**High School Number Sense Lesson 72: Finding the Remainder when a Polynomial Is Divided by a Binomial**

Sometimes math is just beautiful. Today is one of those times. Like several other concepts I've covered previously, this one is quite a bit easier than it looks. It appeared

**5 times**last year, with a median placement at

**question # 71**.

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A typical question in this category looks like this:

**The remainder when x**

^{3}+ 2x^{2}- 3 is divided by (x - 1) is ___**How to Solve:**

- Look at the binomial divisor. See what is subtracted from x: in this case,
**1**. - Substitute this number for x in the polynomial dividend, and solve:

^{3}+ 2(1

^{2}) - 3

= 1 + 2(1) - 3

= 1 + 2 - 3

=

**0**

**Example 1:**

**(4x**

^{3}+ x^{2}- 2x + 3) ÷ (x - 2) has a remainder of ___1.

**2**is being subtracted from x.

2. Substitute

**2**in for x: 4(2

^{3}) + 2

^{2}- 2(2) + 3 = 4(8) + 4 - 4 + 3 = 32 + 3 =

**35**

**Example 2:**

**(5x**

^{2}- 2x + 1) divided by (x - 3) has a remainder of ___1.

**3**is being subtracted from x.

2. Substitute

**3**in for x: 5(3

^{2}) - 2(3) + 1 = 5(9) - 6 + 1 = 45 - 5 =

**40**

**Example 3:**

**(x**

^{3}+ 2x^{2}- x + 1) ÷ (x + 1) has a remainder of ___1. Careful:

**-1**is being subtracted from x...in other words,

**x - (-1)**is the same as

**x + 1**.

2. Substitute

**-1**in for x: (-1)

^{3}+ 2(-1)

^{2}- (-1) + 1 = -1 + 2(1) + 1 + 1 = -1 + 2 + 2 =

**3**.

**Example 4:**

**(x**

^{3}+ 2x^{2}- x + 8) ÷ (x - 2) has a remainder of ___1.

**2**is being subtracted from x.

2. Substitute

**2**in for x: 2

^{3}+ 2(2

^{2}) - 2 + 8 = 8 + 2(4) - 2 + 8 = 8 + 8 - 2 + 8 =

**22**.

**Example 5:**

**The remainder of (2x**

^{2}- 5x - 1) ÷ (x + 3) is ___1. Careful:

**-3**is being subtracted from x.

2. Substitute

**-3**in for x: 2(-3)

^{2}- 5(-3) - 1 = 2(9) + 15 - 1 = 18 + 15 - 1 =

**32**.

**Check back soon for a free worksheet to help you practice RemainPolynom.**

**Up Next for High School: FunctionInver**