The sum of two binomials is $5 x^{2} - 6 x$ . If one of the binomial is $3 x^{2} - 2 x$ , what is the other binomial?

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Solution

Let 's' be the term to be added to $3 x^{2} - 2 x$ to get $5 x^{2} - 6 x$ .
$\Rightarrow (3 x^{2} - 2 x) + s = 5 x^{2} - 6 x$
$\Rightarrow s = (5 x^{2} - 6 x) - (3 x^{2} - 2 x)$
$\Rightarrow s = (5 x^{2} - 3 x^{2}) + (- 6 x + 2 x)$
$\Rightarrow s = 2 x^{2} - 4 x$
So, the second binomial term is $= 2 x^{2} - 4 x$

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