Question

Which of the following is one of the two binomial factors of 6s2 + 40s – 64?

A. s + 10
B. 2s – 16
C. 6s – 12
D. 3s – 4

Answer 1

Binomial Factors really just mean factors of a polynomial, in this case there are two so hence the binomial name. If you are unsure of how to solve a quadratic equation, the best thing is to first simple the coefficients and then move to the quadratic formula. Since all the factors are divisible by 2, you can divide 2 out of the entire expression, so now it will look like
`3s^2+20s-32`. Now that the coefficients are completely simplified, you can put the coefficients into the quadratic formula,
`(-b+ √(b^2-4ac))/(2a) or (-b- √(b^2-4ac))/(2a)`, where a is the coefficient with the
`x^2`, b with
`s` and c the -32. When you plug in the values for a, b and c into the two equations, the two solutions you come up with are
`-8 and (4)/(3)`. If you put this back in factor form, it would look like
`(3s-4)(s+8)`. Matching that with the choices you were given, D.
`(3s-4)` is the answer