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A linear polynomial typically has one term, which is the highest degree term, expressed in the form ( ax + b ), where ( a ) and ( b ) are constants, and ( x ) is the variable. However, it can also be represented with three terms, such as ( ax + b + 0c ), where the third term is effectively zero and does not change the polynomial. In general, a linear polynomial is defined by its degree (1), not the number of terms.
What else can I help you with?
What kind of polynomial is x-3?
The expression ( x - 3 ) is a linear polynomial because it is a polynomial of degree 1. It can be expressed in the standard form ( ax + b ), where ( a = 1 ) and ( b = -3 ). Linear polynomials represent straight lines when graphed on a coordinate plane.
When can you say that an algebraic expression is a polynomial?
A polynomial is a linear combination of non-negative integer powers of a variable. A linear combination means you can multiply the terms by constant numbers before summing them. The terms can consists of only positive integer powers of the variable or a constant.
What is 4x cubed minus 6x squared minus 10x?
The expression ( 4x^3 - 6x^2 - 10x ) is a polynomial in terms of ( x ). It consists of three terms: ( 4x^3 ), which is a cubic term, ( -6x^2 ), which is a quadratic term, and ( -10x ), which is a linear term. This polynomial can be factored to simplify it, but as it stands, it represents a cubic function of ( x ).
How many degrees does a linear polynomial have?
A linear polynomial has a degree of 1. This means it can be expressed in the form ( ax + b ), where ( a ) and ( b ) are constants and ( a \neq 0 ). The degree of a polynomial is determined by the highest power of the variable in the expression, which in the case of a linear polynomial is 1.
Which linear expression is a factor of this polynomial function?
To determine which linear expression is a factor of a given polynomial function, you typically need to perform polynomial division or use the Factor Theorem. If you can substitute a root of the polynomial into the linear expression and obtain a value of zero, then that linear expression is indeed a factor. Alternatively, if you have the polynomial's roots, any linear expression of the form ( (x - r) ), where ( r ) is a root, will be a factor. Please provide the specific polynomial function for a more accurate response.
A fourth degree polynomial that has five terms could have five linear factors.?
No, if it is of degree 4, it can have 4 linear factors, regardless of the number of terms.For example, x squared + 5x + 6 = (x+3)(x+2). The unfactored polynomial has three terms, and is of degree 2. Similarly, you can multiply four linear terms together; and you will get a polynomial of degree 4, which has up to 5 terms.
Classify the polynomial by its degree and by the number of terms.5m?
linear monomial
What is a polynomial with 3 terms?
A trinomial
How many terms does polynomial?
3
When can you say that an algebraic expression is a polynomial?
A polynomial is a linear combination of non-negative integer powers of a variable. A linear combination means you can multiply the terms by constant numbers before summing them. The terms can consists of only positive integer powers of the variable or a constant.
What is a polynomial of 3 items?
An example of a polynomial with 3 terms is 3x3 + 4x + 20, because there are 3 different degrees of x in the polynomial.
What is 4x cubed minus 6x squared minus 10x?
The expression ( 4x^3 - 6x^2 - 10x ) is a polynomial in terms of ( x ). It consists of three terms: ( 4x^3 ), which is a cubic term, ( -6x^2 ), which is a quadratic term, and ( -10x ), which is a linear term. This polynomial can be factored to simplify it, but as it stands, it represents a cubic function of ( x ).
If you multiply a linear polynomial by a quadratic one what is the degree of the product polynomial?
It will be a cubic polynomial.
A polynomial with exactly 3 terms?
A polynomial with three terms is called a trinomial. Example: x² + 16 + 18 is a trinomial. It has three terms (x²), (16), and (18)
What polynomial has more than three terms?
A polynomial of order 3 (a cubic) or higher can have more than three terms. However, the the following polynomial, even though of order 7, has only 2 terms: x7 - 23.
Which linear expression is a factor of this polynomial function?
To determine which linear expression is a factor of a given polynomial function, you typically need to perform polynomial division or use the Factor Theorem. If you can substitute a root of the polynomial into the linear expression and obtain a value of zero, then that linear expression is indeed a factor. Alternatively, if you have the polynomial's roots, any linear expression of the form ( (x - r) ), where ( r ) is a root, will be a factor. Please provide the specific polynomial function for a more accurate response.
Can integer linear programming be solved in polynomial time?
No, integer linear programming is NP-hard and cannot be solved in polynomial time.
