factor the following polynomials 15m⁵ + 12m + 6m³12q⁴ - 72q³ - 120q²36y³ + 18y¹⁰
Answer (1)
Identify the greatest common factor (GCF) of all terms: the coefficients 15, 12, and 6 have GCF 3; the powers of (m) ((m^5), (m^1), (m^3)) have GCF (m^1). Factor out (3m):(15m^5 + 6m^3 + 12m = 3m(5m^4 + 2m^2 + 4)).The quartic (5m^4 + 2m^2 + 4) does not factor further over the reals (substitute (x = m^2) to get (5x^2 + 2x + 4); discriminant (4 - 80 = -76 < 0)).2.
