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 polynomials in the following:
`h(x)=x^4-x^(3/2)+x-1`
Identify constant, linear, quadratic and cubic polynomials from the following polynomials
`p(x)=2x^2-x+4`
If `x = 2` is a root of the polynomial `f(x) = 2x2 – 3x + 7a` find the value of a.
Define zero or root of a polynomial.
Find the remainder when x3 + 4x2 + 4x − 3 is divided by x.
If x140 + 2x151 + k is divisible by x + 1, then the value of k is
If x2 − 1 is a factor of ax4 + bx3 + cx2 + dx + e, then
Factorise the following:
x² + 10x + 24
Factorise the following:
p² – 6p – 16
Factorise the following:
`sqrt(5)"a"^2 + 2"a" - 3sqrt(5)`
