Difference of Squares & Perfect Square Trinomials

Front

What is a perfect square trinomial?

Back

A perfect square trinomial is a quadratic expression that can be expressed as the square of a binomial. It has the form (a ± b)² = a² ± 2ab + b².

Front

Identify the components of a perfect square trinomial: a² - 2ab + b².

Back

a² is the square of the first term, -2ab is twice the product of the first and second terms, and b² is the square of the second term.

Front

What is the formula for factoring a difference of squares?

Back

The formula for factoring a difference of squares is a² - b² = (a - b)(a + b).

Front

Provide an example of a difference of squares.

Back

An example of a difference of squares is 16 - x², which can be factored as (4 - x)(4 + x).

Front

What is the result of factoring 9x² - 49y⁶?

Back

The result is (3x - 7y³)(3x + 7y³).

Front

What is a prime polynomial?

Back

A prime polynomial is a polynomial that cannot be factored into simpler polynomials with real coefficients.

Front

Is x² + 81 a perfect square trinomial?

Back

No, x² + 81 is not a perfect square trinomial; it is a sum of squares and cannot be factored over the real numbers.

Front

What is the significance of the discriminant in determining the nature of roots of a quadratic equation?

Back

The discriminant (b² - 4ac) indicates the nature of the roots: if positive, there are two distinct real roots; if zero, one real root; if negative, no real roots.

Front

How do you recognize a perfect square trinomial from its standard form?

Back

A perfect square trinomial can be recognized by its structure: it has a², b², and a middle term that is ±2ab.

Front

What is the factored form of 3x² - 75?

Back

The factored form is 3(x - 5)(x + 5).