Question

100 points.solve the question in the attatchment.

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Answer 1

since the identity is

        {x+a}{x+b}= x²+{a+b}x+ab.................{1}

now,  we have to find {x+1}{x+2}

here , a=1,b=2, x=x

putting in identity,

⇒x²+ {1+2}x+1×2

⇒x²+3x+2

here on solving we get a quadratic equation,

verification:-

we verify it by breaking the quadratic equation

now solving that with the help of splitting middle term method,

x²+3x+2

x²+2x+x+2

x{x+2}+1{x+2}

{x+1}{x+2}.............{verified}