Question

How do you factor `6g^2 + 11g - 35`?

Answer 1

Into two binomials

Explanation:

In the form `Ax^2 + Bx + C`
The C is negative which tells that one binomial must be positive while the other must be negative.
The B is positive so the positive factor must be larger than the negative factor.
The B is 11 so the difference between the two factors must be 11

35 = 7 x 5
6 = 3 x 2

Combining the larger factors to make the positive factor gives
`3 xx 7 = 21 ( +) Combining the smaller factors to make the negative factor gives` 2 xx 5 = 10 ( -)

Adding the factors gives

`+ 21 + -10 = + 11` so

`6g^2 + 11 g - 35 = ( 3g -5) xx ( 2g +7)`