How do you factor the expression 10x^2-3x-1 ?

2 Answers
mason m
Dec 13, 2015

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

Explanation:

Look for a pair of numbers whose PRODUCT is the product of the first and last numbers (-10) and sum is the middle number (-3).

The two numbers that meet these criteria are -5 and 2.

Rewrite the -3x term in the expression as -5x+2x.

10x^2-5x+2x-1

Factor by grouping.

(10x^2-5x)+(2x-1)

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

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

BeeFree
Dec 13, 2015

Split the middle term (-3x) into two separate terms . Then, use grouping to complete the factoring.

Explanation:

Split the middle term into two separate terms so that the sum is still -3 however, you want the product of the two new terms to equal (10)(-1)=-10. For this problem use 2 and -5

Here is the new expression ...

10x^2+2x-5x-1

Use grouping ...

(10x^2+2x)-(5x+1)

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

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

hope that helped

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