[tex]\boxed{(11x-5)(x+2)}[/tex]
Explanation:
Let's help Diego to write the following expression in factored form:
[tex]11x^2+17x -10[/tex]
In order to do so, let's use the Quadratic Formula:
[tex]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[/tex]
Finally, the factored form is performed as:
[tex]11(x-\frac{5}{11})(x+2) \\ \\ \\ So: \\ \\ \boxed{(11x-5)(x+2)}[/tex]
Learn more:
Absolute value of complex numbers: https://brainly.com/question/12541796
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