Question

Find the product. Equation is below.

Answer 1

12x³ + 19x² + x -5

Explanation:

Polynomials are expressions that have multiple terms.

Breaking Apart Polynomials

When multiplying by a polynomial, we can break apart one of the polynomials, and multiply by each term individually. This means to multiply 3x² + x - 1 by 4x + 5, we can break apart the binomial into its separate terms. Instead of trying to multiply everything at once, we can multiply the trinomial by 4x and then multiply the trinomial by 5. Finally, add together the 2 products for the final answer.

Multiplying Polynomials

First, let's multiply the trinomial by 4x.

• 4x(3x² + x - 1)

To find the product, multiply each term of the trinomial by 4x, then add them back together.

• 4x * 3x² = 12x³
• 4x * x = 4x²
• 4x * -1 = -4x

So, the first product is 12x³ + 4x²- 4x. Next, let's multiply 5(3x² + x - 1) the same way.

• 5 * 3x² = 15x²
• 5 * x = 5x
• 5 * -1 = -5

This means that the second product is 15x² + 5x - 5. Finally, let's add the 2 products together.

• (12x³ + 4x²- 4x) + (15x² + 5x - 5)

Then, simplify the expression.

• 12x³ + 19x² + x - 5

This gives us our final answer. The product of 3x² + x - 1 and 4x + 5 is 12x³ + 19x² + x - 5.

Answer 2

12x^3 + 19x^2 + x - 5

Explanation:

To solve this, I set up the problem like this:

(3x^2 + x - 1)(4x + 5)

Now, just distribute everything from the first set of ( ) to the second set of ( ). Here's what you should have when you do that:

12x^3 + 15x^2 + 4x^2 + 5x - 4x - 5

Now, you would just combine like terms, which would get you to the final answer.

Hope this helps!