lavacow said:
I'm having difficulty factoring m[sup:yd1nzqpb]4[/sup:yd1nzqpb] + 3m[sup:yd1nzqpb]2[/sup:yd1nzqpb] + 4. I know that the final answer is (m[sup:yd1nzqpb]2[/sup:yd1nzqpb] - m +2)(m[sup:yd1nzqpb]2[/sup:yd1nzqpb] + m + 2) but I am completely lost as to how to get there, as it cannot be done with the 'guess and check' method for factoring polynomials that I have been taught. Please help!
Thank you
I agree! This is a bit tricky!
Notice that the first three terms ALMOST constitute a perfect square trinomial. IF that was 4m[sup:yd1nzqpb]2[/sup:yd1nzqpb] for the second term, we'd have (m[sup:yd1nzqpb]2[/sup:yd1nzqpb] + 2][sup:yd1nzqpb]2[/sup:yd1nzqpb]. So, let's try this: ADD m[sup:yd1nzqpb]2[/sup:yd1nzqpb] and SUBTRACT m[sup:yd1nzqpb]2[/sup:yd1nzqpb]....we can do this because m[sup:yd1nzqpb]2[/sup:yd1nzqpb] - m[sup:yd1nzqpb]2[/sup:yd1nzqpb] = 0.
m[sup:yd1nzqpb]4[/sup:yd1nzqpb] + 3m[sup:yd1nzqpb]2[/sup:yd1nzqpb] + m[sup:yd1nzqpb]2[/sup:yd1nzqpb] + 4 - m[sup:yd1nzqpb]2[/sup:yd1nzqpb]
or
m[sup:yd1nzqpb]4[/sup:yd1nzqpb] + 4m[sup:yd1nzqpb]2[/sup:yd1nzqpb] + 4 - m[sup:yd1nzqpb]2[/sup:yd1nzqpb]
Now, group the first three terms together, and factor as the square of a binomial:
(m[sup:yd1nzqpb]4[/sup:yd1nzqpb] + 4m[sup:yd1nzqpb]2[/sup:yd1nzqpb] + 4) - m[sup:yd1nzqpb]2[/sup:yd1nzqpb]
(m[sup:yd1nzqpb]2[/sup:yd1nzqpb] + 2][sup:yd1nzqpb]2[/sup:yd1nzqpb] - m[sup:yd1nzqpb]2[/sup:yd1nzqpb]
Now, you have a difference of two squares, and can factor using this pattern:
a[sup:yd1nzqpb]2[/sup:yd1nzqpb] - b[sup:yd1nzqpb]2[/sup:yd1nzqpb] = (a + b)(a - b)
Apply this pattern...noting that in YOUR problem, (m[sup:yd1nzqpb]2[/sup:yd1nzqpb] + 2) takes the place of "a", and m takes the place of "b"
