Question

factorise the following 15 x4 + 3 x square - 18​

Answer 1

Question:

Factorise the given polynomial;

15x^4 + 3x^2 - 18.

Answer:

3(x-1)(x+1)(5x^2 + 9)

Factorisation:

We have;

=> 15x^4 + 3x^2 - 18

=> 15x^4 + 18x^2 - 15x^2 - 18

=> 3x^2(5x^2 + 9) - 3(5x^2 + 9)

=> (5x^2 + 9)(3x^2 - 3)

=> (3x^2 - 3)(5x^2 + 9)

=> 3(x^2 - 1)(5x^2 + 9)

=> 3(x-1)(x+1)(5x^2 + 9)

Hence,

The factorised form of the given polynomial is 3(x-1)(x+1)(5x^2 + 9).

Moreover,

To find the zeros of the polynomial,

equate it to zero.

Thus,

=> 15x^4 + 3x^2 - 18 = 0

=> 3(x-1)(x+1)(5x^2 + 9) = 0

If (x-1) = 0 ,

then x = 1.

If (x+1) = 0

then x = -1

If (5x^2 + 9) = 0

then 5x^2 = -9

=> x^2 = -9/5

=> x = √(-9/5)

{ This is imaginary root}

Thus,

The zeros of the given polynomial are

x = 1 , -1 .