What value of c makes the statement true for the equation 2x^3c*x^3 = x^2 + 10x + 6 + 2x^5?

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To determine the value of c that makes the equation 2x3c × x3 = x2 + 10x + 6 + 2x5 true, we first need to equate both sides of the equation and simplify.

Start by simplifying the left-hand side.

Left-hand side: 2x3c × x3 = 2c × x6

Now the left-hand side can be rewritten as:

2c × x6

Next, simplify the right-hand side:

Right-hand side: x2 + 10x + 6 + 2x5 = 2x5 + x2 + 10x + 6

Now, we can set the two sides of the equation equal to each other:

2c × x6 = 2x5 + x2 + 10x + 6

To find the value of c, we must express both sides in terms of powers of x. For the left-hand side to equal the right-hand side, the coefficient of x6 on the right side must also be zero, since there is no x6 term on the right side.

This means:

2c = 0

From this equation, we find:

c = 0

Thus, the value of c that makes the statement true is 0.

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