SOLUTION: Factor the following expression completely: x^2-16z+60

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Question 1175475: Factor the following expression completely:
x^2-16z+60
Found 3 solutions by ikleyn, MathLover1, greenestamps:
Answer by ikleyn(52798) About Me  (Show Source):
You can put this solution on YOUR website!
.

    = (x-10)*(x-6).    ANSWER

Such trifles everybody should make on his (or her) own.




Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

x^2-16z+60-> I assume you have-16x, not -16z

x%5E2-16x%2B60....write -16x as -10x-6x
x%5E2-10x-6x%2B60....group
%28x%5E2-10x%29-%286x-60%29
x%28x-10%29-6%28x-10%29
%28x-10%29%2A%28x-6%29

Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


Factor x%5E2-16x%2B60

It will factor into the product of two linear polynomials.

The positive constant ("+60") tells us that the signs in both factors are the same; then the negative linear term ("-16x") tells us the signs are both negative.

So the polynomial factors in the form

x%5E2-16x%2B60+=+%28x-a%29%28x-b%29

With the given coefficients -16 and +60, we need two integers a and b with a sum of 16 and a product of 60. Quick mental arithmetic tells us the two numbers are 6 and 10. So

x%5E2-16x%2B60+=+%28x-6%29%28x-10%29