**High School Number Sense Lesson 33: Substitution (Direct)**

Direct substitution questions appeared more times than there were tests this year:

**22 times**, on average at

**question # 33**. They look different from functions but operate in the same way.

**Number Dojo Level: 139**

For these question types, you will be given one or more variables and their equivalents, and a polynomial. You will be asked to find the value of the polynomial. A simple version is this:

**Let x = -5. Find 4 + 3x. ___**

**OrderOfOper**) to find your answer. So:

- 4 + 3x = 4 + 3(-5) = 4 + (-15) =
**-11**

For many of these questions, it will save you lots of time if you know how to factor polynomials. To learn how to do this, see https://www.khanacademy.org/math/algebra/polynomial-factorization.

**Example 1: Let x = -2. Find 3 - 4x. ___**

- 3 - 4x = 3 - 4(-2) = 3 + 8 =
**11**

**Example 2: Let x = -4. Find 3x - 2. ___**

- 3x - 2 = 3(-4) - 2 = -12 - 2 =
**-14**

**Example 3:**

**If x = 2 and y = 5, then 4x**

^{2}+ 4xy + y^{2}= ___1. This polynomial can be factored to become

**(2x + y)**.

^{2}2. Substitute 2 for x and 5 for y: (2x + y)

^{2}= [2(2) + 5]

^{2}= (4 + 5)

^{2}= 9

^{2}=

**81**.

**Example 4:**

**If x = 5 and y = -1, then x**

^{2}+ 2xy + y^{2}= ___1. This polynomial can be factored to become

**(x + y)**.

^{2}2. Substitute 5 for x and -1 for y: (x + y)

^{2}= [5 + (-1)]

^{2}= (5 - 1)

^{2}= 4

^{2}=

**16**.

**Example 5:**

**If x = 5 and y = 3, then 9x**

^{2}- 6xy + y^{2}= ___1. This polynomial can be factored to become

**(3x - y)**.

^{2}2. Substitute 5 for x and 3 for y: (3x - y)

^{2}= [3(5) - 3]

^{2}= (15 - 3)

^{2}= 12

^{2}=

**144**.

**Example 6:**

**If x = 5 and y = 2, then (x - y)(x**

^{2}+ 2xy + y^{2}) equals ___1. As seen above, (x

^{2}+ 2xy + y

^{2}) can be factored as

**(x + y)**. So now we have

^{2}**(x - y)(x + y)**.

^{2}2. Substitute 5 for x and 2 for y: (x - y)(x + y)

^{2}= (5 - 2)(5 + 2)

^{2}= (3)(7)

^{2}= 3(49) =

**147**.

**Here's a free worksheet to help you practice SubstDirect:**

substdirect.pdf |

**Up Next for High School: BaseNtoBase10**