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If (x+2a) is a factor of X5-4a2x3+2x+2a+3 find a?
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If (x+2a) is a factor of X5-4a2x3+2x+2a+3 find a?

Factor Theorem:

To find the value of 'a', we will use the Factor Theorem which states that if (x - k) is a factor of a polynomial, then the polynomial evaluated at k will be equal to zero.

Given Polynomial:

The given polynomial is X^5 - 4a^2x^3 + 2x + 2a + 3.

Given Factor:

We are given that (x + 2a) is a factor of the given polynomial.

Using Factor Theorem:

If (x + 2a) is a factor, then substituting x = -2a into the polynomial should make the polynomial equal to zero.

Substitute x = -2a:

Substitute x = -2a into the polynomial:

(-2a)^5 - 4a^2(-2a)^3 + 2(-2a) + 2a + 3 = 0
-32a^5 + 32a^5 - 4a^2(8a^3) - 4a + 2a + 3 = 0
-4a^5 - 32a^5 - 32a^5 - 4a + 2a + 3 = 0
-4a - 4a + 3 = 0
-8a + 3 = 0
-8a = -3
a = 3/8

Therefore, the value of 'a' is 3/8.
Community Answer
If (x+2a) is a factor of X5-4a2x3+2x+2a+3 find a?
(x/2+2y)(x^2/4-xy+4y^2) find the following product
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