Factoring Trinomials

Front

What is the general form of a trinomial?

Back

A trinomial is generally expressed in the form ax² + bx + c, where a, b, and c are constants.

Front

How do you factor a trinomial of the form x² + bx + c?

Back

To factor a trinomial of the form x² + bx + c, find two numbers that multiply to c and add to b. These numbers will be the coefficients of the binomial factors.

Front

What is the factored form of the trinomial 4h² - 17h + 4?

Back

The factored form is (h - 4)(4h - 1).

Front

What are the factors and solutions of the equation x² + 2x - 3 = 0?

Back

The factors are (x - 1)(x + 3) and the solutions are x = 1 and x = -3.

Front

How do you determine the signs of the factors of a trinomial when c is negative?

Back

If c is negative, one factor will be positive and the other will be negative.

Front

What is the factored form of the trinomial x² - 15x + 50?

Back

The factored form is (x - 10)(x - 5).

Front

What is the factored form of n² + 5n - 6?

Back

The factored form is (n - 1)(n + 6).

Front

What is the significance of the leading coefficient 'a' in a trinomial?

Back

The leading coefficient 'a' affects the width and direction of the parabola represented by the trinomial when graphed.

Front

What is the process of factoring by grouping?

Back

Factoring by grouping involves rearranging terms and factoring out common factors from pairs of terms.

Front

What is the difference between factoring and expanding a polynomial?

Back

Factoring is the process of breaking down a polynomial into simpler components (factors), while expanding is the process of multiplying out the factors to obtain the polynomial.