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