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Q: Factor the trinomial 15x2 plus 13x - 20?

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(5x - 4)(3x + 5)

12x+x = 13x

The easiest way to factor x2 + 13x + 42 is to look at the last number. The last number is 42. Now, think of what whole numbers you can multiply to equal 42. 1 x 42 2 x 21 3 x 14 6 x 7 If you look at the equation, we notice that the sign pattern is + + + When the sign pattern is + + +, we know that whatever two factors you choose must add up to the middle number, 13. So, automatically we can get rid of some of these factors. 1 x 42 --> 1 + 42 doesn't equal 13 2 x 21 --> 2 + 21 doesn't equal 13 3 x 14 --> 3 + 14 doesn't equal 13 Now, we're automatically left with 6 x 7. So, your answer would be (factored out), (x+6)(x+7) Where x = -7, -6

Provided that x- 2 is not zero: 2x3 + x2 - 13x + 6 = 2x3 - 4x2 + 5x2 - 10x - 3x + 6 = 2x2*(x - 2) + 5x*(x - 2) - 3*(x - 2) = (x - 2)*(2x2 + 5x - 3) Therefore, (2x3 + x2 - 13x + 6)/(x - 2) = (x - 2)*(2x2 + 5x - 3)/(x - 2) = 2x2 + 5x - 3 If x = 2 so that x - 2 = 0, then the expression is not defined.

7-3x = -4x + 13x = 6

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