Problem 118 - Introductory Algebra for College Students

Question

Use a graphing utility to graph each side of the equation in the same viewing rectangle. Do the graphs coincide? If so, this means that the polynomial on the left side has been factored correctly. If not, factor the polynomial correctly and then use your graphing utility to verify the factorization. $$-3 x-6=-3(x-2)$$

Step-by-Step Solution

Answer

Yes, the graphs of -3x - 6 and -3*(x - 2) coincide, demonstrating that the polynomial -3x - 6 has been correctly factored as -3*(x - 2).

Step 1: Graph the function -3x - 6

Firstly, we input the equation -3x - 6 into the graphing utility. Depending on the particular graphing utility used, this can generally be done by typing the equation into a y = or f(x) = textbox and hitting enter.

Step 2: Graph the function -3(x - 2)

Secondly, we input the equation -3(x - 2) into the graphing utility. This is done in the same way as graphing -3x - 6.

Step 3: Interpret the Results

The last step involves the analysis of the two graphs. If they are identical, this indicates that -3x - 6 = -3(x - 2), confirming that the polynomial has been correctly factored.