Question

Factor the following trinomial expression by a method of your choice: 3x2 + 7x-10.
A. (3x + 2)(x - 5)
B. (3x + 5)(x - 2)
C. (3x + 1)(x - 10)
D. (3x + 10)(x - 1)

Answer 1

multiply the first and third terms. what do you get?

Answer 2

30

Answer 3

Trying to factor by splitting the middle term

2.1 Factoring 3x2+7x-10

The first term is, 3x2 its coefficient is 3 .
The middle term is, +7x its coefficient is 7 .
The last term, "the constant", is -10

Step-1 : Multiply the coefficient of the first term by the constant 3 • -10 = -30

Step-2 : Find two factors of -30 whose sum equals the coefficient of the middle term, which is 7 .

-30 + 1 = -29
-15 + 2 = -13
-10 + 3 = -7
-6 + 5 = -1
-5 + 6 = 1
-3 + 10 = 7 That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -3 and 10
3x2 - 3x + 10x - 10

Step-4 : Add up the first 2 terms, pulling out like factors :
3x • (x-1)
Add up the last 2 terms, pulling out common factors :
10 • (x-1)
Step-5 : Add up the four terms of step 4 :
(3x+10) • (x-1)
Which is the desired factorization

Final result :

(x - 1) • (3x + 10)

Answer 4

10 is negative, so you get -30.

now you wanna find two numbers that when multiplied together get -30, and when added together get 7, the middle term.

Answer 5

D @Aureyliant

Answer 6

...

Answer 7

Correct! @cassiesilva0628 please remember to ask if you don't understand something... you won't always have access to openstudy on tests and/or other things school related.

Answer 8

@AriPotta Thank you. :)

Answer 9

okay thank you so much for all you help @Aureyliant

Answer 10

No problem, but @AriPotta deserves the medal more than I do because he/she was answering the Q first, and was actually engaging you rather than I was. :)