Answer:
see explanation
Step-by-step explanation:
Expand the right side and compare the coefficients of like terms
(5x + 2)(ax² + bx + c)
= 5x(ax² + bx + c) + 2(ax² + bx + c) ← distribute parenthesis
= 5ax³ + 5bx² + 5cx + 2ax² + 2bx + 2c ← collect like terms
= 5ax³ + x²(5b + 2a) + x(5c + 2b) + 2c
For the 2 sides to be equal then like terms must equate, that is
5ax³ = 5x³ ⇒ 5a = 5 ⇒ a = 1
2c = - 6 ⇒ c = - 3
5b + 2a = k
5c + 2b = - 7 ← substitute c = - 3
- 15 + 2b = - 7 ⇒ 2b = 8 ⇒ b = 4
Substitute a = 1, b = 4 into 5b + 2a = k
20 + 2 = k ⇒ k = 22
The required values are
a = 1, b = 4, c = - 3 and k = 22
