What are the product factors of x square -12x+32

So with this polynomial, I will be completing the square. Firstly, what two terms have a product of 32x^2 and a sum of -12x? That would be -8x and -4x. Replace -12x with -4x - 8x:

Next, factor x^2 - 4x and -8x + 32 separately. Make sure that they have the same quantity in the parentheses:

Now you can rewrite your expression as , and your factors are (x - 8) and (x - 4).

You can use the C. HL Theorem to prove the triangles congruent.

To use the HL THeorem to prove the triangles congruent, you have to check for three conditions. 
1) The triangles are both right triangles.
2) Their hypotenuses are congruent
3) They have one pair of congruent legs.

The squares at the angle of the triangle indicate the triangles are right triangles. Since the triangles in the picture share one side, the hypotenuse, the hypotenuses of the triangles are congruent. The triangles also have one pair of congruent legs. Since all three conditions of the HL Theorem are met, the triangles are congruent.