Regroup terms.

Factor out of .

Factor out of .

Factor out of .

Rewrite as .

Let . Substitute for all occurrences of .

Consider the form . Find a pair of integers whose product is and whose sum is . In this case, whose product is and whose sum is .

Write the factored form using these integers.

Replace all occurrences of with .

Factor out of .

Factor out of .

Let . Substitute for all occurrences of .

Rearrange terms.

Rewrite as .

Check the middle term by multiplying and compare this result with the middle term in the original expression.

Simplify.

Factor using the perfect square trinomial rule , where and .

Replace all occurrences of with .

Write as a Set of Linear Factors f(x)=x^4+14x^3+46x^2-42x-147