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 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.
Strictly we do not classify polynomials by the number of terms but by the highest power of the variable (its degree).For example, if x is the variable then a polynomial with highest power...... x0 (degree 0) is a constant e.g. 4x0 = 4... x1 (degree 1) is linear e.g. 2x1 + 5 = 2x + 5... x2 (degree 2) is a quadratic e.g. 3x2 - 2x + 1... x3 (degree 3) is a cubic e.g. 2x3 - 3x2 - 2x + 1... x4 (degree 4) is a quartic e.g. 7x4 + 2x3 - 3x2 - 2x + 1(degree 5) quintic, (degree 6) sextic, (degree 7) septic, (degree 8) octic,...Although it appears as if the degree of a polynomial is always one less than the number of terms, in general this not the case. For example, x3 - 9 is cubic with only 2 terms or 4x8 is an octic with only one term.
A coefficient is a number paired with a variable. For example, in the equation4x+2x=16, the numbers 4 and 2 would be coefficients.Coefficients are the factors (usually constants) which are multiplied by the variables in each term. For example, in a second-degree polynomial equation,y = ax2 + bx + ca is called the quadratic coefficient, b is the linear coefficient and c is the constant term.
4x2 + 3x - 6 is a second degree polynomial. Since the polynomial function f(x) = 4x2 + 3x - 6 has 2 zeros, it has 2 linear factors. Since we cannot factor the given polynomial, let's find the two roots of the equation 4x2 + 3x - 6 = 0, which are the zeros of the function. 4x2 + 3x - 6 = 0 x2 + (3/4)x = 6/4 x2 + (3/4)x + (3/8)2 = 6/4 + 9/64 (x + 3/8)2 = 105/64 x + 3/8 = ± √(105/64) x = (-3 ± √105)/8 x = -(3 - √105)/8 or x = -(3 + √105)/8 Thus, the linear factorization of f(x) = 4[x + (3 - √105)/8][x + (3 + √105)/8].
a linear equation
It will be a cubic polynomial.
It is a linear expression.
Linear Form is a homogeneous polynomial of the first degree.
A polynomial with a degree of one, of the form y = ax + b, where a and b are constants.
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.
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.
linear monomial
Yes, any second-degree polynomial is quadratic. Degree 0 - constant (8) Degree 1 - linear (n) Degree 2 - quadratic (n^2) Degree 3 - cubic (n^3) Degree 4 - fourth degree (n^4) Degree 5 - fifth degree (n^5) Degree 6 - sixth degree (n^6) and so on............ Also a degree I find funny is the special name for one hundredth degree. Degree 100 - hectic (n^100)
A linear equation is one which represents a straight line. When drawn (y plotted against x), a degree 1 polynomial produces a straight line.
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.
Yes, it is a linear polynomial.
It can: For example, the linear polynomial 2x + 4 can be factorised into 2 times (x+2) So the question is inappropriate.