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Exercises Equations and inequalities

Example 2 from Algebra and Trigonometry, 2.5 Quadratic Equations

Solve the Quadratic Equation by Factoring

Solve the quadratic equation by factoring: $x^{2} + 8 x + 15 = 0.$

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

Solution
Find two numbers whose product equals $15$ and whose sum equals $8.$ List the factors of $15.$

$\begin{matrix} 1 \cdot 15 \\ 3 \cdot 5 \\ (−1) \cdot (−15) \\ (−3) \cdot (−5) \end{matrix}$
The numbers that add to 8 are 3 and 5. Then, write the factors, set each factor equal to zero, and solve.

$\begin{matrix} (x + 3) (x + 5) & = & 0 \\ (x + 3) & = & 0 \\ x & = & −3 \\ (x + 5) & = & 0 \\ x & = & −5 \end{matrix}$
The solutions are $−3$ and $−5.$

Your turn

The book's Try It right after this example: same idea, new numbers. Only the answer is given.

Solve the quadratic equation by factoring: $x^{2} - 4 x - 21 = 0.$

How did it go?

PreviousFactoring and Solving a Quadratic with Leading Coefficient of 1 Next Using the Zero-Product Property to Solve a Quadratic Equation Written as the Difference of Squares

From Algebra and Trigonometry (1st edition) by OpenStax (Rice University), section 2.5, licensed under CC BY 4.0. Original at openstax.org. We split the solution into steps; the words, numbers and figures are the book's. OpenStax doesn't endorse this site.