Question

if X + 2 is a factor of x cube minus 2 a X square + 16 then value of a​

Answer 1

Answer:

Step-by-step explanation:

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Answer 2

Given,

• $x^3 -2ax^2+16$ is given.
• x+2 is a factor of $x^3 -2ax^2+16$.

To find,

• We have to find the value of a.

Solution,

We can simply find the value of a by substituting the value of x = -2 in the given cubic equation.

Since x +2 is a factor of $x^3 -2ax^2+16$, then $x^3 -2ax^2+16$ must satisfy x = -2.

then,    p(x) = $x^3 -2ax^2+16$

            p(-2) = (-2)³-2a(-2)²+16

                    = -8 -2a(4)+16

                    = -8-8a+16

                    = 8-8a

Since x +2 is a factor of $x^3 -2ax^2+16$, then $x^3 -2ax^2+16$ must satisfy x = -2.

then, 8-8a = 0

             8 =8a

         8/8 = a

              1 = a

Hence, if  X + 2 is a factor of $x^3 -2ax^2+16$ then the value of a is 1.