Factoring Trinomials (a=1)

Front

What is a trinomial?

Back

A trinomial is a polynomial that consists of three terms, typically in the form ax^2 + 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 general form of a factored trinomial when a=1?

Back

The general form is (x + p)(x + q), where p and q are numbers that add to b and multiply to c.

Front

How do you identify the coefficients in a trinomial of the form ax^2 + bx + c?

Back

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.

Front

What is the first step in factoring a trinomial when a=1?

Back

Identify two numbers that multiply to 'c' and add to 'b'.

Front

How do you factor the trinomial z^2 + 100z + 99?

Back

Find two numbers that multiply to 99 and add to 100, which are 1 and 99. Thus, it factors to (z + 1)(z + 99).

Front

What is the factored form of y^2 - 9y + 18?

Back

The factored form is (y - 3)(y - 6), since -3 and -6 multiply to 18 and add to -9.

Front

What is the significance of the signs in the factors of a trinomial?

Back

The signs in the factors indicate whether the roots of the trinomial are positive or negative, affecting the sum and product of the roots.

Front

How do you check if your factorization of a trinomial is correct?

Back

You can check by multiplying the factors back together to see if you obtain the original trinomial.

Front

What is the factored form of m^2 + 6m - 16?

Back

The factored form is (m - 2)(m + 8), since -2 and 8 multiply to -16 and add to 6.