Question

The product of (4z2 + 7z – 8) and (–z + 3) is –4z3 + xz2 + yz – 24. What is the value of x? What is the value of y?

Answer 1

x = 5
y = 29

When you multiply the trinomial and the binomial, you get
-4z^3 + 5z^2 + 29z - 24 . The coefficient of the z^2 term is 5 and the coefficient of the z term is 29.

Answer 2

Hence, the value of x is 5 and y=29

Explanation:

We are asked to find the product of
`4z^2+7z-8` and
`(-z+3)` and equate it to the equation:

`-4z^3 + xz^2 + yz-24` and find the values of x and y in the second equation.

The product of
`4z^2+7z-8` and
`(-z+3)` is:

`(4z^2+7z-8)*(-z+3)= (4z^2+7z-8)*(-z)+3* (4z^2+7z-8)\\=-4z^3-7z^2+8z+12z^2+21z-24=-4z^3+5z^2+29z-24`

Hence on comparing with
`-4z^3 + xz^2 + yz-24` we have:

`-4z^3 + xz^2 + yz-24=-4z^3+5z^2+29z-24`

so we get that x=5, y=29