To factor into one number another number note that is the sum of the two

To factor into one number another number note that is

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To factor: into ( + one number)(+ another number), note that is the sum of the two numbers and is the product of the two numbers So We’ll be looking for the 2 numbers whose product is and whose sum is Note: there are fewer choices for the product, so that’s why we start there first Factoring Trinomials
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Example Factor the polynomial Since our two numbers must have a product of 30 and sum of 13, the two numbers must both be positive Note: there are other factors, but once we find a pair that works, we do not have to continue searching. Factoring quadratic polynomials Positive factors of 30 Sum of factors 1 And 30 31 2 And 15 17 3 And 10 13
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Example Factor the polynomial Factoring quadratic polynomials
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Example Factor the polynomial Since our two numbers must have a product of -35 and Factoring quadratic polynomials
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Example Factor the polynomial Since our two numbers must have a product of 10 and Prime polynomials
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You should always check your factoring results by multiplying the factored polynomial to verify that is equal to the original polynomial Many times you can detect computational errors in the signs of your numbers by checking your results Check your result!
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Example Solve First write the quadratic equation in standard form Now we factor the quadratic We set each factor equal to 0 which will simplify to Solving quadratic equations
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Example continued Check both possible answers in the original equation true true So our solutions for are 8 or -3 Solving quadratic equations
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Solving quadratic equations by the quadratic formula
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