factoring

[higby]

I really need help factoring
10u²+17u-20
its driving me crazy ive tried everything i can think of

 

[galactus]

What two numbers multiplied equal -200 and when added equal 17?.

How about 25 and -8?.

 

[higby]

right but it needs to equal -20, not -200 i need to factor it into a form like

(10u+ )(u- )

 

[Mrspi]

I really need help factoring
10u²+17u-20
its driving me crazy ive tried everything i can think of

You need to be aware that when the coefficient of the squared term is something OTHER THAN 1, there's more to the process than just looking for two numbers which multiply to the constant term and add up to the middle term.

Here's something you can try (and Galactus was steering you in that direction.....).

To factor a trinomial of the form

ax² + bx + c

you can always follow these steps:

1) Multiply the coefficient of the squared term by the constant term (or a * c). In your problem, multiply 10 * -20 to get -200.

2) Look for two factors whose PRODUCT is the value you got in step 1, and whose SUM is the coefficient of the middle term (b). In your problem, you are looking for two numbers whose product is -200, and whose sum is 17. Galactus suggested -8 and 25, since (-8)*(25) = -200, and (-8) + 25 = 17.

3) Use the two numbers you found in step 2 to rewrite the middle term in the trinomial. The numbers we found were -8 and + 25; rewrite 17u as -8u + 25u:

10u² - 8u + 25u - 20

4) Factor by grouping. Remove a common factor from the first two terms, and a common factor from the last two terms:

2u(5u - 4) + 5(5u - 4)
Now, (5u - 4) is a common factor. Remove it to get

(5u - 4)(2u + 5)

This is the factorization you are seeking, and you can verify that it is correct by doing the multiplication. You should get your original expression, 10u² + 17u - 20.

 

[higby]

Thank you all so much mrspi, that was so helpful, I have struggled with this for a while, I had no idea that could be done!