Question

If x-a is a factor of x^3 - 3x²a + 2a^2 x + b, then
the value of b is​

Answer 1

$\large{\underline{\boxed{\tt Answer}}}$

The value of b is = 0

$\large{\underline{\boxed{\tt Explanation}}}$

$\large{\underline{\boxed{\tt Given Problem}}}$

If x-a is a factor of x^3 - 3x²a + 2a^2 x + b, then  the value of b is​?

$\large{\underline{\boxed{\tt Solution}}}$

$\large{\underline{\boxed{\tt To Find}}}$

⇒Value of b

--------------

⇒x-a=0

⇒x=a

⇒x³-3x²a+2a²x+b

⇒a³-3a³+2a³+b=0

⇒0+b=0

⇒b=0

Therefore,

$\huge\boxed{b = 0}$

Answer 2

To find the value of b

Let the given polynomial be f(x)

Given polynomial,

f(x)=x³ -3x²a +2a²x +b

According to factor theorm,

If y-@ is a factor of a polynomial then the value of y would be a zero of the polynomial.

So, a would be a zero of the given polynomial.

We know,

f(x)=f(a)=0

Now,

x³ -3x²a +2xa² +b=0

→a³ -3(a²)a+2a(a²)+b=0

→3a³-3a³+b=0

→b=0

The value of b will be zero