Hon IM1 -- 2-5 Savvas Probs

Factoring a trinomial is like factoring a number because both involve finding components that multiply to give the original expression. How is factoring a trinomial different from factoring a number?

• Factoring a trinomial involves variables, while factoring a number involves only numbers.

• Factoring a trinomial is always easier than factoring a number.

• Factoring a number always results in prime numbers, while factoring a trinomial does not.

• Factoring a trinomial and factoring a number are exactly the same.

Using algebra tiles, what is the process to factor a trinomial and determine its binomial factors?

• Arrange the tiles to form a rectangle and identify the side lengths as the binomial factors.

• Count all the tiles and write the trinomial as a sum.

• Group the tiles by color and add their values.

• Remove all zero pairs and write the remaining tiles as a product.

• Both have the same constant terms in their binomial factors, but the signs of the linear terms are opposite.

• Both have the same linear terms in their binomial factors, but the constant terms are different.

• Both have identical binomial factors.

• Both have completely different binomial factors.

• The student used the wrong signs for the factors.

• The student added the factors instead of multiplying them.

• The student did not find two numbers that multiply to -26 and add to -11.

• The student factored the trinomial as a perfect square.

• 9

• -9

• 10

• -10

What is missing from the last term of the trinomial x^2 + 5xy + 4 so that it is factorable as the product of binomials?

• 4xy

The sign of the last term of a trinomial helps you know what type of factors you are looking for because:

• A positive sign means both factors have the same sign; a negative sign means the factors have opposite signs.

• A positive sign means the factors are always negative; a negative sign means the factors are always positive.

• The sign of the last term does not affect the type of factors.

• A positive sign means the trinomial cannot be factored.

• (x + 3) in. and (x + 4) in.

• (x + 2) in. and (x + 6) in.

• (x + 1) in. and (x + 12) in.

• (x + 7) in. and (x + 1) in.

Factor each trinomial represented by the algebra tiles. SEE EXAMPLE 1.

• (x + 2)(x + 3)

• (x + 1)(x + 5)

• (x + 3)(x + 4)

• (x + 2)(x + 4)

Factor each trinomial represented by the algebra tiles.

• (x + 2)(x + 3)

• (x + 1)(x + 4)

• (x + 3)(x + 3)

• (x + 2)(x + 2)