First Day Precalculus Review

Front

What is the simplified form of \( \sqrt{500x^8y^2} \)?

Back

\( 10x^4y\sqrt{5} \)

Front

Factor completely: \( x^3 - 2x^2 - 9x + 18 \)

Back

\( (x-2)(x-3)(x+3) \)

Front

Write the equation in point-slope form for the line that contains the points (3, -5) and (5, -1).

Back

\( y + 5 = 2(x - 3) \)

Front

What values will make the rational expression \( \frac{(x+1)(x-7)}{(x-4)(x+3)} \) UNDEFINED?

Back

\( x=4, x=-3 \)

Front

What is the solution to the system of equations if it has infinite solutions?

Back

\( Infinite solutions \)

Front

Define the point-slope form of a linear equation.

Back

The point-slope form is \( y - y_1 = m(x - x_1) \), where \( m \) is the slope and \( (x_1, y_1) \) is a point on the line.

Front

What is the definition of a rational expression?

Back

A rational expression is a fraction where the numerator and/or denominator are polynomials.

Front

How do you determine if a rational expression is undefined?

Back

A rational expression is undefined when its denominator equals zero.

Front

What is the process for factoring a polynomial?

Back

To factor a polynomial, look for common factors, use grouping, or apply special factoring formulas.

Front

What is the quadratic formula?

Back

The quadratic formula is \( x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \) for the equation \( ax^2 + bx + c = 0 \).