Let f (x) = 2x2+5x-3, g(x) = x² - 4x + 2, and h(x)=x2+4x-2. Select all of the expressions that are equivalent to 3x2+x-1.

Question

(3 points)

h(z)-f(z)

f(x)+g(z)

f(z)+h(z)

g(z)+f(z)

f(z)-h(z)

g(z)h(z)

Answer 1

To determine which expressions are equivalent to 3x^2 + x - 1, substitute x = z into each expression and simplify:

h(z) - f(z)
= (z^2 + 4z - 2) - (2z^2 + 5z - 3)
= -z^2 - z + 1

f(x) + g(z)
= (2x^2 + 5x - 3) + (z^2 - 4z + 2)
= 2x^2 + 5x + z^2 - 4z - 1

f(z) + h(z)
= (2z^2 + 5z - 3) + (z^2 + 4z - 2)
= 3z^2 + 9z - 5

g(z) + f(z)
= (z^2 - 4z + 2) + (2z^2 + 5z - 3)
= 3z^2 + z - 1

f(z) - h(z)
= (2z^2 + 5z - 3) - (z^2 + 4z - 2)
= z^2 + z -1

g(z) * h(z)
= (z^2 - 4z + 2)(z^2 + 4z - 2)
= z^4 - 2z^2 + 4

The expressions that are equivalent to 3x^2 + x - 1 are:

f(z) + h(z)
g(z) + f(z)