Know Your Keywords — Math, Advanced
Point 2 — Predicting factors for quadratic polynomial
What do we see?
One factor of a quadratic polynomial is given.
What do we understand?
Use the coefficients of the polynomial to predict the other factor.
Tips & traps
Ask yourself: why is this not the same as Question 6 from Point 1? Because the greatest value is asked for — the discriminant gives a bound, not the extreme integer case.
Ask yourself: why can’t we simply plug in a positive integer for b?
Question 1 of 2
38z14 + bz7 + 70
In the given expression, b is a positive integer. If qz7 + r is a factor of the expression, where q and r are positive integers, what is the greatest possible value of b?