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What is the degree of the polynomial in the expression x5 plus 1 - 3x4 plus 3x9 - 2x?
The x^5 at the beginning makes the degree of the polynomial 5.
Example of third-degree polynomial?
pretty sure a third degree polynomial is just one that has a term to the power of 3 eg. x3 + 4x2 + 3x + 5
What is meant by the degree of a monomial and polynomial?
The degree is the highest power of the variable that appears in it.(x2 + x + 9) is a second degree polynomial(Q4 - 72) is a fourth degree polynomial( z ) is a first degree monomialSo the degree of a polynomial in one variable is the highest power of the variable.For example, [ 2x3 - 7x ] has degree 3.The degree of a polynomial in two or more variables is the greatest sum of theexponents in any single term.For example, [ 5m3 + m2n - mn2 ] has degree 4.And a degree of a monomial is the sum of the exponents of its variables.For example, [ 4a2b3 ] has degree 5.
Why do you get 2 solutions in the quadratic equation?
This is due to the zero-product property. In principle, any polynomial equation of degree 2 can be factored as: (x - a)(x - b) = 0 Here is a specific example: (x - 5)(x + 3) = 0 Now, if the product of two factors is zero, it follows that one of the two factors is equal to zero; so the above becomes: x - 5 = 0 OR x + 3 = 0 Solving the individual parts, you get the two solutions. Of course, it is possible that the two factors happen to be the same; in this case, the polynomial is said to have a "double" root (i.e., a double solution). Similarly, a polynomial equation of degree 3 can be separated into 3 factors, a polynomial of degree 4 can be factored into 4 factors, etc.
How do you determine the degrees of a given polynomial?
The degree of a polynomial is the highest power that appears in the polynomial. For more than one variable, you must add the powers for each variable, for example, a3b2 is of degree 3 + 2 = 5.
Is it possible to find a polynomial of degree 3 that has -2 as its only real zero?
5
What is the degree of the polynomial in the expression x5 plus 1 - 3x4 plus 3x9 - 2x?
The x^5 at the beginning makes the degree of the polynomial 5.
Is it true that the degree of polynomial function determine the number of real roots?
Sort of... but not entirely. Assuming the polynomial's coefficients are real, the polynomial either has as many real roots as its degree, or an even number less. Thus, a polynomial of degree 4 can have 4, 2, or 0 real roots; while a polynomial of degree 5 has either 5, 3, or 1 real roots. So, polynomial of odd degree (with real coefficients) will always have at least one real root. For a polynomial of even degree, this is not guaranteed. (In case you are interested about the reason for the rule stated above: this is related to the fact that any complex roots in such a polynomial occur in conjugate pairs; for example: if 5 + 2i is a root, then 5 - 2i is also a root.)
What is the degree of the polynomial 2x plus 5?
The degree of the polynomial 2x + 5 is 1. The highest power of x is x1, i.e. 2x1 + 5x0, hence the designation of first degree.
What is the definition of degree of the polynomial?
The degree of a polynomial is the highest degree of its terms.The degree of a term is the sum of the exponents of the variables.7x3y2 + 15xy6 + 23x2y2The degree of the first term is 5.The degree of the second term is 7.The degree of the third term is 4.The degree of the polynomial is 7.
Degree of a terms of polynomial?
The degree of a polynomial is the highest degree of its terms. The degree of a term is the sum of the exponents of the variables that appear in it.For example, the polynomial 8x2y3 + 5x - 10 has three terms. The first term has a degree of 5, the second term has a degree of 1, and the last term has a degree of 0. Therefore, the polynomial is degree five.
What is the degree of the polynomial 6x3y2 5x4 7z?
5
At most how many unique roots will a fifth-degree polynomial have?
5, Using complex numbers you will always get 5 roots.
How can you get the degree of the polynomials?
The degree of a polynomial is the highest degree of its terms.The degree of a term is the sum of the exponents of the variables.7x3y2 + 15xy6 + 23x2y2The degree of the first term is 5.The degree of the second term is 7.The degree of the third term is 4.The degree of the polynomial is 7.
Example of third-degree polynomial?
pretty sure a third degree polynomial is just one that has a term to the power of 3 eg. x3 + 4x2 + 3x + 5
What is meant by the degree of a monomial and polynomial?
The degree is the highest power of the variable that appears in it.(x2 + x + 9) is a second degree polynomial(Q4 - 72) is a fourth degree polynomial( z ) is a first degree monomialSo the degree of a polynomial in one variable is the highest power of the variable.For example, [ 2x3 - 7x ] has degree 3.The degree of a polynomial in two or more variables is the greatest sum of theexponents in any single term.For example, [ 5m3 + m2n - mn2 ] has degree 4.And a degree of a monomial is the sum of the exponents of its variables.For example, [ 4a2b3 ] has degree 5.
Why do you get 2 solutions in the quadratic equation?
This is due to the zero-product property. In principle, any polynomial equation of degree 2 can be factored as: (x - a)(x - b) = 0 Here is a specific example: (x - 5)(x + 3) = 0 Now, if the product of two factors is zero, it follows that one of the two factors is equal to zero; so the above becomes: x - 5 = 0 OR x + 3 = 0 Solving the individual parts, you get the two solutions. Of course, it is possible that the two factors happen to be the same; in this case, the polynomial is said to have a "double" root (i.e., a double solution). Similarly, a polynomial equation of degree 3 can be separated into 3 factors, a polynomial of degree 4 can be factored into 4 factors, etc.
