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The factored form of a polynomial is valuable because it simplifies the process of finding its roots or zeros, making it easier to solve equations. It also provides insights into the polynomial's behavior, such as identifying multiplicities of roots and understanding its graph. Additionally, factored form can facilitate polynomial division and help in applications such as optimization and modeling in various fields.
What else can I help you with?
Which of the following is the correct factored form of the given equation?
The factored form of a polynomial is comprised of factors in which the sum is equal to the coefficient of the second term and the product is equal to th…
How do you convert factored to general form?
To convert a polynomial from factored form to general form, you need to expand the factored expression by multiplying the factors together. For example, if you have a factored expression like ( (x - 2)(x + 3) ), you would use the distributive property (also known as the FOIL method for binomials) to multiply: ( x^2 + 3x - 2x - 6 ), which simplifies to ( x^2 + x - 6 ). Continue this process for any additional factors until the expression is fully expanded into its general form, which is typically written as a polynomial in standard form.
Which polynomial is in simplest form?
A polynomial is in simplest form when it is expressed with no like terms and no factors that can be further simplified. For example, the polynomial ( 3x^2 + 5x - 2 ) is in simplest form because it cannot be factored or combined further. In contrast, ( 6x^2 + 3x - 1 + 2x^2 ) can be simplified to ( 8x^2 + 3x - 1 ), which is its simplest form. To determine if a polynomial is in simplest form, check for like terms and factorability.
Why does 3n squared plus 9n plus 6 have more than one factor?
The expression (3n^2 + 9n + 6) can be factored into simpler polynomial expressions, indicating that it has more than one factor. A polynomial of degree 2, like this one, generally has two factors when expressed in its factored form. Additionally, since it can be factored using methods such as grouping or the quadratic formula, it reveals multiple combinations of factors. Thus, it showcases the polynomial's ability to be expressed in various multiplicative forms.
What is a polynomial with a single root at x equals 2 and a double root at x equals 5?
That would be (x - 2) ( x - 5) ( x - 5). If you like, you can multiply these polynomials to get a single polynomial in standard form (i.e., not factored).
How do you know if a polynomial is in factored form?
You can't know if a general polynomial is in factored form.
What is the factored form of the polynomial x2 plus 9x plus 20?
It is (x+4)(x+5) when factored
Which of the following is the correct factored form of the given equation?
The factored form of a polynomial is comprised of factors in which the sum is equal to the coefficient of the second term and the product is equal to th…
What is the complete factored form of the following polynomial 15j3 plus 30j2?
15j2(j + 2)
Can you factor on a TI 83 calculator?
Yes, you can factor polynomials on a TI-83 calculator using the "Polynomial Root Finder" feature. To access it, go to the "MATH" menu, select "Polynomial," and choose the appropriate degree (e.g., quadratic). Enter the coefficients of the polynomial, and the calculator will provide the roots, which you can use to express the polynomial in factored form. However, it does not directly display the factored form; you'll need to interpret the roots accordingly.
How do you convert factored to general form?
To convert a polynomial from factored form to general form, you need to expand the factored expression by multiplying the factors together. For example, if you have a factored expression like ( (x - 2)(x + 3) ), you would use the distributive property (also known as the FOIL method for binomials) to multiply: ( x^2 + 3x - 2x - 6 ), which simplifies to ( x^2 + x - 6 ). Continue this process for any additional factors until the expression is fully expanded into its general form, which is typically written as a polynomial in standard form.
Which polynomial is in simplest form?
A polynomial is in simplest form when it is expressed with no like terms and no factors that can be further simplified. For example, the polynomial ( 3x^2 + 5x - 2 ) is in simplest form because it cannot be factored or combined further. In contrast, ( 6x^2 + 3x - 1 + 2x^2 ) can be simplified to ( 8x^2 + 3x - 1 ), which is its simplest form. To determine if a polynomial is in simplest form, check for like terms and factorability.
What is a Definition for algebraic equation?
an equation in the form of a polynomial having a finite number of terms and equated to zeroan equation in the form of a polynomial having a finite number of terms and equated to zero
Why does 3n squared plus 9n plus 6 have more than one factor?
The expression (3n^2 + 9n + 6) can be factored into simpler polynomial expressions, indicating that it has more than one factor. A polynomial of degree 2, like this one, generally has two factors when expressed in its factored form. Additionally, since it can be factored using methods such as grouping or the quadratic formula, it reveals multiple combinations of factors. Thus, it showcases the polynomial's ability to be expressed in various multiplicative forms.
What is a simplified polynomial?
a simplified polynomial is a algebraic equation/expression with variables and constants that can can be written as a sum of terms. Simplified form is the opposite of factored form P(x) = ( 2x - 3)( x+4 ) Is a factored form - product of 2 factors. Simplify P(x) by using the distributive property: P(x) = 2x2 +8x - 3x -12 P(x) = 2x2 + 5x - 12 simplified : a sum of terms!
What is a polynomial with a single root at x equals 2 and a double root at x equals 5?
That would be (x - 2) ( x - 5) ( x - 5). If you like, you can multiply these polynomials to get a single polynomial in standard form (i.e., not factored).
Are a polynomial's factors the values at which the graph of a polynomial meets the y-axis?
Not quite. The polynomial's linear factors are related - not equal to - the places where the graph meets the x-axis. For example, the polynomial x2 - 5x + 6, in factored form, is (x - 2) (x - 3). In this case, +2 and +3 are "zeroes" of the polynomial, i.e., the graph crosses the x-axis. That is, in an x-y graph, y = 0.
