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.
To be a binomial, the answer can have only two terms.
It will have a t2 term (because 7t·5t = 35t2) and it will have a constant term because, according to the
directions, you can't use zero in the box.
Therefore, the t-term must disappear.
Using an 'x' for the term in the box, we have: (7t - 10)(5t + x) = 35t2 - 50t + 7xt - 50x.
We need to get -50t + 7xt to be zero: -50t + 7xt = 0
(dividing out the t) -50 + 7x = 0
7x = 50
x = 7 1/7