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Is the Polynomial Completely Factored?

6.7.4 Is the Polynomial Completely Factored?

6.7.4 • Is the Polynomial Completely Factored?

Cool Down

1.

Explain what it means to factor a polynomial completely.

Compare your answer:

To factor a polynomial completely means that every factor you have found, or the polynomial itself, is prime.

For questions 2 – 7, determine if each polynomial is completely factored. If the answer is no, write the completely factored form.

2.

3 x ( 8 x 2 − 9 x − 3 ) 3 x ( 8 x 2 − 9 x − 3 )

Compare your answer:

yes

3.

60 x 2 y − 75 x y + 30 y 60 x 2 y − 75 x y + 30 y

Compare your answer:

no; 15y(4x2−5x+2)15y(4x2−5x+2)

4.

2 c ( 4 c 2 + 20 c d + 81 d 2 ) 2 c ( 4 c 2 + 20 c d + 81 d 2 )

Compare your answer:

yes

5.

5 n 2 + 5 n + 12 5 n 2 + 5 n + 12

Compare your answer:

yes

6.

5 q 2 − 15 q − 90 5 q 2 − 15 q − 90

Compare your answer:

no; 5(q+3)(q−6)5(q+3)(q−6)

7.

64 x 2 + 16 x y + y 2 64 x 2 + 16 x y + y 2

Compare your answer:

no; (8x+y)2(8x+y)2