Ignoring unwritten factors of 1, what is the sum of the numerical factors in the expression below?
−4(x−2)+(x−2)7−(x+5)(x−2)+(x−2)9+(−3)(x−2)
(1 point)
The sum is
.
To simplify the expression, we can distribute and combine like terms:
−4(x−2) = -4x + 8
(x−2)7 = 7x - 14
(x+5)(x−2) = x^2 + 3x - 10
(x−2)9 = 9x - 18
(−3)(x−2) = -3x + 6
Now we add all the terms together:
-4x + 8 + 7x - 14 + x^2 + 3x - 10 + 9x - 18 - 3x + 6
Combining like terms:
(7x-4x+3x+9x-3x) + (8-14-10-18+6) + x^2
This simplifies to:
12x - 28 + x^2
So the sum of the numerical factors in the expression is:
12 - 28 = -16