Question

P(x)=x³)+6x³+5x-12 has a known factor of (x+3). Rewrite p(x) as a pro

Answer 1

To rewrite the polynomial p(x) = x³ + 6x³ + 5x - 12 using the known factor of (x + 3), perform polynomial long division. The rewritten polynomial is p(x) = x³ + 3x² + 5x - 12, with the known factor of (x + 3) incorporated.

Step-by-step explanation:

To rewrite the polynomial p(x) = x³ + 6x³ + 5x - 12 using the known factor of (x + 3), we can perform polynomial long division.

Step 1:

Divide the leading term of p(x) by the leading term of the known factor:

(x³)/(x) = x².

Step 2:

Multiply the quotient from Step 1 by the known factor:

x²(x + 3) = x³ + 3x².

Step 3:

Subtract the product obtained in Step 2 from p(x):

p(x) - (x³ + 3x²) = 6x³ + 5x - 12 - (x³ + 3x²).

Step 4:

Combine like terms:

p(x) - (x³ + 3x²) = 6x³ + 5x - 12 - x³ - 3x² = 5x³ + 5x - 12.

The rewritten polynomial is p(x) = x³ + 3x² + 5x - 12, with the known factor of (x + 3) incorporated.