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If x + 2 is a factor of x3 – 2ax2 + 16, then value of a is
- a)3
- b)1
- c)4
- d)2
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
If x + 2 is a factor of x3– 2ax2+ 16, then value of a isa)3b)1c)...
To determine whether x + 2 is a factor of x^3, we can use polynomial long division or synthetic division.
Using polynomial long division:
x^2 - 2x + 4
x + 2 | x^3 + 0x^2 + 0x + 8
- (x^3 + 2x^2)
-------------
- 2x^2 + 0x
- (-2x^2) - 4x
--------
4x + 8
So, we have a remainder of 4x + 8. Since the remainder is not zero, x + 2 is not a factor of x^3.
Using synthetic division:
We set up the synthetic division as follows:
-2 | 1 0 0 8
-2 4 -8
---------
1 -2 4 0
The last entry in the bottom row is 0, which means that x + 2 is not a factor of x^3.
Therefore, we can conclude that x + 2 is not a factor of x^3.
Using polynomial long division:
x^2 - 2x + 4
x + 2 | x^3 + 0x^2 + 0x + 8
- (x^3 + 2x^2)
-------------
- 2x^2 + 0x
- (-2x^2) - 4x
--------
4x + 8
So, we have a remainder of 4x + 8. Since the remainder is not zero, x + 2 is not a factor of x^3.
Using synthetic division:
We set up the synthetic division as follows:
-2 | 1 0 0 8
-2 4 -8
---------
1 -2 4 0
The last entry in the bottom row is 0, which means that x + 2 is not a factor of x^3.
Therefore, we can conclude that x + 2 is not a factor of x^3.
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Community Answer
If x + 2 is a factor of x3– 2ax2+ 16, then value of a isa)3b)1c)...
It is given that x+2x+2 is the factore of x^3-2ax^2+16. so, x+2=0. = x= -2. then, x^3-2ax^2+16. = 0 '. = (-2)^3-2a(-2)^2+16 =0. '. = -8 -8a+16 =0. '. = -8a+16 =0. '. = -8a = -16+8. '. = -8a = -8. '. = a =-8/-8. '. = a= 1
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If x + 2 is a factor of x3– 2ax2+ 16, then value of a isa)3b)1c)4d)2Correct answer is option 'B'. Can you explain this answer?
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