The factored form of the given expressions are required.
The factored forms are
[tex](x+2)(x+5)[/tex]
[tex](x-2)(x-1)[/tex]
[tex]-(x+5)(x-8)[/tex]
[tex]9(y-2)(y+2)[/tex]
[tex]-(x-1)(x-4)[/tex]
To solve a quadratic equation of the form [tex]ax^2+bx+c[/tex]
The formula is
[tex]x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
[tex]x^2+7x+10[/tex]
[tex]x=\dfrac{-7\pm \sqrt{7^2-4\times1\times10}}{2\times1}\\\Rightarrow x=-2,-5[/tex]
The factored form is [tex](x+2)(x+5)[/tex].
[tex]x^2-3x+2[/tex]
[tex]x=\dfrac{-7\pm \sqrt{7^2-4\times1\times10}}{2\times1}\\\Rightarrow x=2,1[/tex]
The factored form is [tex](x-2)(x-1)[/tex]
[tex]-x^2+3x+40=-(x^2-3x-40)[/tex]
[tex]x=\dfrac{-\left(-3\right)\pm \sqrt{\left(-3\right)^2-4\times1\cdot \left(-40\right)}}{2\times1}\\\Rightarrow x=-5,8[/tex]
The factored form is [tex]-(x+5)(x-8)[/tex]
[tex]9y^2-36[/tex]
[tex]9y^2-36=0\\\Rightarrow 9y^2=36\\\Rightarrow y^2=\dfrac{36}{9}\\\Rightarrow y=\pm 2[/tex]
The factored form is [tex]9(y-2)(y+2)[/tex]
[tex]-x^2+5x-4=-(x^2-5x+4)[/tex]
[tex]x=\dfrac{-\left(-5\right)\pm \sqrt{\left(-5\right)^2-4\times1\times4}}{2\times1}\\\Rightarrow x=1,4[/tex]
The factored form is [tex]-(x-1)(x-4)[/tex]
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