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Get Started Now- Lesson: 1a54:32
- Lesson: 1b10:52
- Lesson: 2a5:28
- Lesson: 2b1:03
- Lesson: 2c1:10
- Lesson: 2d10:06
- Lesson: 3a2:33
- Lesson: 3b6:26

A Pascal's triangle is a number triangle of the binomial coefficients. The first row of the triangle is always 1.

- 1.Expand:a)i) ${\left( {a + b} \right)^0}$ =

ii) ${\left( {a + b} \right)^1}$ =

iii) ${\left( {a + b} \right)^2}$ =

iv) ${\left( {a + b} \right)^3}$ =

Use Pascal’s Triangle to expand:

i) ${\left( {a + b} \right)^4}$ =

ii) ${\left( {a + b} \right)^5}$ =b)Investigating Pascal’s Trianglec)Use Pascal’s Triangle to expand:

i) ${\left( {a + b} \right)^4}$ =

ii) ${\left( {a + b} \right)^5}$ = - 2.Pascal’s Triangle - sum of numbers in each rowa)
Row Pattern Corresponding binomial expression Sum of the numbers in,the row Express the sum as a power of 2 1 1 ${\left( {a + b} \right)^0}$ 2 1 1 ${\left( {a + b} \right)^1}$ 3 1 2 1 ${\left( {a + b} \right)^2}$ 4 1 3 3 1 ${\left( {a + b} \right)^3}$ 5 1 4 6 4 1 ${\left( {a + b} \right)^4}$ : : : : : n ${\left( {a + b} \right)^{n - 1}}$ n+1 ${\left( {a + b} \right)^n}$ b)What is the sum of the numbers in the 10th row of Pascal’s Triangle?c)What is the sum of the coefficients in the expansion of ${\left( {a + b} \right)^{50}}$ ?d)Express the number pattern of Pascal’s triangle in "combination" form, then deduce the following formula:

$\;$ ${}_n^{}{C_0}$ + ${}_n^{}{C_1}$ + ${}_n^{}{C_2}$ + ${}_n^{}{C_3}$ + … + ${}_n^{}{C_{n - 2}}$ + ${}_n^{}{C_{n - 1}}$ + ${}_n^{}{C_n}$ = ${2^n}$ - 3.Without using a calculator, evaluate:a)${}_{10}^{}{C_0}$ + ${}_{10}^{}{C_1}$ + ${}_{10}^{}{C_2}$ + … + ${}_{10}^{}{C_9}$ + ${}_{10}^{}{C_{10}}$b)${}_5^{}{C_0}$ + ${}_5^{}{C_1}$ + ${}_5^{}{C_2}$ + ${}_5^{}{C_3}$ + ${}_5^{}{C_4}$

9.

Polynomials

9.1

Characteristics of polynomials

9.2

Adding and subtracting polynomials

9.3

Multiplying polynomial by polynomial

9.4

Polynomial long division

9.5

Polynomial synthetic division

9.6

Remainder theorem

9.7

Rational zeroes theorem

9.8

Characteristics of polynomial graphs

9.9

Repeated factors (Multiplicities) in polynomials

9.10

Imaginary zeros of polynomials

9.11

Determining the equation of a polynomial function

9.12

Pascal's triangle

9.13

Binomial theorem

9.14

What is a polynomial function?

9.15

Applications of polynomial functions

9.16

Solving polynomial inequalities

9.17

Fundamental theorem of algebra

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