Readiness - Exponents & Polynomials

Front

What is an exponent?

Back

An exponent is a number that indicates how many times to multiply the base by itself. For example, in 2^3, 2 is the base and 3 is the exponent, meaning 2 is multiplied by itself 3 times (2 * 2 * 2 = 8).

Front

What is a polynomial?

Back

A polynomial is a mathematical expression that consists of variables, coefficients, and exponents, combined using addition, subtraction, and multiplication. For example, 4x^3 - 2x + 7 is a polynomial.

Front

How do you evaluate a polynomial function?

Back

To evaluate a polynomial function, substitute the given value of the variable into the polynomial and perform the arithmetic operations. For example, for g(x) = 4x^3 - 2x + 7, to find g(1), substitute 1 for x: g(1) = 4(1)^3 - 2(1) + 7 = 10.

Front

What is the degree of a polynomial?

Back

The degree of a polynomial is the highest power of the variable in the expression. For example, in the polynomial 4x^3 - 2x + 7, the degree is 3.

Front

What is the zero exponent rule?

Back

Any non-zero number raised to the power of zero equals one. For example, x^0 = 1, where x is not equal to zero.

Front

What is the product of powers rule?

Back

When multiplying two powers with the same base, add the exponents. For example, x^a * x^b = x^(a+b).

Front

What is the power of a power rule?

Back

When raising a power to another power, multiply the exponents. For example, (x^a)^b = x^(a*b).

Front

What is the quotient of powers rule?

Back

When dividing two powers with the same base, subtract the exponents. For example, x^a / x^b = x^(a-b).

Front

How do you simplify the expression (x^10)(x^2)^-3?

Back

Using the product of powers rule and the power of a power rule, (x^10)(x^2)^-3 = x^(10 + (2*-3)) = x^(10 - 6) = x^4.

Front

What is the value of k(2) if k(x) = x^4 - 3x^3 + 2x - 5?

Back

To find k(2), substitute 2 into the polynomial: k(2) = (2)^4 - 3(2)^3 + 2(2) - 5 = 16 - 24 + 4 - 5 = -9.