The idea is to pair up the terms, factor each sub-group, and then pull out the overall GCF to fully factor.
x^3+5x^2-6x-30
(x^3+5x^2)+(-6x-30)
x^2(x+5)+(-6x-30)
x^2(x+5)-6(x+5)
(x^2-6)(x+5)
-------------
Answer: (x^2-6)(x+5)
Let us use the Pythagorean theorem in identifying what triangle can be formed.
Let us assume that the 2 wooden dowels each measure 8 inches. We cut off one wooden dowel into half, so it becomes 2 pcs of 4 inches each.
The 3 wooden dowels now measure, 4 inches, 4 inches, and 8 inches.
The Pythagorean theorem states:
a² + b² = c²
4² + 4² = 8²
16 + 16 = 64
34 ≠ 64
The measure of the cut wooden dowel must be longer than the uncut wooden dowel to create a triangle.
I also tried this on a piece of paper, I cut each piece according to the assumed measure. No triangle can be formed under this activity.
The answer is “No” because the line is not proportional.
