Find the value of b, if (x – a) is a factor of x3 – 3x2a – 2a2x + b.

Let p(x) = x3 – 3x2a – 2a2x + b be the given polynomial. According to the Factor theorem, if p(x) is a polynomial of degree n ≥ 1 and a is any real number, then (x - a ) is a factor of p(x) when p(a)=0. Now, p(a) = a3 – 3a3 – 2a3 + b => 0 = b - 4a3=> b = 4a3 Hence, the value of b is 4a3.

Find the value of b, if (x – a) is a factor of x3 – 3x2a – 2a2x + b.

Let p(x) = x3 – 3x2a – 2a2x + b be the given polynomial. According to the Factor theorem, if p(x) is a polynomial of degree n ≥ 1 and a is any real number, then (x - a ) is a factor of p(x) when p(a)=0. Now, p(a) = a3 – 3a3 – 2a3 + b => 0 = b - 4a3=> b = 4a3 Hence, the value of b is 4a3.

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Find the value of b, if (x – a) is a factor of x³ – 3x²a – 2a²x + b.

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Detailed Solution

Let p(x) = x³ – 3x²a – 2a²x + b be the given polynomial.

According to the Factor theorem, if p(x) is a polynomial of degree n $\geq$ 1 and a is any real number, then (x - a ) is a factor of p(x) when p(a)=0.

Now, p(a) = a³ – 3a³ – 2a³ + b

=> 0 = b - 4a³

=> b = 4a³

Hence, the value of b is 4a³.

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