Question

Which model shows the correct factorization of x2 2x – 8? An algebra tile configuration. 5 tiles are in the Factor 1 spot: 1 is labeled x, 2 are labeled , and 2 are labeled negative. 3 tiles are in the Factor 2 spot: 1 is labeled x and 2 are labeled negative. 15 tiles are in the Product spot: 1 is labeled x squared, 4 are labeled negative x, the 2 tiles below x squared are labeled x, and the 8 tiles below the negative x tiles are labeled negative. An algebra tile configuration. 5 tiles are in the Factor 1 spot: 1 is labeled x, 2 are labeled , and 2 are labeled negative. 3 tiles are in the Factor 2 spot: 1 is labeled x and 2 are labeled negative. 15 tiles are in the Product spot: 1 is labeled x squared, 4 are labeled negative x, the 2 tiles below x squared are labeled x, and the 8 tiles below the negative x tiles are labeled negative. An algebra tile configuration. 5 tiles are in the Factor 1 spot: 1 is labeled x, 4 are labeled negative. 3 tiles are in the Factor 2 spot: 1 is labeled x and 2 are labeled. 15 tiles are in the Product spot: 1 is labeled x squared, 4 are labeled x, the 2 tiles below x squared are labeled negative x, and the 8 tiles below the x tiles are labeled negative. An algebra tile configuration. 5 tiles are in the Factor 1 spot: 1 is labeled x, 4 are labeled. 3 tiles are in the Factor 2 spot: 1 is labeled x and 2 are labeled negative. 15 tiles are in the Product spot: 1 is labeled x squared, 4 are labeled x, the 2 tiles below x squared are labeled negative x, and the 8 tiles below the x tiles are labeled negative.

Answer 1

Using the Factor Theorem, it is found that the correct factorization  $\rm x^2+2x-8=0$ is  (x+4) (x-2).

What is the Factor Theorem?

The Factor Theorem states that a polynomial function with roots  is given by:

$\rm f(x)=a(x-x_1)(x-x_2).........(x-x_n)$

In this problem, the polynomial is:

$\rm x^2+2x-8=0$

Which is a quadratic equation with coefficients a = 1, b =2, c = -8.

$\rm \triangle=b^2-4ac\\\\ \triangle=(2)^2-4\times 1 \times (-8)\\\\ \triangle=4+32\\\\ \triangle=36$

Then,

The correct factorization is;

$\rm x^2+2x-8=0\\\\x^2+4x-2x-8=0\\\\x(x+4)-2(x+4)=0\\\\(x+4)(x-2)=0$

Hence, the correct factorization is (x+4) (x-2).

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