Question

Algebra 2: Factoring The Polynomial. Some are guess and test.

Answer 1

Multiply the first and last term.  Now find two numbers that when you multiply gives you that product and when you add them gives you the middle term.  Replace the middle term with those two numbers and factor using the grouping method.

10w² - 37w + 15

                          10 x 15 = 150 (1 x150, 2 x 75, 3 x 50, 5 x 30, 6 x 25, 10 x 15)

None of those pairs have a sum of -37 so this polynomial is prime.

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4z² + 4z - 3

                   4 x -3 = -12 ( -1 x 12, -2 x 6, -3 x 4)  ⇒ -2 + 6 = 4

= 4z² - 2z   + 6z - 3

= 2z(2z - 1)   +3(2z - 1)

= (2z + 3)(2z - 1)

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18v² - 15v - 18

= 3(6v² - 5v - 6)

                            6 x -6 = -36 (1 x -36, 2 x -18, 3 x -12, 4 x -9, 6 x -6) ⇒ 4 x -9 = -5

= 3(6v² + 4v    -9v - 6)

= 3[2v(3v + 2)  -3(3v + 2)]

= 3(2v - 3)(3v + 2)

Answer 2

3) 18v2−15v−18

=3(6v2−5v−6)

=3(2v−3)(3v+2)