Answer:
Hence, the value of x is 5 and y=29
Step-by-step explanation:
We are asked to find the product of [tex]4z^2+7z-8[/tex] and [tex](-z+3)[/tex] and equate it to the equation:
[tex]-4z^3 + xz^2 + yz-24[/tex] and find the values of x and y in the second equation.
The product of [tex]4z^2+7z-8[/tex] and [tex](-z+3)[/tex] is:
[tex](4z^2+7z-8)\times(-z+3)= (4z^2+7z-8)\times(-z)+3\times (4z^2+7z-8)\\=-4z^3-7z^2+8z+12z^2+21z-24=-4z^3+5z^2+29z-24[/tex]
Hence on comparing with [tex]-4z^3 + xz^2 + yz-24[/tex] we have:
[tex]-4z^3 + xz^2 + yz-24=-4z^3+5z^2+29z-24[/tex]
so we get that x=5, y=29
