Josh is trying to factorize the polynomial, $2 x^{2} - 13 x + 21$ by splitting the middle term ( $- 13 x$ ). Which of the following ways should he split the middle term such that the factorization is possible?

2 x^{2} - 3 x - 7 x + 21

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2 x^{2} - 6 x - 7 x + 21

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2 x^{2} - 14 x - 2 x + 21

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2 x^{2} + 7 x - 6 x + 21

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Solution

The correct option is B $2 x^{2} - 6 x - 7 x + 21$
The middle term -13 $x$ has to be divided into two terms such that the product of the coefficients of these terms is $2 \times 21 = 42$
So, -13 $x$ can be divded into -7 $x$ and -6 $x.$

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