Question

Factor to find the zeros of the function defined by the quadratic expression. 16x2 − 240x + 896 A) x = 7 or x = 8 B) x = 7 or x = −8 C) x = −7 or x = 8 D) x = −7 or x = −8

Answer 1

The correct answer is A).

Explanation:

He have the quadratic functions f(x) = 16x²-240x+896. The first step should be to check if the coefficients 240 and 896 are divisible by 16, which is true. Then, extracting 16 as common factor we have

f(x) = 16(x²-15x+56).

Now we can use directly the formula to find the roots of a quadratic equation, or a more efficient way in terms of calculations. We must find to numbers such that their product is +56 and their addition or subtraction is -15. It is not difficult to check that -7 and -8 fulfill those conditions. Hence,

f(x) = 16(x²-15x+56)= 16(x-7)(x-8).

Therefore, the solutions are x=8 and x=7.

Answer 2

16x2 − 240x + 896 --->divide all by 16
16(x2 - 15x +56)
16{x2- 7x -8x +56x}
16{x(x-7) -8(x-7)}
16(x-8)(x-7)
x1=8/1= 8
x2= 7/1= 7

The answer would be A) x = 7 or x = 8