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A polynomial g(x) of degree zero is added to the polynomial 2 x 3 5 x 2 - 14 x 10 so that it become exactly divisible by 2 x -3 find the gfx?
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A polynomial g(x) of degree zero is added to the polynomial 2 x 3 5 ...
Finding the polynomial g(x) that makes the given polynomial divisible by 2x-3
To make the polynomial 2x^3 - 5x^2 - 14x + 10 exactly divisible by 2x - 3, we need to find the polynomial g(x) of degree zero that when added to the given polynomial results in a polynomial that is divisible by 2x - 3.
Using the factor theorem
We can use the factor theorem to find the value of g(x). According to the factor theorem, if a polynomial f(x) is divisible by (x - a), then f(a) = 0.
Applying the factor theorem
In this case, we know that the polynomial should be divisible by 2x - 3. So, we substitute x = 3/2 into the polynomial 2x^3 - 5x^2 - 14x + 10 and solve for g(x).
Calculating g(x)
Substitute x = 3/2 into the polynomial:
f(3/2) = 2(3/2)^3 - 5(3/2)^2 - 14(3/2) + 10
f(3/2) = 27/4 - 45/4 - 21 + 10
f(3/2) = -19/4
Therefore, g(x) = -19/4.
Conclusion
The polynomial g(x) that should be added to 2x^3 - 5x^2 - 14x + 10 to make it exactly divisible by 2x - 3 is -19/4.
Community Answer
A polynomial g(x) of degree zero is added to the polynomial 2 x 3 5 ...
GX=4
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A polynomial g(x) of degree zero is added to the polynomial 2 x 3 5 x 2 - 14 x 10 so that it become exactly divisible by 2 x -3 find the gfx?
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A polynomial g(x) of degree zero is added to the polynomial 2 x 3 5 x 2 - 14 x 10 so that it become exactly divisible by 2 x -3 find the gfx? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about A polynomial g(x) of degree zero is added to the polynomial 2 x 3 5 x 2 - 14 x 10 so that it become exactly divisible by 2 x -3 find the gfx? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A polynomial g(x) of degree zero is added to the polynomial 2 x 3 5 x 2 - 14 x 10 so that it become exactly divisible by 2 x -3 find the gfx?.
A polynomial g(x) of degree zero is added to the polynomial 2 x 3 5 x 2 - 14 x 10 so that it become exactly divisible by 2 x -3 find the gfx? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about A polynomial g(x) of degree zero is added to the polynomial 2 x 3 5 x 2 - 14 x 10 so that it become exactly divisible by 2 x -3 find the gfx? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A polynomial g(x) of degree zero is added to the polynomial 2 x 3 5 x 2 - 14 x 10 so that it become exactly divisible by 2 x -3 find the gfx?.
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