Factoring Trinomials with lead Coefficient

Front

What is a trinomial?

Back

A trinomial is a polynomial with three terms, typically in the form ax² + bx + c.

Front

What does it mean to factor a trinomial?

Back

Factoring a trinomial involves rewriting it as a product of two binomials.

Front

What is the lead coefficient in a trinomial?

Back

The lead coefficient is the coefficient of the term with the highest degree (the first term) in a polynomial.

Front

How do you factor a trinomial with a lead coefficient greater than 1?

Back

To factor a trinomial with a lead coefficient greater than 1, find two numbers that multiply to ac (a is the lead coefficient and c is the constant term) and add to b (the coefficient of x).

Front

Factor the trinomial: 9x² - 6x - 8

Back

(3x + 2)(3x - 4)

Front

Factor the trinomial: 4h² - 17h + 4

Back

(h - 4)(4h - 1)

Front

Factor the trinomial: 5x² + 17x + 6

Back

(5x + 2)(x + 3)

Front

What is the first step in factoring a trinomial?

Back

The first step is to identify the coefficients a, b, and c in the trinomial ax² + bx + c.

Front

What is the significance of the discriminant in factoring?

Back

The discriminant (b² - 4ac) helps determine the nature of the roots of the trinomial; if it's positive, there are two real roots, if zero, one real root, and if negative, no real roots.

Front

Factor the trinomial: 4x² - 25x + 25

Back

(x - 5)(4x - 5)