The Grammar and Language of Algebra

In algebra, a letter such as x usually represents a 1($).

The phrase 'five more than x' is written algebraically as:

Select all statements that correctly describe algebra.

Translate 'twice a number y' into algebraic notation.

Which of the following is an algebraic expression?

Arrange the following from simplest symbolic form to more complex symbolic form.

Match the phrase with the correct algebraic form.

Match the phrase with the correct algebraic form.

Algebra acts as the 1($) of mathematics.

Classify the following into expressions or equations.

Classify the following into expressions or equations.

The symbol '=' means two quantities are:

Which of the following expressions qualifies as a polynomial in \(x\)?

What is the degree of the polynomial \(3x^5 + 2x^3 - x + 7\)?

According to the Remainder Theorem, if a polynomial \(p(x)\) is divided by \((x - a)\), the remainder is:

According to the Factor Theorem, if \(x = a\) is a zero of polynomial \(p(x)\), then:

Consider the arithmetic pattern below:

\(3^2\) is 1 bigger than \(2 \times 4\)

\(4^2\) is 1 bigger than \(3 \times 5\)

\(5^2\) is 1 bigger than \(4 \times 6\)

Which algebraic identity correctly generalises this pattern for any natural number \(n\)?

Match each instruction in ordinary language to its equivalent algebraic expression.

Match each instruction in ordinary language to its equivalent algebraic expression.

In mathematics, the process of reasoning from particular results to a general conclusion is called:

Pierre de Fermat conjectured that \(2^{2^n} + 1\) is prime for every natural number \(n\). Which mathematician disproved this conjecture, and for which value of \(n\)?

Consider the polynomial \(q(x) = x^2 - x - 6\).

Which of the following are zeros of \(q(x)\)? (Select all that apply.)

Sort the following polynomial types in ascending order based on the maximum number of zeros they can have.