Question

How do I factor 4z^2+z-14?

Answer 1

Factorizations of 4 are 1, 4 and 2, 2
Factorizations of 14 are 1,14 and 2,7

There are very few to try. Dive in!

Answer 2

The way I was taught was to multiply the coefficient of the a term to the c term, then find 2 factors that would add up to be the B term... What method are you using?

Answer 3

That's right. A factored result will look like one of these:

(4z something)(z something)
or
(2z something)(2z something)

The "something"s are the signs and factors of -14. Multiplied with the values already established, you hunt for the "+z" in the middle.

Answer 4

Hold up... how did you figure out that (4z something) (z something) format? Is there a rule or something that guides how you set this up?

Answer 5

4z^2+8z-7z-14
4z(z+2)-7(z+2)
(4z-7)(z+2)

Answer 6

Factorizations of 4, the leading coefficient.

Answer 7

Please note that factorization by grouping is mostly luck. It is not a systematic process. Factorization be exhaustion, as I tried to demonstrate, is systematic and complete.

Answer 8

So... cutestpearl used grouping right?

Answer 9

That's correct. I dare you to tell me where "8z-7z" came from. Grouping relies significantly on knowing in advance what is wanted. If you don't know in advance, it is not of much value. It makes for interesting demonstrations - almost magic!

Answer 10

Hmm... thanks!