Algebra Tutorials!

 Monday 16th of September

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 Number of inequalities to solve: 23456789
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# Solving Quadratic Equations by Factoring

Solve: 3x2 - 9x = 120

Solution

 Step 1 Write the quadratic equation in the form ax2 + bx + c = 0. Subtract 120 from both sides. Step 2 Factor the polynomial. Factor out the GCF, 3. To factor the trinomial, find two integers whose product is -40 and whose sum is -3. They are -8 and 5. 3x2 - 9x = 120 3x2 - 9x - 120 = 0   3(x2 - 3x - 40) = 0 3(x - 8)(x + 5) = 0 Step 3 Use the Zero Product Property. Set each binomial factor equal to 0. Step 4 Solve each equation. There are two solutions. Step 5 Check each answer. We leave the check to you. x - 8 = 0 or x + 5 = 0   x = 8 or x = -5

Note:

When we used the Zero Product Property, you may wonder why we did not set the factor 3 equal to 0. Of course, 3 is not equal to 0.

Furthermore, the product 3(x - 8)(x + 5) is 0 because either (x - 8) is 0 or (x + 5) is 0.

The constant 3 does not make the product 0.

Example 2

Solve: 6 = (x - 4)(x + 1)

Solution

 Step 1 Write the quadratic equation in the form ax2 + bx + c = 0. Multiply the binomials on the right side. Then simplify. Subtract 6 from both sides. Step 2 Factor the polynomial. Find two integers whose product is -10 and whose sum is -3. They are -5 and 2. 6 = (x - 4)(x + 1) 6 = x2 - 3x - 4 0 = x2 - 3x - 10   0 = (x - 5)(x + 2) Step 3 Use the Zero Product Property. Set each factor equal to 0. Step 4 Solve each equation. Step 5 Check each answer. We leave the check to you. x - 5 = 0 or x + 2 = 0   x =5 or x = -2

Note:

We can also write a quadratic equation with 0 on the left side:

That is, 0 = ax2 + bx + c is a quadratic equation.