4)
Let f(x)=2x^2+5x−3
, g(x)=x^2−4x+2
, and h(x)=−x^2+4x−2
. Select all of the expressions that are equivalent to 3x^2+x−1
.
(3 points)
g(x)-h(x)
g(x)+f(x)
f(x)+g(x)
f(x)-h(x)
h(x)-f(x)
f(x)+h(x)
To determine which expressions are equivalent to 3x^2+x-1, we can simplify each expression and see if it matches the given expression.
g(x)-h(x): (x^2-4x+2) - (-x^2+4x-2) = x^2-4x+2+x^2-4x+2 = 2x^2-8x+4 ≠ 3x^2+x-1
g(x)+f(x): (x^2-4x+2) + (2x^2+5x-3) = 3x^2+x-1
f(x)+g(x): (2x^2+5x-3) + (x^2-4x+2) = 3x^2+x-1
f(x)-h(x): (2x^2+5x-3) - (-x^2+4x-2) = 2x^2+5x-3+x^2-4x+2 = 3x^2+x-1
h(x)-f(x): (-x^2+4x-2) - (2x^2+5x-3) = -x^2+4x-2-2x^2-5x+3 = -3x^2-x+1 ≠ 3x^2+x-1
f(x)+h(x): (2x^2+5x-3) + (-x^2+4x-2) = 2x^2+5x-3-x^2+4x-2 = x^2+9x-5 ≠ 3x^2+x-1
Therefore, the expressions g(x)+f(x), f(x)+g(x), and f(x)-h(x) are equivalent to 3x^2+x-1.