SAT Math Prep by Kaplan Test Prep

Author:Kaplan Test Prep
Language: eng
Format: epub
Publisher: Kaplan Publishing
Published: 2020-06-04T00:00:00+00:00

To solve a radical equation, follow these steps:

•Isolate the radical part of the equation.

•Remove the radical using an inverse operation. For example, to remove a square root, square both sides of the equation; to remove a cube root, cube both sides; and so on.

•Solve for the variable. Note: If x2 = 81, then x = ±9, BUT only.

•Check for extraneous (invalid) solutions.

Polynomials

A polynomial is an expression or equation with one or more terms consisting of variables with nonnegative integer exponents and coefficients, joined by addition, subtraction, and multiplication. You can combine like terms in polynomials as you did with linear expressions and equations. Adding and subtracting polynomials is straightforward—simply combine like terms, paying careful attention to negative signs. Multiplying polynomials is slightly more involved, requiring a careful distribution of terms followed by combining like terms if possible. You can use FOIL (First, Outer, Inner, Last) when you multiply two binomials.

When a polynomial is written in descending order, the term with the highest power (called the leading term) tells you the basic shape of its graph and how many x-intercepts (also called roots or zeros) its graph can have. To find the zeros of a polynomial equation, factor the equation and set each factor equal to 0. You can have simple zeros and/or multiple zeros. For example, in the equation y = (x + 6)(x − 3)2, the factor x + 6 gives a simple zero of x = −6, while the factor (x − 3)2 gives a double zero of x = 3 (because technically, the factor is (x − 3)(x − 3)). Graphically, when a polynomial has a simple zero (multiplicity 1) or any zero with an odd multiplicity, its graph will cross through the x-axis. When a polynomial has a double zero (multiplicity 2) or any zero with an even multiplicity, its graph just touches the x-axis, creating a turning point in the graph.

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