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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

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