Solving Absolute Value Equations Learn absolute value equations concept. The equation |x| = 4. This means that x could be 4 or x could be -4. When you take the absolute value of 4, the solution is 4 and when you take the absolute value of -4, the solution is also 4. An absolute value problem, you have to get into account that there can be two solutions that will make the equation true. Learning absolute value equation, you set the quantity inside the absolute value symbol equal to the positive and negative value on the other side of the equal symbol. Solve Absolute Value Equations Below are the examples on how to solve absolute value equations Example 1: |x + 1| = 4 Know More About How to Factor a Trinomial
Solution: The quantity inside the absolute value symbol can be equal to 4 or -4 x + 1 = 4 or x + 1 = - 4 Subtract 1 on both side of the given equation x + 1 - 1 = 4 - 1 or x + 1 - 1 = -4 - 1 x = 3 or x = -5 So the solution are x = 3 and x = -5 Example 2: |2x - 3| = x - 5 Solution: When solving this equation, you have to be careful when solving opposite of (x - 5) 2x - 3 = x - 5 or 2x - 3 = -(x - 5) Learn More About Subtracting Polynomials
x - 3 = -5 or 2x -3 = -x + 5 x = -2 or 3x – 3 = 5 3x = 8 x= So, the solution is x = -2 and x = 83 Example 3 :- |x + 1| = 5 Solution: The quantity inside the absolute value symbol can be equal to 5 or -5 x + 1 = 5 or x + 1 = -5 Subtract 1 on both side of the given equation x + 1 - 1 = 5 - 1 or x + 1 - 1 = - 5 - 1 x = 4 or x = - 6 So the solution are x = 4 and x = - 6
Degree of a Polynomial The degree of polynomial is the greatest exponent of a term. The greatest exponent should have a non-zero coefficient in a polynomial expressed as a sum or difference of terms which is commonly known as Canonical form. The sum of the powers of all variables in the term is the degree of the polynomial. The degree can also be specified as order. The degree of polynomial is for the single variable or the combination of two or more variables with the powers. Properties of Degree of Polynomial According to the degree of polynomials the names are assigned. Below listed are the degree of polynomials: The name of the zero degree polynomial is constant. The name of the 1 degree polynomial is linear. The name of the 2 degree polynomial is quadratic.
The name of the 3 degree polynomial is cubic. The name of the 4 degree polynomial is quartic The name of the 5 degree polynomial is quintic. The multiplicative inverse 1a have degree -1 The square root has a degree as 12 The logarithm has a degree as 0, example log b. The exponential function’s degree is infinity. How to Find the Degree of Polynomial In this section, learn how to find the degree of polynomial Using one variable: Let us consider the polynomial, 8x3 + 7x4 + 6x2 + 5x + 1. The degree of the first term is 3. The degree of the second term is 4 The degree of the third term is 2 The degree of the fourth term is 1 and Read More About Properties of Equality
The degree of the last term is 0. Here the greatest degree among all the degrees is 4. So the degree of the polynomial 8x3+7x4+6x2+5x+1 is 4. Using two variables: Let us consider the given polynomial is 5x2y4+2xy3+8y2+2y+x3+1 The degree of the first term is sum of the power of x and y. So the degree for the first term is 2+4 which is 6. The degree of the second term is 1+ 3=4. The degree of the third term is 2. The degree of the fourth term is 1. The degree of the fifth term is 3 and The degree of the last term is 0. Here the maximum degree is 4. So 4 is the degree of the polynomial 5x2y4+2xy3+8y2+2y+x3+1
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