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A Number Plus Its Reciprocal: Use Factorisation

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Exploring Algebraic Identities · Dimensions and area applications · 3:17

You'll learn: Clear a non-zero denominator, factor the quadratic and check both solutions.

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A Number Plus Its Reciprocal: Use Factorisation

3:17

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A Number Plus Its Reciprocal: Use Factorisation

You'll learn: Clear a non-zero denominator, factor the quadratic and check both solutions.

Now playing

Same topic

Dimensions and area applications

4

Recover a Rectangle’s Dimensions from Its Tiles
3:32
Recover a Rectangle’s Dimensions from Its Tiles
You'll learn: Turn a square, strips and unit squares into a factored area expression.
Find Pool Dimensions by Factoring an Equation
3:30
Find Pool Dimensions by Factoring an Equation
You'll learn: Model a length difference and known area, then apply the zero-product property.
Factor Areas and Volumes to Suggest Dimensions
3:52
Factor Areas and Volumes to Suggest Dimensions
You'll learn: Interpret factors as possible positive dimensions and divide an area by a given width.
How Much Area Does a Path Around a Square Add?
3:29
How Much Area Does a Path Around a Square Add?
You'll learn: Subtract the original square area from the larger outside square.

Next topic

Chapter challenge problems

4

Two Given Linear Factors Constrain a Quadratic
3:26
Two Given Linear Factors Constrain a Quadratic
You'll learn: Use the stated factors to compare coefficients and prove a relationship.
Use a Sum and Pairwise Products in a Cubic Identity
3:38
Use a Sum and Pairwise Products in a Cubic Identity
You'll learn: Express the second factor using the square-of-a-sum identity.
Why Is n³−n Always Divisible by Six?
3:26
Why Is n³−n Always Divisible by Six?
You'll learn: Factor into three consecutive integers and reason about divisibility.
Evaluate Cubic Expressions from a Given Relationship
3:36
Evaluate Cubic Expressions from a Given Relationship
You'll learn: Use a three-variable cubic identity to avoid finding individual variable values.

Next topic

Chance, randomness and the probability scale

6

Probability Measures How Likely Something Is
3:50
Probability Measures How Likely Something Is
You'll learn: Introduce uncertainty and likelihood using the chapter’s everyday questions.
Know What Could Happen Without Knowing What Will Happen
3:50
Know What Could Happen Without Knowing What Will Happen
You'll learn: Explain random experiments, individual trials and possible outcomes.
Why Can a Coin Toss Be a Fair Way to Decide?
3:39
Why Can a Coin Toss Be a Fair Way to Decide?
You'll learn: Connect fairness to a symmetric coin and an unbiased random toss.
Read the Probability Scale from Zero to One
3:47
Read the Probability Scale from Zero to One
You'll learn: Place impossible, less likely, even-chance, more likely and certain events on a scale.
Fractions, Decimals and Percentages Describe the Same Chance
4:01
Fractions, Decimals and Percentages Describe the Same Chance
You'll learn: Translate between numerical forms and interpret probability statements.
Explain a Likelihood Ranking Instead of Guessing a Number
4:00
Explain a Likelihood Ranking Instead of Guessing a Number
You'll learn: Rank the chapter’s everyday events and explain the assumptions behind each judgement.

Next topic

Experimental and theoretical probability

1

Estimate Probability from What Actually Happened
4:00
Estimate Probability from What Actually Happened
You'll learn: Define experimental probability as event frequency divided by trials.