`x ^(2) -10x -7`
Which of the following expression is equivalent to the expression above ?

Options

A. `(x-5) ^(2) -32`
B. `(x-5) ^(2) + 32`
C. ` (x+5) ^(2) -32`
D. `(x+5) ^(2) + 32`

Answer

A

Explanation

There are no integer factors of `x ^(2) -10x -7,` since no two integers whose product is `-7 ` add up to -10. Note that the answer cihocies are stated in vertex format, the same as you would abtain by completing the square of the given expression. Half of the x-coefficient, `-10,` is -5, so the constant term needed to complete the square is `(-5) ^(2)=25.` Thus , you can rewrite and group the given expression as `(x ^(2) -10x +25) -25-7.` This simplifies to `(x-5)^(2)-32,` which is (A). noticing taht `x ^(2)-10+25` is a classic quadratic makes the process of factoring very quixk.