Pre Calc End of Q2 Review Fall 2024

Front

What is the result of the subtraction \( (4+7i)-(1+i) \)?

Back

The result is \( 3+6i \).

Front

What is the result of \( \sqrt{4} \cdot \sqrt{-6} \)?

Back

The result is \( 2i \sqrt{6} \).

Front

How many roots does the polynomial \( P(x) = (x - 2)(x + 1)(x - 7) \) have?

Back

The polynomial has 3 roots.

Front

Expand \( (x - 1)^4 \).

Back

The expansion is \( x^4 - 4x^3 + 6x^2 - 4x + 1 \).

Front

What is \( \left(\frac{a^3}{b^5}\right)^4 \)?

Back

The result is \( \frac{a^{12}}{b^{20}} \).

Front

Define a complex number.

Back

A complex number is a number that can be expressed in the form \( a + bi \), where \( a \) and \( b \) are real numbers and \( i \) is the imaginary unit.

Front

What is the imaginary unit \( i \)?

Back

The imaginary unit \( i \) is defined as \( i = \sqrt{-1} \).

Front

What is the degree of a polynomial?

Back

The degree of a polynomial is the highest power of the variable in the polynomial.

Front

What is the formula for the difference of squares?

Back

The difference of squares formula is \( a^2 - b^2 = (a - b)(a + b) \).

Front

What is the quadratic formula?

Back

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