2. Find the product (11x2 + 7x - 3) (-5x + 1).

-55x3 - 24x2 + 22x - 3

The product is - 55x³ - 24x² + 22x - 3

Step-by-step explanation:

* Lets revise how to find the product of trinomial and binomial

- If (ax² ± bx ± c) and (dx ± e) are two binomials, where a, b, c, d, e

are constant, their product is:

# Multiply (ax²) by (dx) ⇒ 1st term in the trinomial and 1st term in the

binomial

# Multiply (ax²) by (e) ⇒ 1st term in the trinomial and 2nd term in

the binomial

# Multiply (bx) by (dx) ⇒ 2nd term the trinomial and 1st term in

the binomial

# Multiply (bx) by (e) ⇒ 2nd term in the trinomial and 2nd term in

the binomial

# Multiply (c) by (dx) ⇒ 3rd term in the trinomial and 1st term in

the binomial

# Multiply (c) by (e) ⇒ 3rd term the trinomial and 2nd term in

the binomial

# (ax² ± bx ± c) (dx ± e) = adx³ ± aex² ± bdx² ± bex ± cdx ± ce

- Add the terms aex² and bdx² because they are like terms

- Add the terms bex and cdx because they are like terms

* Now lets solve the problem

- There are a trinomial and a binomials (11x² + 7x - 3) and (-5x + 1)

- We can find their product by the way above

∵ (11x²) (-5x) = - 55x³ ⇒ 1st term in the trinomial and 1st term in the binomial

∵ (11x²) (1) = 11x² ⇒ 1st term in the trinomial and 2nd term in the binomial

∵ (7x) (-5x) = - 35x² ⇒ 2nd term the trinomial and 1st term in the binomial

∵ (7x) (1) = 7x ⇒ 2nd term in the trinomial and 2nd term in the binomial

∵ (-3) (-5x) = 15x ⇒ 3rd term in the trinomial and 1st term in the binomial

∵ (-3) (1) = - 3 ⇒ 3rd term the trinomial and 2nd term in the binomial

∴ (11x² + 7x - 3) (-5x + 1) = - 55x³ + 11x² - 35x² + 7x + 15x - 3

- Add the like terms ⇒ 11x² - 35x² = - 24x²

- Add the like terms ⇒ 7x + 15x = 22x

∴ The product is - 55x³ - 24x² + 22x - 3