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Sagot :
The general form of a quadratic polynomial is given by:
[tex]ax^2+bx+c[/tex]You have the following quadratic expression:
[tex]5x^2-17x-40[/tex]In order to factorize the previous expression, you first use the quadratic formula, which is given by;
[tex]x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]where a = 5, b = -17, c = -40. You replace these values into the quadratic formula:
[tex]\begin{gathered} x=\frac{-(-17)\pm\sqrt[]{(-17)^2-4(5)(-40)}}{2(5)} \\ x=\frac{17\pm\sqrt[]{1089}}{10}=\frac{17\pm33}{10} \\ x_1=5 \\ x_2=\text{ -}\frac{16}{10}=-\frac{8}{5} \end{gathered}[/tex]The factors of the quadratic polynomial, based on the previous calculated zeros of the piolynomial are as follow:
[tex](x-x_1)(x-x_2)=(x-5)(x+\frac{8}{5})[/tex]
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