Question

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

Answer 1

`(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)`

Answer 2

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