2. find the product (11x2 + 7x - + 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

55? i think maybe

step-by-step explanation: