Factoring binomials

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This lesson contains 30 slides, with interactive quizzes, text slides and 1 video.

Items in this lesson

Factoring binomials

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Slide 1 - Slide

Today

Start (5 min)

New subject (25 min)

Bettermarks (20 min)

Exercise together (10 min)

Bettermarks (15 min)

End lesson (5 min)

Slide 2 - Slide

Slide 3 - Video

Slide 4 - Slide

f (x) = - 3 x^{​ 2 ​ ​} + 4 x + 3

Slide 5 - Slide

f (x) = - 3 x^{​ 2 ​ ​} + 4 x + 3

x = \frac{​ - b \pm \sqrt ​ b ^{​ 2 ​ ​} - 4 a c ​ ​ ​ ​ ​}{​ 2 a ​}

Slide 6 - Slide

Find a, b and c in the formula

f (x) = - 3 x^{​ 2 ​ ​} + 4 x + 3

timer

1:00

Slide 7 - Open question

f (x) = - 3 x^{​ 2 ​ ​} + 4 x + 3

x = \frac{​ - b \pm \sqrt ​ b ^{​ 2 ​ ​} - 4 a c ​ ​ ​ ​ ​}{​ 2 a ​}

a = - 3

b = 4

c = 3

Slide 8 - Slide

Solving with the quadratic formula

f (x) = - 3 x^{​ 2 ​ ​} + 4 x + 3

Slide 9 - Slide

Solving with the quadratic formula

0 = - 3 x^{​ 2 ​ ​} + 4 x + 3

Slide 10 - Slide

Solving with the quadratic formula

0 = - 3 x^{​ 2 ​ ​} + 4 x + 3

x = \frac{​ - b \pm \sqrt ​ b ^{​ 2 ​ ​} - 4 a c ​ ​ ​ ​ ​}{​ 2 a ​}

Slide 11 - Slide

Solving with the quadratic formula

0 = - 3 x^{​ 2 ​ ​} + 4 x + 3

x = \frac{​ - b \pm \sqrt ​ b ^{​ 2 ​ ​} - 4 a c ​ ​ ​ ​ ​}{​ 2 a ​}

a = - 3

b = 4

c = 3

Slide 12 - Slide

Solving with the quadratic formula

0 = - 3 x^{​ 2 ​ ​} + 4 x + 3

x = \frac{​ - b \pm \sqrt ​ b ^{​ 2 ​ ​} - 4 a c ​ ​ ​ ​ ​}{​ 2 a ​}

a = - 3

b = 4

c = 3

x = \frac{​ - 4 \pm \sqrt ​ 4 ^{​ 2 ​ ​} - 4 \cdot - 3 \cdot 3 ​ ​ ​ ​ ​}{​ 2 \cdot - 3 ​}

Slide 13 - Slide

Solving with the quadratic formula

0 = - 3 x^{​ 2 ​ ​} + 4 x + 3

x = \frac{​ - b \pm \sqrt ​ b ^{​ 2 ​ ​} - 4 a c ​ ​ ​ ​ ​}{​ 2 a ​}

a = - 3

b = 4

c = 3

x = \frac{​ - 4 \pm \sqrt ​ 4 ^{​ 2 ​ ​} - 4 \cdot - 3 \cdot 3 ​ ​ ​ ​ ​}{​ 2 \cdot - 3 ​}

x = \frac{​ - 4 + \sqrt ​ 5 2 ​ ​ ​ ​ ​}{​ - 6 ​}

x = \frac{​ - 4 - \sqrt ​ 5 2 ​ ​ ​ ​ ​}{​ - 6 ​}

Slide 14 - Slide

Solving with the quadratic formula

0 = - 3 x^{​ 2 ​ ​} + 4 x + 3

x = \frac{​ - b \pm \sqrt ​ b ^{​ 2 ​ ​} - 4 a c ​ ​ ​ ​ ​}{​ 2 a ​}

a = - 3

b = 4

c = 3

x = \frac{​ - 4 \pm \sqrt ​ 4 ^{​ 2 ​ ​} - 4 \cdot - 3 \cdot 3 ​ ​ ​ ​ ​}{​ 2 \cdot - 3 ​}

