# Factoring Polynomials

At times, it can be difficult to tell whether or not a

quadratic of the form ax^{2} + bx + c can be factored

into the form (dx + e)( fx + g) , where a, b, c, d, e, f,

and g are integers. If b^{2} − 4ac is a perfect square, then

the quadratic can be factored in the above manner.

For each of the following problems,

(a) Compute b^{2} − 4ac .

(b) Use the information from part (a) to

determine whether or not the quadratic can

be written as factors with integer coefficients.

(Do not factor; simply answer Yes or No.)

Factor the following polynomials. If the polynomial

can not be rewritten as factors with integer

coefficients, then write the original polynomial as your

answer.

Factor the following. Remember to first factor out the

Greatest Common Factor (GCF) of the terms of the

polynomial, and to factor out a negative if the leading

coefficient is negative.

Factor the following polynomials. (Hint: Factor first

by grouping, and then continue to factor if possible.)