factor x^2 −10x+16

Answer 1

To factor the quadratic expression x^2 - 10x + 16, we need to find two numbers that multiply to 16 (the constant term) and add up to -10 (the coefficient of the x term).

The two numbers that satisfy these conditions are -8 and -2, because -8 * -2 = 16 and -8 + (-2) = -10.

Therefore, we can rewrite the expression as:
x^2 - 8x - 2x + 16

Now we can factor by grouping:
x(x - 8) - 2(x - 8)

Finally, we can factor out the common factor of (x - 8) to get:
(x - 8)(x - 2)

So, the factored form of x^2 - 10x + 16 is (x - 8)(x - 2).