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If the polynomial 3x3−4x2−17x−k is exactly divisible by x−3, then the value of ‘k’ is
- a)5
- b)– 6
- c)6
- d)0
Correct answer is option 'B'. Can you explain this answer?
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If the polynomial3x3−4x2−17x−k is exactly divisible ...
If the polynomial 3x3−4x2−17x−k is exactly divisible by x−3, then
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If the polynomial3x3−4x2−17x−k is exactly divisible ...
Given polynomial: 3x^3 + 4x^2 + 17xk
To check if the polynomial is exactly divisible by x^3, we need to divide the polynomial by x^3 and check if the remainder is 0.
Let's perform the division:
Dividend: 3x^3 + 4x^2 + 17xk
Divisor: x^3
We start by dividing the highest power term of the dividend by the highest power term of the divisor:
3x^3 / x^3 = 3
Now, we multiply the entire divisor (x^3) by the quotient (3) and subtract it from the dividend:
3(x^3) = 3x^3
3x^3 - 3x^3 = 0
Next, we bring down the next term from the dividend, which is 4x^2:
0 + 4x^2 = 4x^2
We repeat the process of dividing the highest power term of the remaining polynomial (4x^2) by the highest power term of the divisor (x^3):
4x^2 / x^3 = 0
Since the highest power term of the dividend is smaller than the highest power term of the divisor, we can conclude that the polynomial is not divisible by x^3.
Therefore, the value of k is irrelevant in determining whether the polynomial is exactly divisible by x^3. The correct answer is option 'B' which is 6.
To check if the polynomial is exactly divisible by x^3, we need to divide the polynomial by x^3 and check if the remainder is 0.
Let's perform the division:
Dividend: 3x^3 + 4x^2 + 17xk
Divisor: x^3
We start by dividing the highest power term of the dividend by the highest power term of the divisor:
3x^3 / x^3 = 3
Now, we multiply the entire divisor (x^3) by the quotient (3) and subtract it from the dividend:
3(x^3) = 3x^3
3x^3 - 3x^3 = 0
Next, we bring down the next term from the dividend, which is 4x^2:
0 + 4x^2 = 4x^2
We repeat the process of dividing the highest power term of the remaining polynomial (4x^2) by the highest power term of the divisor (x^3):
4x^2 / x^3 = 0
Since the highest power term of the dividend is smaller than the highest power term of the divisor, we can conclude that the polynomial is not divisible by x^3.
Therefore, the value of k is irrelevant in determining whether the polynomial is exactly divisible by x^3. The correct answer is option 'B' which is 6.
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If the polynomial3x3−4x2−17x−k is exactly divisible byx−3, then the value of ‘k’ isa)5b)– 6c)6d)0Correct answer is option 'B'. Can you explain this answer?
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