Question

Find (a*b)(x). a(x)=x+4 b(x)=ˣ²+5x Write your answer as a polynomial in simplest form.

Answer 1

To find (a*b)(x), we need to multiply the two polynomials a(x) and b(x) using the distributive property. The resulting polynomial is x^3 + 9x^2 + 20x.

Step-by-step explanation:

To find (a*b)(x), we need to multiply the two polynomials a(x) and b(x). Let's substitute the given expressions for a(x) and b(x) into the expression:

(a*b)(x) = (x+4)(x^2+5x)

To simplify this expression, we can use the distributive property to multiply each term in the first polynomial by each term in the second polynomial:

(a*b)(x) = x(x^2+5x) + 4(x^2+5x)

Next, we can simplify each term:

(a*b)(x) = x^3 + 5x^2 + 4x^2 + 20x

Combining like terms, we get the final simplified polynomial:

(a*b)(x) = x^3 + 9x^2 + 20x