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Are a polynomial's factors the values at which the graph of a polynomial meets the x-axis?
false
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
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 with the equation of 6A2 - B 2?
The given polynomial does not have factors with rational coefficients.
You can use the BLANK of a polynomial to help you find its factors or roots?
Graph factor
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 is the polynomial in descending order for 12x2 plus 20x - 25?
12x2 + 20x - 25 IS a polynomial that factors into (2x + 5)(6x - 5)
How do you write each factor as a polynomial in descending order?
To write each factor as a polynomial in descending order, first identify the terms of the polynomial and arrange them based on the degree of each term, starting with the highest degree. For example, if you have factors like (x^2 + 3x - 5) and (2x - 1), you would express each factor individually, ensuring that the term with the highest exponent comes first. Finally, combine all terms, maintaining the descending order for clarity and consistency.
What is the step of factorising by grouping?
Factorising by grouping involves rearranging and grouping terms in a polynomial to factor out common factors. First, you split the polynomial into two groups, then factor out the greatest common factor from each group. If done correctly, these groups will have a common binomial factor, which can then be factored out, resulting in a simplified expression. This method is particularly useful for polynomials with four terms.
What is an expression that completely divides a given polynomial?
An expression that completely divides a given polynomial without leaving a remainder is called a factor of the polynomial. This means that when the polynomial is divided by the factor, the result is another polynomial with no remainder. Factors of a polynomial can be found by using methods such as long division, synthetic division, or factoring techniques like grouping, GCF (greatest common factor), or special patterns.
What is the step-by-step process of solving polynomial equations using the Ruffini method?
The Ruffini method, also known as synthetic division, is a step-by-step process for solving polynomial equations. Here is a concise explanation of the process: Write the coefficients of the polynomial equation in descending order. Identify a possible root of the polynomial equation and use synthetic division to divide the polynomial by the root. Repeat the process until the polynomial is fully factored. Use the roots obtained from the synthetic division to write the factors of the polynomial equation. Solve for the roots of the polynomial equation by setting each factor equal to zero. This method allows for the efficient solving of polynomial equations by breaking them down into simpler factors.
Express the polynomial below as a product of its factors Use the caret to enter exponents 20x3 - 15x2?
20x3-15x2=8,000-225=7,775
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.
How do you factorise completely?
To factorise a polynomial completely, first look for the greatest common factor (GCF) of the terms and factor it out. Next, apply techniques such as grouping, using the difference of squares, or recognizing special patterns (like trinomials or perfect squares) to break down the remaining polynomial. Continue this process until you can no longer factor, resulting in a product of irreducible factors. Always check your work by expanding the factors to ensure you return to the original polynomial.
What is x2-x-30 factored as a polynomial in descending order?
You must look for two numbers with a sum of (-1), and a product of (-30). This, of course, is -6 and 5; so the factors are (x-6) (x+5).
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.
Are a polynomial's factors the values at which the graph of a polynomial meets the x-axis?
false
