Question

Factorise 2x3 – x2 – 16x + 15 using factor theorem.

Answer 1

Answer:

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

Step-by-step explanation:

To factorise

$2 {x}^{3} - {x}^{2} - 16x + 15$

The first factor can be find using hit and trial method; for x= 1

$= 2 {(1)}^{3} - {(1)}^{2} - 16(1) + 15 \\ \\ = 2 - 1 - 16 + 15 \\ \\ = 17 - 17 \\ \\ = 0$

hence (x-1) is a factor of polynomial.

Now as we know that it's a polynomial of degree three,so it should have three factors.

To find the other to factors

$x - 1 \: )2 {x}^{3} - {x}^{2} - 16x + 15(2 {x}^{2} + x - 15 \\ \: \: \: \: \: \: \: \: \: \: \: \: 2 {x}^{3} - 2 {x}^{2} \\ \: \: \: \: \: \: \: \: ( -) \: \: \: \: ( + ) \\ \: \: \: \: \: \: \: \: - - - - - \\ \: \: \: \: \: \: \: \: {x}^{2} - 16x \\ \: \: \: \: \: \: \: \: {x}^{2} - x \\ \: \: \: \: \: ( - ) \: \: ( + ) \\ \: \: \: \: \: \: \: - - - - - \\ \: \: \: \: \: \: \: \: \: \: - 15x + 15 \\ \: \: \: \: \: \: \: \: \: - 15x + 15 \\ \: \: \: \: \: \: \: ( + ) \: \: \: ( - ) \\ \: \: \: \: \: \: - - - - - - \\ \: \: \: \: \: \: \: \: \: \: \: 0$

So now factorise

$2 {x}^{2} + x - 15 \\ \\ 2 {x}^{2} + 6x - 5x - 15 \\ \\ 2x(x + 3) - 5(x + 3) \\ \\ (x + 3)(2x - 5)$

Thus all three factors of given polynomial are

$(x + 3)(2x - 5)(x - 1)$

Hope it helps you.

Answer 2

Answer:

factors are

(x+3) (2x-5)  (x+1)

Step-by-step explanation:

hopes it will help you