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When is a negative number raised to an odd power negative?
It is always negative when raised to an odd power and always positive when raised to an even power -2 to the third power = -2 x -2 x -2 = -8 -2 to the fourth power = -2 x -2 x -2 x -2 = +16
What are the rules fr multiplication and divisions of integers?
(positive number) x (positive number) = positive number (positive number)/(positive number) = positive number (positive number) x ( negative number) = negative number (positive number)/( negative number) = negative number (negative number) x (negative number) = positive number (negative number)/(negative number) = positive number
What is the minimum number of x-intercepts that a 7th degree polynomial might have?
1
When multiplying a negative number by a positive number is the result going to be negative or positive?
The result will always be negative. Positive X Positive = Positive Negative X Negative = Positive Positive X Negative = Negative
What is the number in front of the term with the highest degree in a polynomial?
It is the Coefficient. It only refers to the given term that it is front. e.g. 2x^2 - 3x + 1 The '2' in front of 'x^2' only refers to 'x^2'. The '-3' in front of 'x' is the coefficient of '-3' The '1' is a constant.
Is -4x a polynomial?
Yes, -4x is a polynomial. A polynomial is an expression that consists of variables raised to non-negative integer powers, multiplied by coefficients. In this case, -4 is the coefficient and x is the variable raised to the first power, which meets the criteria for a polynomial. Thus, -4x is a linear polynomial.
Is this a polynomial 5x5 - 3x3 x?
Yes, the expression (5x^5 - 3x^3 x) is a polynomial. It can be simplified to (5x^5 - 3x^4), which consists of terms with non-negative integer exponents on (x). Polynomials are defined as expressions that involve sums and products of variables raised to whole number powers, and this expression fits that definition.
How a like polynomial and non-polynomial?
A polynomial is an expression made up of variables raised to non-negative integer exponents, combined using addition, subtraction, and multiplication, such as ( f(x) = 2x^3 - 4x + 7 ). In contrast, a non-polynomial can include variables raised to negative exponents, fractional exponents, or involve operations like division by a variable, such as ( g(x) = \frac{1}{x} ) or ( h(x) = x^{1/2} ). Polynomials exhibit smooth behavior and can be graphed as continuous curves, while non-polynomials may have discontinuities or asymptotic behavior.
What is the difference be a polynomial function and an exponential function?
In a polynomial function, the variable x is raised to some integer power. f(x) = 5x³ + 8x⁵ g(x) = (x + 5)² In an exponential function, some real number is raised to the power of variable x or some function of x f(x) = 5ˣ g(x) = eˣ⁺²
What is a number a variable or a product of numbers and variables raised to natural number powers?
A number is a specific value or quantity, while a variable represents an unknown or changing quantity, often denoted by letters like x or y. A product of numbers and variables raised to natural number powers is referred to as a polynomial. Polynomials consist of terms that can include constants (numbers), variables, and exponents that are whole numbers (non-negative integers). For example, (3x^2 + 2x + 1) is a polynomial where (3), (2), and (1) are coefficients, and (x) is the variable raised to the powers of 2 and 1.
When is a negative number raised to an odd power negative?
It is always negative when raised to an odd power and always positive when raised to an even power -2 to the third power = -2 x -2 x -2 = -8 -2 to the fourth power = -2 x -2 x -2 x -2 = +16
Is x to the power of -2 a polynomial?
No. By the definition of a polynomial, the powers can only be non-negative integers.
How do you find Polynomial?
A polynomial is a sum of a finite number of terms in which each term is of the form a*Xn where a is a coefficient, X is a variable and n is a non-negative integer.a may be integer, rations, real or complex;X may be a numerical variable or a matrix.
Which polynomial will definitely have nonreal zeros?
A polynomial will definitely have nonreal zeros if it has an odd degree and a negative leading coefficient. For example, the polynomial ( f(x) = -x^3 + 2 ) has a degree of 3, which is odd, and the leading coefficient is negative. By the Fundamental Theorem of Algebra, it must have at least one nonreal zero, as it cannot cross the x-axis an odd number of times while remaining entirely above or below it.
What does 10 to the negative 73 power equal?
Any number x raised to a negative power -y is equivalent to the reciprocal of x raised to y. So, 10-73 would be the fraction 1 over the number 1 with 73 zeroes after it. A very small number indeed!
What is x to the negative 7th power?
When a number is raised to a negative exponent, it is equivalent to its reciprocal raised to the positive exponent. Therefore, x to the power of -7 is equal to 1 divided by x to the power of 7, or 1/x^7.
When is a function considered polynomial function?
A polynomial function of a variable,x, can be written as a sum of non-negative integer powers of x. For example, f(x) = 5x5 + 27x2 - 37/3 x + 2.36.
