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In words, Explain how to factor a polynomial by grouping.

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1) To factor a polynomial by grouping, let's take 2 examples and do it step by step

2) Consider this quadratic equation, let's factor x² + 7x +12 by grouping

x² +7x +12 =0 Which two numbers whose sum is 7 and whose product is 12

S =___ + ___ = 7 4 + 3

P = ___x ___ = 12 4x 3

Then we can rewrite 7x as 4x +3x

x² +4x +3x +12 = 0 Let's group these terms into two parentheses:

(x² +4x) +(3x +12)

Now let's write them as factors, the GCD outside the parentheses x, 4x and 3, 12

x(x +4) +3(x +4)

Since we have a repetition of the factor (x +4) we can write it as a product

(x+4) (x+3) = x² +7x +12

Another example:

x³ -2x² +5x -10 Group them into two parentheses

(x³-2x²) +(5x -10) Factor out the GCD x³, 2x² =x² and 5, 10 =5

(x-2) +5(x-2) Now let's write them as a factor, (x -2x) is common to both

(x²+5) (x -2)

(x²+5) (x -2) = x³ -2x² +5x -10

3) So, in words.

1. Rewrite the polynomial into two parentheses grouping the terms

2. Factor out the GCD of the terms, leaving it outside the parentheses

3. Rewrite it as a product writing the outside factors into parentheses and the common term.

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