Factor the following completely 2x3+3x3−5x+8x2y+12xy−20y

Question

Factor the following completely  2x3+3x3−5x+8x2y+12xy−20y

sovienesY · Accepted Answer

Let us find the factors of given equation

2 x^{3} + 3 x^{2} - 5 x + 8 x^{2} y + 12 x y - 20 y

Splitting the 6−terms polynomial into two 3−term polynomials

(8 x^{2} y + 12 x y - 20 y) + (2 x^{3} + 3 x^{2} - 5 x)

Now simplify each 3 term polynomials and taking out the common term of each polynomials

4 y (2 x^{2} + 3 x - 5) + x (2 x^{2} + 3 x - 5)

Here simplified two polynomial having common term

(2 x^{2} + 3 x - 5)

Equation:

(4 y + x) (2 x^{2} + 3 x - 5)

Now factor this term

(2 x^{2} + 3 x - 5)

sum of two number (coefficient of x) is 3
product of first term and last term is 10

a = 5, b = - 2

= 2 x^{2} + 5 x - 2 x - 5

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

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

(x + 4 y) (x - 1) (2 x + 5)

Factors of given equation
Factors of

2 x^{3} + 3 x^{2} - 5 x + 8 x^{2} y + 12 x y - 20 y

is

(x + 4 y) . (x - 1) . (2 x + 5)

Factor the following completely. 2x^3+3x^3-5x+8x^2y+12xy-20y