Consider the equation 3y - 6x = 9. Write another equation that forms a system of equations
with the equation above that has either one solution or
infinitely many solutions.
Without graphing, explain how you know that your system
has one solution or infinitely many solutions.
Justify your equation by graphing the system of equations.
Explain how your graph supports your choice of equation.
Show your work. Use words,
models, and numbers to explain
your answer.
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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).