Factoring polynomials is as much an art as it is a skill and we can get better with practice. It helps to know some important facts about them to make our work easier. For instance, if all the coefficients are real and we are factoring over the real numbers, we'll always be able to factor down to degree 1 or degree 2 polynomials. We can "cheat" by graphing the polynomial and checking when it crosses the x-axis. And we can "cheat" by using a bunch of tools from Pre-Calculus topics: Descartes' Rule of signs, synthetic division, etc. Finally there is the option of using software on a calculator, computer, or the internet. Then going back to another strategy with the foreknowledge of the actual solution (shameful).
Here we employ a couple of handy strategies. Grouping is our most important tool and we exploit it ruthlessly. Next we notice that if we replace 7x^2 with 5x^2 + 2x^2 (on line 2 of the solution) we get two polynomials that can be factored - each with a common factor of x+1. On line six we use the same strategy by writing 5x^2 as 2x^2+3x^2
Here we employ a couple of handy strategies. Grouping is our most important tool and we exploit it ruthlessly. Next we notice that if we replace 7x^2 with 5x^2 + 2x^2 (on line 2 of the solution) we get two polynomials that can be factored - each with a common factor of x+1. On line six we use the same strategy by writing 5x^2 as 2x^2+3x^2
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