(x + a)(x + 3)(2x+1) = bx^3 + cx^2 + dx -12, find the values of a, b, c and d.
This question is an example of expanding algeba and equating coefficients. If the brackets on the left-hand side are expanded the unknown values can be found from the coefficients on the right-hand side.Step 1) Expand the brackets(x2 + (3 + a)x + 3a)(2x + 1) = bx 3 + cx2 + dx - 122x3 + (6 + 2a)x2 + 6ax + x2 + (3 + a)x + 3a = bx 3 + cx2 + dx - 12Now expanded, the equation should be simplified.2x3 + (7 + 2a)x2 + (7a + 3)x + 3a = bx 3 + cx2 + dx - 12Now one by one, the variables can be calculated.a = -4, Hence:2x3 - x2 - 25x - 12b = 2, c = -1, d = -25(This is an example question from an OCR GCSE higher paper June 2018)
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