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Given a quadratic equation with the leading coefficient of 1, factor it.
Factor and solve the equation: x2+x−6=0.
To factor x2+x−6=0, we look for two numbers whose product equals −6 and whose sum equals 1. Begin by looking at the possible factors of −6.
The last pair, 3⋅(−2) sums to 1, so these are the numbers. Note that only one pair of numbers will work. Then, write the factors.
To solve this equation, we use the zero-product property. Set each factor equal to zero and solve.
The two solutions are 2 and −3. We can see how the solutions relate to the graph in [link] . The solutions are the x- intercepts of y=x2+x−6=0.
Factor and solve the quadratic equation: x2−5x−6=0.
(x−6)(x+1)=0;x=6,x=−1
Solve the quadratic equation by factoring: x2+8x+15=0.
Find two numbers whose product equals 15 and whose sum equals 8. List the factors of 15.
The numbers that add to 8 are 3 and 5. Then, write the factors, set each factor equal to zero, and solve.
The solutions are −3 and −5.
Solve the quadratic equation by factoring: x2−4x−21=0.
(x−7)(x+3)=0, x=7, x=−3.
Solve the difference of squares equation using the zero-product property: x2−9=0.
Recognizing that the equation represents the difference of squares, we can write the two factors by taking the square root of each term, using a minus sign as the operator in one factor and a plus sign as the operator in the other. Solve using the zero-factor property.
The solutions are 3 and −3.
When the leading coefficient is not 1, we factor a quadratic equation using the method called grouping, which requires four terms. With the equation in standard form, let’s review the grouping procedures:
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