Question

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

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.

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Answer 2

Answer:

Let, f(x) = x² + 5x + 6

x² + 3x + 2x + 6

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

= (x+2)(x+3)

So, roots of this equation are (-2) and (-3) whereas factors are (x+2) and (x+3).