Exercise 71 Page 365

Rewrite the given expression so that it is easier to make groups.

(a-4)(a-2)(5a+2b)

Practice makes perfect

To factor by grouping, we will take the greatest common factor of the first three terms and the greatest common factor of the second three terms.

5a^3-30a^2+40a+2a^2b-12ab+16b

Factor out 5a

5a(a^2-6a+8) + 2a^2b-12ab+16b

Factor out 2b

5a(a^2-6a+8)+2b( a^2-6a+8)

Factor out ( a^2-6a+8)

( a^2-6a+8)(5a+2b)

We can now rewrite -6a as -4a-2a to factor the expression completely.

( a^2-6a+8)(5a+2b)

Rewrite -6a as -4a-2a

( a^2-4a-2a+8)(5a+2b)

Factor out a

( a(a-4)-2a+8)(5a+2b)

Factor out -2

( a(a-4)-2(a-4))(5a+2b)

Factor out (a-4)

(a-4)(a-2)(5a+2b)

Check Your Understanding p.363

Practice and Problem Solving p.363-364

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Standardized Test Practice p.365

Spiral Review p.365

Skills Review p.365

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