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Q: How does knowing one linear factor of a polynomial help find the other factors?

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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.

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.

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).

yes, you can. but it's preferable to Avoid decimals, if it is necessary simplify your equation.

Certainly. It could, for example, be a power relationship such as y = x^3

Related questions

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.

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).

It is a quadratic factor.

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.

It will be a cubic polynomial.

Yes, it is a linear polynomial.

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.

Linear Form is a homogeneous polynomial of the first degree.

It can: For example, the linear polynomial 2x + 4 can be factorised into 2 times (x+2) So the question is inappropriate.

A polynomial with a degree of one, of the form y = ax + b, where a and b are constants.

It is a linear expression.

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.

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