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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…
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.
What is 3y-6y in factored form?
3y-6y in factored form = -3
What is the coefficient of the first term of a polynomial that is written in standard form?
It would be the "A" value/term. Standard from is Ax+By=C.
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)
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
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.
What is 3y-6y in factored form?
3y-6y in factored form = -3
How do you write 466x as a polynomial in standered form?
That already is a polynomial in standard form.
What is the coefficient of the first term of a polynomial that is written in standard form?
It would be the "A" value/term. Standard from is Ax+By=C.
Why the graph of a polynomial function with real coefficients must have a y-intercept but may have no x-intercept?
For a polynomial of the form y = p(x) (i.e., some polynomial function of x), having a y-intercept simply means that the polynomial is defined for x = 0 - and a polynomial is defined for any value of "x". As for the x-intercept: from left to right, a polynomial of even degree may come down, not quite reach zero, and then go back up again. A simple example is y = x2 + 1. Why is the situation for "x" and for "y" different? Well, the original equation is a polynomial in "x"; but if you solve for "x", you don't get a polynomial in "y".
