Factorise the following quadratic polynomial by splitting the middle term:
$x^{2}-12x+20$
$x^{2}-12x+20$
(A) To factorise the quadratic polynomial $x^{2}-12x+20$,we need to find two numbers whose product is $20$ and whose sum is $-12$.
These two numbers are $-2$ and $-10$,since $(-2) \times (-10) = 20$ and $(-2) + (-10) = -12$.
Now,split the middle term $-12x$ as $-2x - 10x$:
$x^{2} - 2x - 10x + 20$
Group the terms:
$(x^{2} - 2x) - (10x - 20)$
Factor out the common terms from each group:
$x(x - 2) - 10(x - 2)$
Finally,factor out the common binomial $(x - 2)$:
$(x - 2)(x - 10)$
These two numbers are $-2$ and $-10$,since $(-2) \times (-10) = 20$ and $(-2) + (-10) = -12$.
Now,split the middle term $-12x$ as $-2x - 10x$:
$x^{2} - 2x - 10x + 20$
Group the terms:
$(x^{2} - 2x) - (10x - 20)$
Factor out the common terms from each group:
$x(x - 2) - 10(x - 2)$
Finally,factor out the common binomial $(x - 2)$:
$(x - 2)(x - 10)$
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