Problem to solve
Factor the expression \[4x^3+20x^2+13x-12\]
Solution
STEP 1
Factor the following: 4 x^3 + 20 x^2 + 13 x - 12
STEP 2
Hint: | Find all linear factors of 4 x^3 + 20 x^2 + 13 x - 12 via the rational root theorem. Do this by finding rational roots. The candidates are x = ± p/q for all p that are divisors of the constant term -12 and for all q that are divisors of the leading coefficient 4. The possible rational roots of 4 x^3 + 20 x^2 + 13 x - 12 are x = ± 1/4, x = ± 3/4, x = ± 1/2, x = ± 3/2, x = ± 1, x = ± 2, x = ± 3, x = ± 4, x = ± 6, x = ± 12. Of these, x = 1/2, x = -3/2 and x = -4 are roots. This gives 2 x - 1, 2 x + 3 and x + 4 as all factors: Answer: | | (2 x - 1) (2 x + 3) (x + 4)
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Edited by tododemate® - 2021