Question

Multiply the polynomials.
(p² +5p-3) (p²-2p - 2)

Answer 1

The product of the polynomials (p² +5p-3) and (p²-2p - 2) is p^4 + 3p^3 - 15p^2 - 4p + 6. This result is obtained by multiplying each term of the first polynomial by each term of the second, combining like terms, and simplifying.

Step-by-step explanation:

Step by Step Multiplication of Polynomials

To multiply the polynomials (p² +5p-3) and (p²-2p - 2), apply the distributive property which states that each term in the first polynomial must be multiplied by each term in the second polynomial.

1. Multiply p² by p² to get p^4.
2. Multiply p² by -2p to get -2p^3.
3. Multiply p² by -2 to get -2p^2.
4. Multiply 5p by p² to get 5p^3.
5. Multiply 5p by -2p to get -10p^2.
6. Multiply 5p by -2 to get -10p.
7. Multiply -3 by p² to get -3p^2.
8. Multiply -3 by -2p to get 6p.
9. Multiply -3 by -2 to get 6.

Now, combine like terms:

• p^4 remains as-is, since it is unique.
• -2p^3 and 5p^3 combine to 3p^3.
• -2p^2, -10p^2, and -3p^2 combine to -15p^2.
• -10p and 6p combine to -4p.
• 6 remains as-is, since it is unique.

Finally, the product of the two polynomials is p^4 + 3p^3 - 15p^2 - 4p + 6.