WEBVTT
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Find, by factoring, the zeros of the function đť‘“ of đť‘Ą equals 12đť‘Ą squared minus 14đť‘Ą minus six.
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So in order to find these zeros, we need to set it equal to zero.
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And now we can take out a greatest common factor of two.
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So focusing on the polynomial on the inside, weâ€™re going to use a method that we call slip and slide.
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So Iâ€™m going to slip the six to the back, and we will take six times negative three.
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And now we need to come up with two numbers that multiply to be negative 18 and add to be negative seven.
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So here are a few pairs that multiply to be negative 18.
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So the pair that adds to be negative seven would be negative nine and two.
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Now our next step is to slide the six that we brought to the back underneath the nine and the two.
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And now we simplify; thatâ€™s how we get our slip and slide method.
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However, we donâ€™t wanna leave our factors in the terms of fractions, so the two thatâ€™s left on the bottom we will move it up with the đť‘Ą and the same with the three.
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Now when solving for zeros, you wouldnâ€™t necessarily have to do this step.
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You could leave it as đť‘Ą minus three-halves and đť‘Ą plus one-third and solve.
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It would actually be easier, but most of the time, you do see it in this form of two đť‘Ą minus three and three đť‘Ą plus one.
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And also donâ€™t forget to bring down your two.
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So now we set every factor equal to zero.
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Now as we said weâ€™re solving; it will be easier to use whatâ€™s underlined.
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Now setting two equal to zero, our greatest common factor doesnâ€™t do anything; thatâ€™s not even true, so you can just mark it out.
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Now we would add three-halves to the right and we would subtract one-third to the right.
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So three-halves and negative one-third would be the zeros of this function.