Question

which expression is equivalent to $2x^2 - 2x + 7$?
○ $(4x + 12) + \left(2x^2 - 6x + 5\
ight)$
○ $\left(x^2 - 5x + 13\
ight) + \left(x^2 + 3x - 6\
ight)$
○ $\left(4x^2 - 6x + 11\
ight) + \left(2x^2 - 4x + 4\
ight)$
○ $\left(5x^2 - 8x + 120\
ight) + \left(-3x^2 + 10x - 13\
ight)$

Explanation:

Step1: Simplify Option 1

Combine like terms:
$(4x+12)+(2x^2-6x+5) = 2x^2 + (4x-6x) + (12+5) = 2x^2 -2x +17$

Step2: Simplify Option 2

Combine like terms:
$(x^2-5x+13)+(x^2+3x-6) = (x^2+x^2) + (-5x+3x) + (13-6) = 2x^2 -2x +7$

Step3: Simplify Option 3

Combine like terms:
$(4x^2-6x+11)+(2x^2-4x+4) = (4x^2+2x^2) + (-6x-4x) + (11+4) = 6x^2 -10x +15$

Step4: Simplify Option 4

Combine like terms:
$(5x^2-8x+120)+(-3x^2+10x-13) = (5x^2-3x^2) + (-8x+10x) + (120-13) = 2x^2 +2x +107$

Answer:

B. $(x^2 - 5x + 13)+(x^2 + 3x - 6)$