Question

 

The product of (7x³ + 5x - 8)(2 - 3x) is _______

Is (x + 2) a factor of P(x) = 4x³ - 6x² + 2x - 12?  Explain.

1.) Using synthetic substitution and the Remainder Theorem, I know that the remainder is ________

2.) Based upon this answer in #1, and in applying the Factor Theorem, I know that (x + 2)_____    is/isn't a factor of P(x) because ______

SHOW how you can completely factor the polynomial expression x³ + x² - 16x + 20

 

Answer 1

Solution :

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Solution : ( 1 )

Write down the coefficients of the polynomial p(x). Put the zero from ( x + 2 ) = 0 ( x = − 2 ) at the left.

Bring down the leading coefficient to the bottom row.

Multiply by the number on the left, and carry the result into the next column:  −2*4 = −8

Add down the column:  −6 + (−8) = −14

Multiply by the number on the left, and carry the result into the next column:  −2 * (−14) = 28

Add down the column:  2 + 28 = 30

Multiply by the number on the left, and carry the result into the next column:  −2 * 30 = −60

Add down the column:  −12 + (−60) = −72

Remainder is the last entry in the bottom row  (−72).

The synthetic division table is:

Because the remainder ( − 72 ) is not zero, this means the (x + 2) a factor of P(x) = 4x³ - 6x² + 2x - 12

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