Pascal'S Triangle And Polynomials Worksheet printable pdf download

Pascal'S Triangle And Polynomials Worksheet

Pascal’s Triangle and Polynomials

The figure below is referred to as Pascal’s Triangle, named after Blaise Pascal who was a Frenchman

from the 1600s, even though it was in use for centuries before his birth. Pascal’s Triangle, which contains

infinitely many rows (even though in this one, it stops at 8 rows) and contains many patterns. Even the way it’s

developed is a pattern. Use the figure to answer the questions below.

1) Examine the numbers placed in the triangle. Find the pattern and

fill in the bottom two rows.

2) The outer two diagonals of the triangle are always the number ______.

3) Explain how a hexagonal cell is calculated.

4) There is a relationship between Pascal’s triangle and polynomials. Multiply out the polynomials below and

see what you get. Remember to use the distributive property or a website that expands polynomials. (There is

one at under “R.4 Interactive Multiplication of

polynomials”)

a) (x + y)

b) (x + y)

c) (x + y)

d) (x + y)

5) What is the relationship between the numbers in Pascal’s triangle and the polynomials you get above?

6) The second diagonals are what kind of numbers? ______________________________What is the difference

between each of the numbers in the diagonal?

7) Add each row of Pascal’s Triangle. Fill in the chart below based on the row and sum of numbers in each row.

Row

Sum

What kind of numbers are the sums of the numbers in the rows?

8) On the next page is a larger Pascal’s Triangle. Fill in the triangle.

9) What would be the sum of the final row of the Pascal’s Triangle on the next page?

10) Shade all of the even numbers in with a highlighter pen. Check out the pattern!

Pascal'S Triangle And Polynomials Worksheet