Chapter 8.5, Problem 42PPE

To determine

To correct the error: in factoring the trinomial $x^2-10x-24=\left(x-6\right)\left(x-4\right)$

Answer to Problem 42PPE

The correct factors of $x^2-10x-24$ are $x^2-10x-24=\left(x-12\right)\left(x+2\right)$

Explanation of Solution

Given Information:The trinomial is factored as $x^2-10x-24=\left(x-6\right)\left(x-4\right)$ .

Concept used:

Factorize $x^2-10x-24$ by splitting the middle term.

Split the middle term $-10x$ in to two so that product of the coefficients is $-24$ .

The error made in the above factorization is that product of two coefficients is $24$ which should be $-24$

Formula used:

Split as $-10x=-12x+2x$

Calculations:

  $\begin{array}{c}{x}^2-10x-24=x^2-12x+2x-24\\ =x\left(x-12\right)+2\left(x-12\right)\\ =\left(x-12\right)\left(x+2\right)\end{array}$

The correct factors of $x^2-10x-24$ are $x^2-10x-24=\left(x-12\right)\left(x+2\right)$