Answer:
The product is 2x³ - 11x² + 16x - 3 ⇒ 3rd answer
Explanation:
* Lets explain how to find the product of binomial by trinomial
- If (ax² ± bx ± c) and (dx ± e) are trinomial and binomial, 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
∵ The binomial is (x - 3) and the trinomial is (2x² - 5x + 1)
∴ (x)(2x²) = 2x³
∵ (x)(-5x) = -5x²
∵ (x)(1) = x
∵ (-3)(2x²) = -6x²
∵ (-3)(-5x) = 15x
∵ (-3)(1) = -3
∴ (x - 3)(2x² - 5x + 1) = 2x³ + -5x² + x + -6x² + 15x + -3
- Add the like terms
∵ -5x² and -6x² are like term
∴ Their sum is -11x²
∵ x and 15 x are like terms
∴ Their sum = 16x
∴ (x - 3)(2x² - 5x + 1) = 2x³ - 11x² + 16x - 3
* The product is 2x³ - 11x² + 16x - 3