Factoring Trinomials (when a = 1)

What is the significance of the constant term in a trinomial?

• It determines the leading coefficient of the trinomial.

• It affects the product of the binomial factors.

• It indicates the degree of the polynomial.

• It represents the sum of the roots of the trinomial.

What is a trinomial?

• A polynomial with two terms

• A polynomial with three terms, typically in the form ax^2 + bx + c.

• A polynomial with four terms

• A polynomial with one term

Factor the trinomial: x^2 - 8x + 15

• (x - 5)(x - 3)

• (x - 6)(x - 2)

• (x + 5)(x + 3)

• (x - 4)(x - 4)

What does it mean to factor a trinomial?

• Rewriting it as a product of two binomials.

• Adding the coefficients of the terms.

• Finding the roots of the equation.

• Multiplying the trinomial by a constant.

What is the leading coefficient in a trinomial?

• The coefficient of the term with the highest degree, usually 'a' in ax^2.

• The constant term in the trinomial.

• The coefficient of the term with the lowest degree.

• The sum of all coefficients in the trinomial.

What is the standard form of a quadratic equation?

• ax^2 + bx + c = 0, where a, b, and c are constants.

• a^2 + b^2 = c^2, where a, b, and c are sides of a triangle.

• y = mx + b, where m is the slope and b is the y-intercept.

• x^2 - 4x + 4 = 0, which is a specific quadratic equation.

How can you check if your factorization is correct?

• By adding the coefficients of the factors together.

• By multiplying the binomial factors back together to see if you get the original trinomial.

• By finding the roots of the original trinomial.

• By graphing the factors on a coordinate plane.

What is the relationship between the roots of a trinomial and its factors?

• The roots of a trinomial are the values of x that make the trinomial equal to zero, and they correspond to the values that make each binomial factor equal to zero.

• The roots of a trinomial are always positive integers that represent the factors of the trinomial.

• The roots of a trinomial are the coefficients of the trinomial when expressed in standard form.

• The roots of a trinomial are the values of x that make the trinomial equal to one.

What is a binomial?

• A polynomial with three terms, such as (x + 3 + 5)

• A polynomial with two terms, such as (x + 3) or (k - 4)

• A single term polynomial, such as (5x)

• A polynomial with four terms, such as (x + 1 + 2 + 3)

How do you identify the coefficients in a trinomial?

• In the trinomial ax^2 + bx + c, 'a' is the coefficient of x, 'b' is the coefficient of x^2, and 'c' is the constant term.

• In the trinomial ax^2 + bx + c, 'a' is the constant term, 'b' is the coefficient of x^2, and 'c' is the coefficient of x.

• In the trinomial ax^2 + bx + c, 'a' is the coefficient of x^2, 'b' is the coefficient of x, and 'c' is the constant term.

• In the trinomial ax^2 + bx + c, 'a' is the coefficient of x^2, 'b' is the constant term, and 'c' is the coefficient of x.