The binomial x-3 divides exactly the polynomial x^3-2x^2+cx-12 and c is a whole number then c is what?
Already answered
To find the value of c, we can use polynomial long division to divide x^3-2x^2+cx-12 by x-3. The result should be an expression with no remainder.
Let's go step by step through the polynomial long division process:
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x - 3 | x^3 - 2x^2 + cx - 12
- (x^3 - 3x^2)
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x^2 + cx
- (x^2 - 3x)
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4x + cx
- (4x - 12)
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cx + 12
After completing the division, we see that cx + 12 remains without any remainder. For this to be true, the coefficient of x in cx + 12 must be equal to zero. Therefore, we have:
cx + 12 = 0
Solving this equation for c, we find that:
c = -12
Thus, if the binomial x-3 divides exactly the polynomial x^3-2x^2+cx-12, where c is a whole number, then c is equal to -12.