Question

${x}^{2} + 5x + 6$
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Answer 1

{ two number whose sum is 5 and when we multiply the two numbers the product is 6 are 2 and 3 as their sum is 5 and product is 6}

x²+5x+6

so x²+2x+3x+6

=x(x+2)+3(x+2)

=(x+2)(x+3)

Answer 2

Answer:

Given equation

x2 + 5x + 6

Let us try factorizing this polynomial using splitting the middle term method.

Factoring polynomials by splitting the middle term:

We need to find two numbers ‘a’ and ‘b’ such that a + b =5 and ab = 6.

On solving this we obtain, a = 3 and b = 2

Thus, the above expression can be written as:

x2 + 5x + 6

= x2 + 3x + 2x + 6

= x(x + 3) + 2(x + 3)

= (x + 3)(x + 2)

Thus, x+3 and x+2 are the factors of the polynomial x2 + 5x + 6.