Example Card: Factoring When c is Positive
Master Factoring When c is Positive in Grade 9 Algebra 1. Let's see how finding two simple numbers can unlock the factors of a trinomial, which is an important key idea from this lesson.
Key Concepts
Let's see how finding two simple numbers can unlock the factors of a trinomial, which is an important key idea from this lesson.
Factor the trinomial $x^2 + 8x + 15$.
1. In this trinomial, $b$ is $8$ and $c$ is $15$. Because $b$ is positive, it must be the sum of two positive numbers that are factors of $c$. 2. Two pairs of positive numbers have a product of $15$. $$ (1)(15) = 15 \qquad (3)(5) = 15 $$ 3. Only one pair of these numbers has a sum of $8$. $$ (1) + (15) = 16 \qquad (3) + (5) = 8 $$ 4. The constant terms in the binomials are $3$ and $5$. $$ x^2 + 8x + 15 = (x+3)(x+5) $$ 5. The factored form of $x^2 + 8x + 15$ is $(x+3)(x+5)$.
Common Questions
What is Factoring When c is Positive in Algebra 1?
Factoring When c is Positive is a core Grade 9 Algebra 1 concept covering properties and applications.
How do you work with Factoring When c is Positive in Grade 9 math?
Factoring a trinomial like is like being a detective trying to figure out which two smaller expressions, called binomials, were multiplied together to create it. Think of it as 'un-multiplying' to find the original ingredients! Here’s the main trick: For a trinomial in the form , you need to find tw.
What are common mistakes when learning Factoring When c is Positive?
Factoring a trinomial like is like being a detective trying to figure out which two smaller expressions, called binomials, were multiplied together to create it. Think of it as 'un-multiplying' to find the original ingredients! Here’s the main trick: For a trinomial in the form , you need to find two numbers that: 1. Multiply to equal the last numb.