Talk it: Group Factoring

By Tangerine

Objectives for Group Factoring:> Factoring with Four Terms> Factoring Trinomials by Grouping

Factoring a Four-Term Polynomial1. Factor the GCF from each

group of two terms2. Factor out the binomial left

Just like this:

4n3 + 8n2 - 5n - 10= 4n2(n + 2) - 5(n + 2)= (4n2 - 5) (n + 2)

Factoring Completely1. Factor out the GCF2. Factor by grouping3. Factor again

Just like this:

12p4 + 10p3 - 36p2 - 30p= 2p(6p3 + 5p2 - 18p -15)= 2p[(p2(6p + 5) - 3(6p + 5)]= 2p(p2 - 3)(6p + 5)

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Factoring Trinomialsby Grouping(ax2 + bx + c)1. Find the product of ac.2. Find the two factors of a and

c that sums to bx3. Rewrite using the sum4. Factor by grouping

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Just like this:

48x2 + 46x + 5= 48x2 + (6 + 40)x + 5= 48x2 + 4x + 6x + 5= 6x(8x + 1) + 5(8x + 1)= (6x + 5)(8x + 1)

Reminders:1. Before you factor by grouping, you may need to factor the GCF of all the terms of a polynomial. Remember, a polynomial is not completely factored until there are no common factors other than one.

Reminders:2. Some may want to factor 5, instead of -5, from -5 - 10 and get 5(-n - 2). To make the new factor turn out the way they should,they need to factor out - 1 as well.

Reminders:3. Always look for a GCF to factor out.