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Question

Factorise by splitting middle term
$$3x^{2} + 7x + 2$$


Solution

Let $$p(x) = 3x^{2} + 7x + 2$$
Here we have to split middle term of p(x)
i.e. $$7$$ into two parts such that their sum is $$7$$ and product is $$2 \times 3 = 6.$$
$$6$$ and $$1$$ are such numbers whose sum is $$7$$ and product is $$6$$
$$\therefore 3x^{2} + 7x + 2 = 3x^{2} + 6x + x + 2$$
$$= 3x(x + 2) + 1(x + 2)$$
$$= (x + 2)(3x + 1)$$

Mathematics

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