Question

Factoriese
${x}^{2} - 11x + 30$
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Answer 1

Given equation,

x²-11x+30=0

By splitting the middle term,

→x²-6x-5x+30=0

→x(x-6)-5(x-6)=0

→(x-6)(x-5)=0

→x-6=0 or x-5=0

→x=6,5

The roots are 6 and 5

Answer 2

Solution

Let us first find two numbers whose product is 30 and sum (-11).

Since the product is positive, therefore, either both the numbers will be positive or negative.

But the sum is negative, hence, both the numbers will also be negative.

Required factors of 30 are (-6) and (-5).

${x}^{2} - 11x + 30$

$= {x}^{2} + \: ( - 6) + ( - 5)x + 30$

$= {x}^{2} - 6x - 5x + 30$

$= x(x - 6) - 5(x - 6)$

$= (x - 6)(x - 5)$

Therefore the answer is (x-6) (x-5).