(2x - 1) is a factor of the polynomial 6x^6+x^5-92x^4+45x^3+184x^2+4x-48. Determine whether the statement is true or false. Justify your answer.

Efan Halliday 2021-09-18 Answered

(2x1) is a factor of the polynomial 6x6+x592x4+45x3+184x2+4x48. Determine whether the statement is true or false. Justify your answer.

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Expert Answer

yagombyeR
Answered 2021-09-19 Author has 92 answers

The factors of a polynomial decompose the polynomial into two or more polynomials, so the product of the factors gives the polynomial. In other words, a factor of a polynomial is a polynomial that divides the original polynomial with the remainder, 0.
To check, whether 2x1 is the factor of 6x6+x592x4+45x3+184x2+4x48 or not, substitute the value of x from 2x1 and if this results in zero, then 2x1 is the factor of f(x). Substitute x with 12 in f(x) and simplify each power.
2x1=0
2x=1
x=12
f(x)=6x6+x592x4+45x3+184x2+4x48
f(12)=0
6(12)6+(12)592(12)4+45(12)3+184(12)2+4(12)48=0
Cancel the common factors from the numerator and the denominator of each term and combine the terms with the same signs. Perform the addition and then subtraction to obtain 0. Hence, 2x1 is the factor of
6x6+x592x4+45x3+184x2+4x48
6(12)6+(12)592(12)4+45(12)3+184(12)2+4(12)48=0
6(164)+(132)92(116)+45(12)3+184(12)2+4(12)48=0
332+132234+458+4646=0

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