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Study Guides > ALGEBRA / TRIG I

Summary: Factoring Methods

Key Concepts

Factoring Trinomials in the form ax2+bx+cax^{2}+bx+c

To factor a trinomial in the form ax2+bx+cax^{2}+bx+c, find two integers, r and s, whose sum is b and whose product is ac.

rs=acr+s=b\begin{array}{l}r\cdot{s}=a\cdot{c}\\r+s=b\end{array}

Rewrite the trinomial as ax2+rx+sx+cax^{2}+rx+sx+c and then use grouping and the distributive property to factor the polynomial.

How to factor a trinomial in the form ax2+bx+ca{x}^{2}+bx+c by grouping

  1. List factors of acac.
  2. Find pp and qq, a pair of factors of acac with a sum of bb.
  3. Rewrite the original expression as ax2+px+qx+ca{x}^{2}+px+qx+c.
  4. Pull out the GCF of ax2+pxa{x}^{2}+px.
  5. Pull out the GCF of qx+cqx+c.
  6. Factor out the GCF of the expression.

Factoring Trinomials in the form x2+bx+cx^{2}+bx+c

To factor a trinomial in the form x2+bx+cx^{2}+bx+c, find two integers, r and s, whose product is c and whose sum is b.

rs=c and r+s=b\begin{array}{l}r\cdot{s}=c\\\text{ and }\\r+s=b\end{array}

Rewrite the trinomial as x2+rx+sx+cx^{2}+rx+sx+c and then use grouping and the distributive property to factor the polynomial. The resulting factors will be (x+r)\left(x+r\right) and (x+s)\left(x+s\right).

How to factor a trinomial in the form x2+bx+c{x}^{2}+bx+c

  1. List factors of cc.
  2. Find pp and qq, a pair of factors of cc with a sum of bb.
  3. Write the factored expression (x+p)(x+q)\left(x+p\right)\left(x+q\right).

Glossary

Prime trinomial - A trinomial that cannot be factored using integers  

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