the answer is 6 because of the order of operations. you must do the multiplication first
2x2+2=6
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3x4 plus 5x3 plus x2 - 5 divided by x 2 =[(3x4) + (5x3) + (x2 - 5)]/x2 =(12 + 15 + x2 -5)/x2 =(27 - 5 + x2)/x2 =(22 + x2)/x2
x2 + 3x + 2 factors into (x + 1) (x + 2)
-x2 + 6x + 16 = -(x2 - 6x - 16) = -(x - 8)(x + 2) = -(8 - x)(x + 2)
x2 + 4x + 6 can not be factored. If you want, you can reduce it to an expression with a single x term by comleting the square: x2 + 4x + 6 = x2 + 4x + 4 + 2 = (x + 2)2 + 2
x2 + 3x + 7 = 5 ∴ x2 + 3x + 2 = 0 ∴ (x + 1)(x + 2) = 0 ∴ x ∈ {-2, -1}