Donovan eats 2 granola bars and drinks 1 glass of orange juice for breakfast every day. The price of a granola bar is B dollars and the price of a glass of orange juice is J dollars.
The expression 7(2B + I) describes how much Donovan spends on breakfast in one week.
Match each amount in the situation with the expression that represents it.
Situation
Expression
Amount Donovan spends on breakfast each day
2B
Amount Donovan spends on granola bars each day
2B + J
Amount Donovan spends on juice each day
J
Number of days Donovan buys breakfast.
7

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).