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How do you do this SAT question For polynomial p(x) the value of p(3) is -2. which of the following must be true about p(x)?
Wiki User
∙ 7y ago
A) x-5 is a factor of p(x)
B) x-2 is a factor of p(x)
C) x+2 is a factor of p(x)
D) The remainder when p(x) is divided by x-3 is -2
I need help solving this question because I didn't really get the answer explanation that college board gave it. Thanks in advance!
Wiki User
∙ 7y ago
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What is a zero of polynomial function?
A zero of a polynomial function - or of any function, for that matter - is a value of the independent variable (often called "x") for which the function evaluates to zero. In other words, a solution to the equation P(x) = 0. For example, if your polynomial is x2 - x, the corresponding equation is x2 - x = 0. Solutions to this equation - and thus, zeros to the polynomial - are x = 0, and x = 1.
An expression must have a monomial of degree 2 or higher to be a polynomial?
False
What number must be added to the polynomial to complete the perfect square x2-24x?
144
If the coefficient of the expression axn is a fraction and the exponent is positive will the expression be a polynomial?
Not necessarily. Every exponent in the exponent must be a non-negative integer. This is not what you have specified. For example, if n = 3.5, it is not a term in a polynomial expression.
Explain Why the product of two nonzero absolute values is always a positive number?
An absolute value must be greater or equal to zero. If the absolute value is known to be nonzero then it must be greater than zero: that is, it must be positive. The product of two (or more) positive numbers must be positive.
What is a polynomial of degree 3 that has no real zeros?
If the coefficients of a polynomial of degree three are real it MUST have a real zero. In the following, asymptotic values are assumed as being attained for brevity: If the coeeff of x3 is positive, the value of the polynomial goes from minus infinity to plus infinity as x goes from minus infinity to plus infinity. The reverse is true if the coefficient of x3 is negative. Since all polynomials are continuous functions, the polynomial must cross the x axis at some point. That's your root.
Is the x-intercepts the same thing as zeros?
Yes, the places where the graph of a polynomial intercepts the x-axis are zeros. The value of y at those places must be 0 for the polynomial to intersect the x axis.
What is a zero of a function?
Assuming the polynomial is written in terms of "x": It means, what value must "x" have, for the polynomial to evaluate to zero? For example: f(x) = x2 - 5x + 6 has zeros for x = 2, and x = 3. That means that if you replace each "x" in the polynomial with 2, for example, the polynomial evaluates to zero.
What is a zero of polynomial function?
A zero of a polynomial function - or of any function, for that matter - is a value of the independent variable (often called "x") for which the function evaluates to zero. In other words, a solution to the equation P(x) = 0. For example, if your polynomial is x2 - x, the corresponding equation is x2 - x = 0. Solutions to this equation - and thus, zeros to the polynomial - are x = 0, and x = 1.
What is a quadratic polynomial which has no zeros?
A quadratic polynomial must have zeros, though they may be complex numbers.A quadratic polynomial with no real zeros is one whose discriminant b2-4ac is negative. Such a polynomial has no special name.
Can a polynomial equation have no answer?
It depends on the domain. In the complex domain, a polynomial of order n must have n solutions, although some of these may be multiple solutions. In the real domain, a polynomial of odd order must have at least one real solution, while a polynomial of even order may have no real solutions.
What is polynomial division?
That means that you divide one polynomial by another polynomial. Basically, if you have polynomials "A" and "B", you look for a polynomial "C" and a remainder "R", such that: B x C + R = A ... such that the remainder has a lower degree than polynomial "B", the polynomial by which you are dividing. For example, if you divide by a polynomial of degree 3, the remainder must be of degree 2 or less.
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".
The exponents in the terms of a polynomial must be?
why the exponents can not be negative
What polynomial must be subtracted from it to obtain 29x 2 -7?
The answer depends on what "it" is. That has not been specified: I could make a guess but then I may as well make up my own question and answer it!
An expression must have a monomial of degree 2 or higher to be a polynomial?
False
Which of the following keys must be unique within a given table?
There is insufficient information in the question to properly answer it. You did not provide "the following". Please restate the question. In general, however, unique indexes with a not null constraint must be unique, and primary key constraints must be unique.
