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Factoring Trinomials

Factoring Quadratic Trinomials

 

WHAT TO DO:

HOW TO DO IT:

1. Now consider the trinomial with last sign -

Two numbers with a product of 15 and difference of 2 are 5 and 3

1. x 2 + 2x - 15
The larger gets the "middle sign" +

Rewriting the terms to factor by grouping:

x 2 + 5x - 3x + 15
Then group the terms 2 × 2 into two terms.

Factor common factors. Bring down the middle sign.

Find the common factor for each group.

Watch the sign of the second group.

Factor out the common factor (x + 5)(x - 3) Answer
Check by multiplying back out by

FOIL method.

First - Outer - Inner - Last

Note O-I terms.

 

2. Consider the trinomial with last sign " +"

Two numbers with a product of and sum of are

Rewriting the terms to factor by grouping:

Then group the terms 2 × 2 into two terms.

Factor common factors. Bring down the middle sign.

Find the common factor for each group.
Factor out the common factor Answer
Check by multiplying back out by

FOIL method.

First - Outer - Inner - Last

Note O-I terms.

Consider the trinomial of degree 6 with middle term degree 3

The last sign is - , two numbers with a product of 18 and difference of 7 are 9 and 2

x 6 - 7x 3 - 18
The larger gets the "middle sign" " - "  
Rewriting the terms to factor by grouping:

Then group the terms 2 × 2 into two terms.

Factor common factors. Bring down the middle sign.

Find the common factor for each group.

Watch the sign of the second group.

Factor out the common factor ( x 3 - 9 ) Answer (x 3 - 9)(x 3 + 2)
Check by multiplying back out by

FOIL method.

First - Outer - Inner - Last

Note O - I terms.

 
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