Product = 2 and sum = – 3
Split the middle term as – x and – 2x
x² – 3x + 2 = x2 – x – 2x + 2
= x(x – 1) – 2(x – 1)
= (x – 1)(x – 2)
a4 – 3a2 + 2 = (a2 – 1)(a2 – 2) ...[But a2 = x]
= (a + 1)(a – 1)(a2 – 2)
APPEARS IN
RELATED QUESTIONS
Identify constant, linear, quadratic and cubic polynomials from the following polynomials:
`g(x)=2x^3-7x+4`
If the polynomials ax3 + 3x2 − 13 and 2x3 − 5x + a, when divided by (x − 2) leave the same remainder, find the value of a.
Find the remainder when x3 + 3x2 + 3x + 1 is divided by x + 1.
f(x) = x5 + 3x4 − x3 − 3x2 + 5x + 15, g(x) = x + 3
f(x) = 2x3 − 9x2 + x + 12, g(x) = 3 − 2x
x3 + 13x2 + 32x + 20
Factorize of the following polynomials:
4x3 + 20x2 + 33x + 18 given that 2x + 3 is a factor.
2x4 − 7x3 − 13x2 + 63x − 45
Factorise the following:
9 – 18x + 8x2
Factorise:
x3 – 6x2 + 11x – 6
