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When a polynomial is divided by one of its binomial factors what is the quotient called?
When a polynomial is divided by one of its binomial factors, the quotient is called the "reduced polynomial" or simply the "quotient polynomial." This resulting polynomial represents the original polynomial after removing the factor, and it retains the degree that is one less than the original polynomial.
What is the relationship between zeros and factors?
Zeros and factors are closely related in polynomial functions. A zero of a polynomial is a value of the variable that makes the polynomial equal to zero, while a factor is a polynomial that divides another polynomial without leaving a remainder. If ( x = r ) is a zero of a polynomial ( P(x) ), then ( (x - r) ) is a factor of ( P(x) ). Thus, finding the zeros of a polynomial is equivalent to identifying its factors.
How do you know if you have simplified a polynomial correctly?
I suppose you mean factoring the polynomial. You can check by multiplying the factors - the result should be the original polynomial.
What is the Factor the polynomial expression. Write each factor as a polynomial in descending order.?
To factor a polynomial expression, you identify common factors among the terms and express the polynomial as a product of simpler polynomials. For example, consider the polynomial ( x^2 - 5x + 6 ); it factors into ( (x - 2)(x - 3) ). Each factor is written in descending order, starting with the highest degree term. The specific steps to factor will depend on the polynomial you are working with.
What are prime polynomials?
A polynomial that can't be separated into smaller factors.
When a polynomial is divided by one of its binomial factors what is the quotient called?
When a polynomial is divided by one of its binomial factors, the quotient is called the "reduced polynomial" or simply the "quotient polynomial." This resulting polynomial represents the original polynomial after removing the factor, and it retains the degree that is one less than the original polynomial.
Are a polynomial's factors the values at which the graph of a polynomial meets the x-axis?
false
How do you know if you have simplified a polynomial correctly?
I suppose you mean factoring the polynomial. You can check by multiplying the factors - the result should be the original polynomial.
Why might it be useful to know the linear factors of a polynomial function?
It is useful to know the linear factors of a polynomial because they give you the zeros of the polynomial. If (x-c) is one of the linear factors of a polynomial, then p(c)=0. Here the notation p(x) is used to denoted a polynomial function at p(c) means the value of that function when evaluated at c. Conversely, if d is a zero of the polynomial, then (x-d) is a factor.
How do you find a degree of a graphed polynomial?
Factors
To find the factors of a polynomial from its graph follow this rule If the number is a root of a polynomial then x - b is a factor?
a
To find the factors of a polynomial from its graph follow this rule If the number is a root of a polynomial then x - a is a factor?
B
To find the factors of a polynomial from its graph follow this rule If the number is a root of a polynomial then x - c is a factor?
a
What is the polynomial when each of its factors is prime?
Completely Factored
If the factors of a polynomial are x - 2 and x - 5 what values of x make that polynomial 0?
2 or 5
How do you factor a polynomial if their are more than one factors?
Factor it once, and then factor the factors.
How do you factor a polynomial with the equation of 6A2 - B 2?
The given polynomial does not have factors with rational coefficients.
