  ### Home > INT3 > Chapter 8 > Lesson 8.3.3 > Problem8-132

8-132.

Generally, when you are asked to factor, it is understood that you are only to use integer coefficients in your factors. If you are allowed to use irrational or complex numbers, then any quadratic expression can be written in factored form.

By setting the polynomial equal to zero and solving the quadratic equation, you can work backwards to “force factor” any quadratic polynomial. Use the solutions of the corresponding quadratic equations to write each of the following expressions as a product of two linear factors. Homework Help ✎

1. $\quad x ^ { 2 } - 10$

$x^{2} − 10 = 0$

$x^{2} = 10$

$x= \pm \sqrt{10}$

$(x + \sqrt{10})(x - \sqrt{10})$

1. $x ^ { 2 } - 3 x - 7$

Use the Quadratic Formula, then use those solutions as factors.

$\left(x - \frac{3 + \sqrt{37}}{2}\right)\left(x- \frac{3 - \sqrt{37}}{2}\right)$

1. $x ^ { 2 } + 4$

Follow the steps outlined in part (a).

$(x + 2i)(x - 2i)$

1. $x ^ { 2 } - 2 x + 2$

See part (b).