Question

Factorise: x²+14x+45

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Answer 1

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Answer 2

Question given:

To factorise:

x²+14x+45

⟾x²+14+45

⟾x²+(9+5)x+(9)(5)

⟾x²+9x+5x+(9)(5)

⟾x(x+9)+5(x+9)

⟾(x+9)(x+5)

Explanation about the answer:-

The above equation is solved by taking identity:-

(x+a)(x+b)=x²+(a+b)x+ab

There is a constant term 45 that can be factorised as 45= 15 × 3 on 9 × 5.

In this, I considered the factors of 45 whose sum is equal to 14(that is the coefficient of middle term).

Therefore,the factor 15+3 is not suitable as 15+3≠14.

Hence,we have to take the other pair of factors, and i.e., 9+4=14

Thus the required factors of 45 are 9 and 5.

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