Question

7.1 polynomials quiz

identify the polynomial: (x^2 - 4x + 4)

binomial, quadratic
monomial, linear
trinomial, cubic
trinomial, quadratic

Explanation:

Count the number of terms

The given expression is \(x^2 - 4x + 4\).
It consists of three distinct terms separated by addition or subtraction:

1. \(x^2\)
2. \(-4x\)
3. \(4\)

A polynomial with exactly three terms is called a trinomial.

Determine the degree of the polynomial

The degree of a polynomial is the highest exponent of its variable.

• The term \(x^2\) has a degree of 2.
• The term \(-4x\) has a degree of 1.
• The constant term \(4\) has a degree of 0.

The highest exponent is 2, so the degree of the polynomial is 2.
A polynomial of degree 2 is called a quadratic polynomial.

Combine the classifications

Combining the classification by the number of terms (trinomial) and by the degree (quadratic), the polynomial \(x^2 - 4x + 4\) is a trinomial, quadratic.

Answer:

• Binomial, quadratic
• Monomial, linear
• Trinomial, cubic
• Trinomial, quadratic (Correct answer)