How do you factor completely $x^2+11x+30$ ?

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Answer 1 · 2016-04-22T16:42:26

$color(green)((x + 6)( x +5)$ is the factorised form of the expression.

$x^2 + 11x + 30$

We can Split the Middle Term of this expression to factorise it.

In this technique, if we have to factorise an expression like $ax^2 + bx + c$ , we need to think of 2 numbers such that:

$N_1*N_2 = a*c = 1* 30 = 30$

AND

$N_1 +N_2 = b = 11$

After trying out a few numbers we get $N_1 = 5$ and $N_2 =6$
$5*6 = 30$ , and $5 + 6 = 11$

$x^2 + 11x + 30 = x^2 + 5x + 6x + 30$

$= x ( x + 5) + 6 (x +5)$

$(x + 5 )$ is a common factor to each of the terms

$=color(green)((x + 6)( x +5)$

How do you factor completely x^2+11x+30x^2+11x+30?