FACTORING PERFECT SQUARE TRINOMIALS

Front

What is a perfect square trinomial?

Back

A perfect square trinomial is a polynomial that can be expressed as the square of a binomial, typically in the form (a + b)² = a² + 2ab + b² or (a - b)² = a² - 2ab + b².

Front

How can you identify a perfect square trinomial?

Back

A trinomial is a perfect square if the first and last terms are perfect squares and the middle term is twice the product of the square roots of the first and last terms.

Front

What is the standard form of (x - 3)²?

Back

The standard form is x² - 6x + 9.

Front

What is the value of k in the perfect square trinomial 225a² + 30ab + k?

Back

The value of k is b².

Front

Which of the following is NOT a perfect square trinomial: x² - 10x + 20 or x² - 6x + 9?

Back

x² - 10x + 20 is NOT a perfect square trinomial.

Front

Is the polynomial x² - 16x + 16 a perfect square?

Back

Yes, it is a perfect square and can be factored as (x - 8)².

Front

What is the factored form of a perfect square trinomial?

Back

The factored form of a perfect square trinomial a² + 2ab + b² is (a + b)², and a² - 2ab + b² is (a - b)².

Front

What are the steps to factor a perfect square trinomial?

Back

1. Identify the first and last terms as perfect squares. 2. Check if the middle term is twice the product of the square roots of the first and last terms. 3. Write the trinomial as the square of a binomial.

Front

Can a perfect square trinomial have negative coefficients?

Back

Yes, a perfect square trinomial can have negative coefficients, as long as it still fits the form of (a ± b)².

Front

What is the relationship between the coefficients in a perfect square trinomial?

Back

In a perfect square trinomial of the form a² + 2ab + b², the coefficient of the middle term (2ab) is equal to twice the product of the coefficients of the first and last terms.