Answer:

Step 1: Look for a GCF and factor it out first.

Step 2: Multiply the coefficient of the leading term a by the constant term c. List the factors of this

product (a • c) to find the pair of factors, f1 and f2, that sums to b, the coefficient of the middle

term.

• When c is positive, factors of a • c have the same sign –

o If the middle term bx is positive, both factors are positive.

o If the middle term bx is negative, both factors are negative.

o Find the pair of factors that adds to b.

• When c is negative, factors of a • c have opposite signs –

o The larger of these factors has the same sign as the middle term.

o Find the pair of factors that subtracts to b.

Step 3: Rewrite (split) the middle term bx using the factors, f1 and f2, found in Step 2. The expression

now has 4 terms:

ax^2 + bx + c =  

ax^2+ fx+ + fx + c

Step 4: Group the terms of the expression into binomial pairs as shown:

(ax^2 + fx) (fx + c)

Step 5: Factor out a “gcf” from each pair. If the expression can be factored by grouping, the terms will

share a common "binomial" factor.

Step 6: Factor out the common binomial factor to write the factorization.

Step 7: Check the result by multiplying

Step-by-step explanation: