find the LCM AND hcf of (m2-2m-15), (m3-125-15m2+75m) and (m2-125)
Answers
Answer:
LCM of these polynomial will be (m - 5)³(m+3)(m+5)
the HCF of these polynomial will be (m-5)
Step-by-step explanation:
The given terms can be factorized as follows,
m² - 2m - 15 = m² - 5m + 3m - 15 = (m-5)(m+3)
m³ - 125 - 15m² + 75m = (m - 5)³
m² - 25 = (m-5)(m+5)
The only common term between these factors is (m-5)
Hence the HCF of these polynomial will be (m-5)
multiplying the highest power of (m-5) which is (m - 5)³ with other terms , we get
the LCM of these polynomial will be (m - 5)³(m+3)(m+5)
Answer:
the LCM AND hcf of (m2-2m-15), (m3-125-15m2+75m) and (m2-125)
HCF = m-5
LCM = (m+3)(m-5)³(m+5)
Step-by-step explanation:
m²-2m-15
= m² - 5m + 3m - 15
= m(m-5) +3(m-5)
= (m+3)(m-5)
m³-125 - 15m²+75m
a³ - b³ = (a-b)(a² +b² + ab) a = m b = 5
m³-125 = (m-5)(m² + 25 + 5m)
= (m-5)(m²+25 + 5m) -15m(m-5)
= (m-5)(m² -10m + 25)
=(m-5)(m-5)²
m²-125
=(m+5)(m-5)
HCF = m-5
LCM = (m+3)(m-5)(m-5)²(m+5) = (m+3)(m-5)³(m+5)