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# Algebra

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What non-zero rational number must be placed in the square so that the simplified product of these two binomials is a binomial: $(7t - 10)(3t + \square)$? Express your answer as a mixed number.

Jan 29, 2022

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Let's call the unknown number $$x$$. By subsituting, we have $$(7t-10)(3t+x)$$. If we simplify this equation, we get $$21t^2+7tx-30t-10x$$

A binomial must have exactly $$2$$ terms, so $$7tx-30t$$ will have to equal $$0$$

The only way this can be possible is if $$\color{brown} \boxed {x=4 {2\over 7}}$$

Jan 30, 2022