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

Yasmin

Yasmin

Answered question

2021-09-12

Factor the following completely
2x3+3x35x+8x2y+12xy20y

Answer & Explanation

sovienesY

sovienesY

Skilled2021-09-13Added 89 answers

Let us find the factors of given equation
2x3+3x25x+8x2y+12xy20y
Splitting the 6−terms polynomial into two 3−term polynomials
(8x2y+12xy20y)+(2x3+3x25x)
Now simplify each 3 term polynomials and taking out the common term of each polynomials
4y(2x2+3x5)+x(2x2+3x5)
Here simplified two polynomial having common term (2x2+3x5)
Equation:
(4y+x)(2x2+3x5)
Now factor this term
(2x2+3x5)
sum of two number (coefficient of x) is 3
product of first term and last term is 10
a=5,b=2
=2x2+5x2x5
=x(2x+5)1(2x+5)
=(x1)(2x+5)
(x+4y)(x1)(2x+5)
Factors of given equation
Factors of 2x3+3x25x+8x2y+12xy20y is
(x+4y).(x1).(2x+5)

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