x = \frac{​ - 4 + \sqrt ​ 5 2 ​ ​ ​ ​ ​}{​ - 6 ​}

x = \frac{​ - 4 - \sqrt ​ 5 2 ​ ​ ​ ​ ​}{​ - 6 ​}

x \approx - 0, 54

x \approx 1, 87

Slide 15 - Slide

Remove the brackets

m (m - 3)

timer

0:45

2 m - 3

m^{​ 2 ​ ​} - 3

m^{​ 2 ​ ​} - 3 m

2 m - 3 m

Slide 16 - Quiz

Remove the brackets

m (m - 3)

Slide 17 - Slide

Quadratic formulas

c = 0

y = 4 x^{​ 2 ​ ​} - 8 x + 12

y = - x^{​ 2 ​ ​} + 25 x

y = x^{​ 2 ​ ​}

y = 9 x^{​ 2 ​ ​} - 13

y = - 5 x^{​ 2 ​ ​} + 2 x

y = x^{​ 2 ​ ​} + 9 x

y = 3 x^{​ 2 ​ ​} - 12 x

y = - x^{​ 2 ​ ​} - x

Slide 18 - Slide

13.2: Factoring binomials

You can factorize (=make brackets) a formula if c = 0. You have to find the biggest number and letter, that is a divisor of both terms

Example: Factor

You can divide both and by

Answer:

y = 6 x^{​ 2 ​ ​} + 4 x

6 x^{​ 2 ​ ​}

4 x

2 x

y = 2 x (3 x + 2)

6 x^{​ 2 ​ ​} : 2 x = 3 x

4 x : 2 x = 2

timer

4:00

Slide 19 - Slide

Example

Factor

16 x^{​ 2 ​ ​} - 12 x

Slide 20 - Slide

Factor

18 p^{​ 2 ​ ​} + 3 p

timer

1:30

Slide 21 - Open question

7.2 Solving equations

Example: Solve

Step 1, factorize:

Step 2, make two equations: or

Step 3, use the balance method: or

Step 4, answer: or

15 m^{​ 2 ​ ​} + 6 m = 0

3 m (5 m + 2) = 0

3 m = 0

5 m + 2 = 0

m = 0

5 m = - 2

m = - \frac{​ 2 ​ ​}{​ 5 ​}

m = 0

timer

3:00

Slide 22 - Slide

Example

Solve

2 p^{​ 2 ​ ​} + 7 p = 0

Slide 23 - Slide

Solve the equation

2 x^{​ 2 ​ ​} + 8 x = 0

timer

2:30

Slide 24 - Open question

Solve the equation

2 x^{​ 2 ​ ​} + 8 x = 0

Slide 25 - Slide

Bettermarks

Work on 13.2
20 min
Raise your finger if you have any questions or when you're finished
Communicate in English please

timer

20:00

Slide 26 - Slide

Question together

Ipads on the corner of the table

Slide 27 - Slide

13.2 Question 16

Slide 28 - Slide

Question 15

Slide 29 - Slide

Bettermarks

Work on 13.2
Until the end of the lesson
Raise your finger if you have any questions or when you're finished
Communicate in English please

Slide 30 - Slide

Factoring binomials

Items in this lesson

Slide 1 - Slide

Slide 2 - Slide

Slide 3 - Video

Slide 4 - Slide

Slide 5 - Slide

Slide 6 - Slide

Slide 7 - Open question

Slide 8 - Slide

Slide 9 - Slide

Slide 10 - Slide

Slide 11 - Slide

Slide 12 - Slide

Slide 13 - Slide

Slide 14 - Slide

Slide 15 - Slide

Slide 16 - Quiz

Slide 17 - Slide

Slide 18 - Slide

Slide 19 - Slide

Slide 20 - Slide

Slide 21 - Open question

Slide 22 - Slide

Slide 23 - Slide

Slide 24 - Open question

Slide 25 - Slide

Slide 26 - Slide

Slide 27 - Slide

Slide 28 - Slide

Slide 29 - Slide

Slide 30 - Slide

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