Question

Factorise 2x3
-13x2
+6x+45​

Answer 1

Solution :-

=> 2x³-13x²+6x+45

= 2x^3-13x^2+6x+45

can be divided by 3 different polynomials,including by x-5

= Polynomial Long Division

Dividing : 2x³-13x²+6x+45

("Dividend")

By : x-5 ("Divisor")

dividend 2x³ - 13x² + 6x + 45

- divisor * 2x² 2x³ - 10x²

remainder - 3x² + 6x + 45

- divisor * -3x¹ - 3x² + 15x

remainder - 9x + 45

- divisor * -9x^0 - 9x + 45

remainder 0

Quotient : 2x²-3x-9 Remainder: 0

= Factoring 2x²-3x-9

2x² - 6x + 3x - 9

Step-1 : Add up the first 2 terms, pulling out like factors :

2x • (x-3)

Add up the last 2 terms, pulling out common factors :

3 • (x-3)

Step-2 : Add up the four terms of step 1 :

(2x+3) • (x-3)

Which is the desired factorization

Answer:-(x - 3) • (2x + 3) • (x - 5)

I hope it helps you......