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If 3x-1is a factor of the polynomial 6x Sq x-1then find the other factors?
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If 3x-1is a factor of the polynomial 6x Sq x-1then find the other fac...
6x^2+x-1
6x^2+3x-2x-1
3x(2x+1)-1(2x+1)
(3x-1)(2x+1)
so the another factor is (2x-1)
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If 3x-1is a factor of the polynomial 6x Sq x-1then find the other fac...
Factorization of the Polynomial
Given that 3x-1 is a factor of the polynomial 6x^2 + x - 1, we can use the factor theorem to find the other factors.
Using the Factor Theorem
The factor theorem states that if a polynomial f(x) has a factor (x - a), then f(a) = 0.
In this case, since 3x - 1 is a factor, we can set 3x - 1 = 0 and solve for x:
3x - 1 = 0
3x = 1
x = 1/3
Finding the Other Factors
Now that we know x = 1/3 satisfies the polynomial, we can use synthetic division or polynomial long division to divide 6x^2 + x - 1 by (3x - 1) to find the other factor.
6x^2 + x - 1 / 3x - 1
We divide 6x^2 + x - 1 by 3x - 1 to get:
2x + 1
Therefore, the other factor of the polynomial 6x^2 + x - 1 is 2x + 1.
Final Factorization
So, the complete factorization of the polynomial 6x^2 + x - 1 is:
(3x - 1)(2x + 1)
Given that 3x-1 is a factor of the polynomial 6x^2 + x - 1, we can use the factor theorem to find the other factors.
Using the Factor Theorem
The factor theorem states that if a polynomial f(x) has a factor (x - a), then f(a) = 0.
In this case, since 3x - 1 is a factor, we can set 3x - 1 = 0 and solve for x:
3x - 1 = 0
3x = 1
x = 1/3
Finding the Other Factors
Now that we know x = 1/3 satisfies the polynomial, we can use synthetic division or polynomial long division to divide 6x^2 + x - 1 by (3x - 1) to find the other factor.
6x^2 + x - 1 / 3x - 1
We divide 6x^2 + x - 1 by 3x - 1 to get:
2x + 1
Therefore, the other factor of the polynomial 6x^2 + x - 1 is 2x + 1.
Final Factorization
So, the complete factorization of the polynomial 6x^2 + x - 1 is:
(3x - 1)(2x + 1)
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If 3x-1is a factor of the polynomial 6x Sq x-1then find the other factors? for Class 9 2024 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about If 3x-1is a factor of the polynomial 6x Sq x-1then find the other factors? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If 3x-1is a factor of the polynomial 6x Sq x-1then find the other factors?.
If 3x-1is a factor of the polynomial 6x Sq x-1then find the other factors? for Class 9 2024 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about If 3x-1is a factor of the polynomial 6x Sq x-1then find the other factors? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If 3x-1is a factor of the polynomial 6x Sq x-1then find the other factors?.
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