Question

Find the product of ( (x^3 + 2x^2 - 5x + 1) ) and ( (x^2 + 7x + 1) ).

a) ( x^5 + 9x^4 - 31x^3 + 6x^2 - 34x + 1 )
b) ( x^5 + 5x^4 - 24x^3 + 9x^2 - 12x + 1 )
c) ( x^5 + 9x^4 - 24x^3 + 9x^2 - 12x + 1 )
d) ( x^5 + 5x^4 - 31x^3 + 6x^2 - 34x + 1 )

Answer 1

To find the product of two polynomials, we multiply each term of the first polynomial by each term of the second polynomial. In this case, the product is x^5 + 9x^4 - 31x^3 + 6x^2 - 34x + 1.

Step-by-step explanation:

To find the product of two polynomials, we need to multiply each term of the first polynomial by each term of the second polynomial. In this case, we have:

(x^3 + 2x^2 - 5x + 1) * (x^2 + 7x + 1)

Using the distributive property, we can multiply each term:

x^3 * (x^2 + 7x + 1) + 2x^2 * (x^2 + 7x + 1) - 5x * (x^2 + 7x + 1) + 1 * (x^2 + 7x + 1)

Expanding each multiplication, we get:

x^5 + 7x^4 + x^3 + 2x^4 + 14x^3 + 2x^2 - 5x^3 - 35x^2 - 5x + x^2 + 7x + 1

Combining like terms, the product simplifies to:

x^5 + 9x^4 - 31x^3 + 6x^2 - 34x + 1