0
How does knowing one linear factor of a polynomial help find the other factors?
Wiki User
∙ 8y ago
If you know one linear factor, then divide the polynomial by that factor. The quotient will then be a polynomial whose order (or degree) is one fewer than that of the one that you stared with. The smaller order may make it easier to factorise.
Wiki User
∙ 8y ago
Add your answer:
Earn +20 pts
What is a linear factor?
What is a linear factor What is a linear factor A linear factor is defined as a small change here will effect a small change there by a set value or factor.
What is a linear fraction?
A linear fraction is an expression of the form n/(ax + b) where n, a and b are integers.More generally, an algebraic fraction with a denominator which is a polynomial of order 2 (quadratic) or higher can sometimes be rewritten as a sum of fractions each of whose denominators are binomial expressions or linear fraction. This is particularly important for integration.
How do you find out the number of imaginary zeros in a polynomial?
Descartes' rule of signs (see related link) can help you determine the maximum number of real roots. If the polynomial is odd powered, then there will be at least one real root. Any even powered polynomial can be factored into a bunch of quadratics [though they may not be rational or even pretty], and any odd-powered polynomial can be factored into a bunch of quadratics and one linear (this one would have the real root). So the quadratics may have pairs of real or complex roots (having an imaginary component).To clarify, when I say complex, I'm referring to the fact that there will be an imaginary component to the root, because actually the real numbers is a subset of the set of complex numbers.The order of the polynomial will tell you how many roots it will have. If you can graph the polynomial, then you can see if it crosses the x axis. If it is a 5th order polynomial, and crosses the x axis 3 times, then there are 3 real roots (the other two roots are complex).
How do you convert meter to linear meter?
A meter is a linear measurement, therefore 1 meter is the same as 1 linear meter.
How many linear yards equals a linear foot?
1/3 or .3333333333
Why might it be useful to know the linear factors of a polynomial function?
It is useful to know the linear factors of a polynomial because they give you the zeros of the polynomial. If (x-c) is one of the linear factors of a polynomial, then p(c)=0. Here the notation p(x) is used to denoted a polynomial function at p(c) means the value of that function when evaluated at c. Conversely, if d is a zero of the polynomial, then (x-d) is a factor.
What is the factor of the polynomial x3-4x2 x-4?
It is not possible to be sure about the answer because there is no sign before the linear term. If the polynomial is x3-4x2+x-4 then, the factors are (x-4) and (x2+1).
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.
If you multiply a linear polynomial by a quadratic one what is the degree of the product polynomial?
It will be a cubic polynomial.
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.
Is x minus the square root of 11 a polynomial?
Yes, it is a linear polynomial.
What is the definition for linear form?
Linear Form is a homogeneous polynomial of the first degree.
Why linear polynomial cannot be factorised?
It can: For example, the linear polynomial 2x + 4 can be factorised into 2 times (x+2) So the question is inappropriate.
What is linear polynomial?
A polynomial with a degree of one, of the form y = ax + b, where a and b are constants.
What is A polynomial of degree 1 called?
It is a linear expression.
What is a linear factor?
What is a linear factor What is a linear factor A linear factor is defined as a small change here will effect a small change there by a set value or factor.
Given that 3 is a zero of the polynomial g of x equals x cubed plus x squared-4x-24 express g of x as a product of linear factors?
The Factor Theorem says (x − r) is a factor of a polynomial g(x) if and only if r is a root of g(x). Since 3 is a zero, we know g(x) can be divided by (x-3)In fact, g(x)=(x-3)(x2 +4x+8)The (x2 +4x+8) has no real roots, (rational roots theorem tells us this) but we can still write it as a product of linear factors using complex numbers.Since (x+2-2i)(x+2+2i)=(x2 +4x+8)we have g(x)=(x-3)(x+2-2i)(x+2+2i) which is a product of linear factor.
