## 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)(5t+B

Question

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)(5t+Box )? Express your answer as a mixed number.

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2 days 2021-09-09T09:28:21+00:00 2 Answers 0

7 1/7.

Step-by-step explanation:

The middle 2 numbers in the expansion will be cancelled out  if one of them is + 50 t so the required  rational number is  50/7:

(7t – 10)(5t + 50/7) = 35t^2 – 50t + 350/7 t – 500/7)

=  35t^2 – 50t + 50t – 500/7)

= 35t^2 – 500/7)

So  50 / 7 = 7 1/7 (answer).

2. The product would expand to

This is a trinomial, and the only way to make it a binomial is to cancel out a coefficient using our variable .

So, we can cancel either the linear term or the constant term.

In the first case, we require

In the second case, we require

But must be a non-zero rational number, so this solution is not feasible.