Question

what is the value of M cube minus 15 m square + 75 M - 125​

Answer 1

Step-by-step explanation:

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m³-15m²+75m-125=0

if we take m=0

0-15(0)+75(0)-125=0

-125≠0

if we take m=1

1-15(1)+75(1)-125=0

76-140=0

-64≠0

if we take m=5

125-375+375-125=0

0=0

So,

m=5

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Answer 2

Correct Question :-

• Factorise :- x³ - 15x² + 75x - 125 ? ( In place of M i took x ).

Concept Used :-

• Factor Theorem states that if f(a) = 0 in this case, then the binomial (x - a) is a factor of polynomial f(x).

Solution :-

→ x³ - 15x² + 75x - 125

Re - arranging The Terms ,

→ (x³ - 125) + (-15x² + 75x)

→ (x³ - 5³) - 15x(x - 5)

using (a³ - b³) = (a - b)(a² + b² + ab)

→ [ {(x - 5)(x² + 5² + 5x)} - 15x(x - 5) ]

Taking (x - 5) common now,

→ (x - 5)(x² + 5x - 15x + 25)

→ (x - 5)(x² - 10x + 25)

Splitting The Middle Term of The Quadratic Part,

→ (x - 5)(x² - 5x - 5x + 25)

→ (x - 5)[x(x - 5) -5(x - 5)]

→ (x - 5)[(x - 5)(x - 5)]

→ (x - 5)(x - 5)(x - 5)

→ (x - 5)³. (Ans).