What is the top row going to look like if one is using synthetic division to divide 8x5 − 2x4 + 7x2 − 5 by some value?
Question
What is the top row going to look like if one is using synthetic division to divide 8x^5 − 2x^4 + 7x^2 − 5 by some value?
Solution
The top row in synthetic division represents the coefficients of the polynomial you are dividing. In this case, the polynomial is 8x^5 - 2x^4 + 7x^2 - 5.
However, it's important to note that synthetic division requires all powers of the variable to be present. If a power is missing, you must include it with a coefficient of 0.
In this case, the x^3 and x terms are missing. So, we rewrite the polynomial as 8x^5 - 2x^4 + 0x^3 + 7x^2 + 0x - 5.
So, the top row for synthetic division of this polynomial will be: 8, -2, 0, 7, 0, -5.
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