Polynomials

Algebra Level 2

If x − a x-a is a factor of x 3 − 3 x 2 a + 2 a 2 x + b x^3-3x^2a+2a^2x+b , then find the value of b b .

2 1 3 0

Sravanth C. by Sravanth C. , 21, India

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3 solutions

Sravanth C.
Aug 27, 2015

As ( x − a ) (x-a) is the factor, x = a x=a . So, p ( a ) = a 3 − 3 a 3 + 2 a 3 + b = 0 3 a 3 − 3 a 3 + b = 0 b = 0 p(a)=a^3-3a^3+2a^3+b=0\\ 3a^3-3a^3+b=0\\ \boxed{b=0}

16 Helpful 1 Interesting 1 Brilliant 3 Confused

Good solution.

Sai Ram - 5 years, 9 months ago
Josh Banister
Oct 30, 2016

We can factorise this expression as ( x − a ) 3 + a 2 ( x − a ) + b (x-a)^3 + a^2(x-a) + b . This implies x − a x-a is a factor of b b which is only possible when b = 0 b = 0 (since b b is independent of x and a)

0 Helpful 1 Interesting 1 Brilliant 3 Confused

Won't the second term be negative in the expression above?

Krish Shah - 1 year, 2 months ago
Uahbid Dey
Aug 27, 2015

f(a) = a³ - 3.a².a + 2.a².a + b = 0 ... ... ... ... => b = 0

0 Helpful 0 Interesting 0 Brilliant 2 Confused

Why don't you use latex ?

Sai Ram - 5 years, 9 months ago

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Thanks for your suggestion. I also use latex, but only when it is difficult to express the solutions clearly by using symbols.

Uahbid Dey - 5 years, 9 months ago

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