Question

To write 11x^2+17x -10 in factored form, Diego fist listed pairs of factors of -10

Answer 1

$\boxed{(11x-5)(x+2)}$

Explanation:

Let's help Diego to write the following expression in factored form:

$11x^2+17x -10$

In order to do so, let's use the Quadratic Formula:

$x=\frac{-b \pm \sqrt{b^2-4ac}}{2a} \\ \\ \\ Here: \\ \\ a=11 \\ b=17 \\\ c=-10 \\ \\ \\ x=\frac{-17 \pm \sqrt{17^2-4(11)(-10)}}{2(11)} \\ \\ x=\frac{-17 \pm \sqrt{289+440}}{22} \\ \\ x=\frac{-17 \pm \sqrt{289+440}}{22} \\ \\ x=\frac{-17 \pm \sqrt{729}}{22} \\ \\ x=\frac{-17 \pm \sqrt{729}}{22} \\ \\ x=\frac{-17 \pm 27}{22} \\ \\ \\ So: \\ \\ x_{1}=\frac{5}{11} \\ \\ x_{2}=-2$

Finally, the factored form is performed as:

$11(x-\frac{5}{11})(x+2) \\ \\ \\ So: \\ \\ \boxed{(11x-5)(x+2)}$

Learn more:

Absolute value of complex numbers: brainly.com/question/12541796

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