Question

Which expression is equivalent​ to x2-9x+20

Answer 1

$\text{The expression equivalent to } x^2-9x+20 \text{ is } (x-4)(x-5)$

Solution:

Given that we have to find the equivalent expression

Given expression is:

$x^2-9x+20$

We can find the equivalent expression by find the factors

$\mathrm{Break\:the\:expression\:into\:groups}$

$x^2-9x+20=\left(x^2-4x\right)+\left(-5x+20\right)$

$\mathrm{Factor\:out\:}x\mathrm{\:from\:}x^2-4x\mathrm{:\quad }x\left(x-4\right)$

Thus, the expression becomes,

$x^2-9x+20=x\left(x-4\right)+\left(-5x+20\right)$

$\mathrm{Factor\:out\:}-5\mathrm{\:from\:}-5x+20\mathrm{:\quad }-5\left(x-4\right)$

Thus, the expression becomes,

$x^2-9x+20=x\left(x-4\right)-5(x-4)$

$\mathrm{Factor\:out\:common\:term\:}x-4$

$x^2-9x+20=(x-4)(x-5)$

Thus the equivalent expression is found