Vijay has a collection of 50 number cubes that are each 1 cubic inch. He finds a box that is 2 inches high. He fits 10 cubes into the bottom of the box. Can Vijay fit all his number cubes into the box? How many can he fit in?

If f(x)=2x-6 and g(x)=3x+9, find (f-g)(x)

Prove that 16^4-2^13-4^5 is divisible by 11.

Evaluate 8x2 + 9x − 1 2x3 + 3x2 − 2x dx. solution since the degree of the numerator is less than the degree of the denominator, we don't need to divide. we factor the denominator as 2x3 + 3x2 − 2x = x(2x2 + 3x − 2) = x(2x − 1)(x + 2). since the denominator has three distinct linear factors, the partial fraction decomposition of the integrand has the form† 8x2 + 9x − 1 x(2x − 1)(x + 2) = correct: your answer is correct. to determine the values of a, b, and c, we multiply both sides of this equation by the product of the denominators, x(2x − 1)(x + 2), obtaining 8x2 + 9x − 1 = a correct: your answer is correct. (x + 2) + bx(x + 2) + cx(2x − 1).