Find constants A, B for which -1 + t t 2 - 2t

Question

Notify Me Bookmark

Find constants A, B for which -1 + t t 2 - 2t - 3 = A f + B g , where f, g are linear polynomials with leading coefficient 1 such that fg = t 2 - 2t - 3. Enter your answer in the form A * x + B * y or B * x + A * y and put brackets around fractions. For example, if A = 0 and B = 1/5, then enter 0 * x + (1/5) * y or (1/5) * x + 0 * y.

$Find constants A, B for which -1 + t t 2 - 2t - 3 = A f + B g , where f, g are linear polynomials with leading coefficient 1 such that fg = t 2 - 2t - 3. Enter your answer in the form A * x + B * y or B * x + A * y and put brackets around fractions. For example, if A = 0 and B = 1/5, then enter 0 * x + (1/5) * y or (1/5) * x + 0 * y.$

Please show your work, and how you got to the answer. Thanks