Polynomials Flashcards

1
Q

Polynomial

A

Expression in the form ax^5 + bx^4 + cx^3 etc..

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2
Q

Expression in the form ax^5 + bx^4 + cx^3 etc..

A

Polynomial

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3
Q

Coefficient

A

No. in front of a certain variable

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4
Q

No. in front of a certain variable

A

Coefficient

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5
Q

Two things to remember when writing polynomials

A

You do not require all the powers

Powers must be written in descending order

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6
Q

What is a root of a polynomial function

A

a value of x that makes f(x) = 0

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7
Q

Factorise 5x^3 - 10x

A

5x (x^2 - 2)

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8
Q

Factorise 9x^2 - 16

A

(3x - 4) (3x + 4)

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9
Q

Factorise 6x^2 - 7x - 5

A

(2x + 1) (3x - 5)

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10
Q

Find the roots of 3x^2 - 12 = 0

A

2 and -2

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11
Q
A
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12
Q
A
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13
Q

Value of x^4 - 5x^3 + 6x + 3 when x = -3

A
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14
Q

Value of a missing power

A

0

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15
Q

Quotient

A

Product of division

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16
Q

Product of division

A

Quotient

17
Q

Remainder

A

Number left from division

18
Q

Number left from division

A

Remainder

19
Q

Divisor

A

Number you are dividing by

20
Q

Number you are dividing by

A

Divisor

21
Q

Quotient divisor remainder original relationship

A

Original = divisor x quotient + remainder

22
Q

Method for synthetic division

A
  1. Draw L shape and write down coefficients
  2. Set divisor = 0 and find value
  3. Divide
  4. Write down quotient and remainder
23
Q
  1. Draw L shape and write down coefficients
  2. Set divisor = 0 and find value
  3. Divide
  4. Write down quotient and remainder
A

Method for synthetic division

24
Q
A
25
Q
A
26
Q
A
27
Q

Factor

A

Number that divides a given number exactly and does not leave a remainder

28
Q

Number that divides a given number exactly and does not leave a remainder

A

Factor

29
Q

What does it mean if f(h) = 0

A

(x - h) is a factor of f(x)

30
Q
A
31
Q
A
32
Q
A
33
Q
A

x=-1

x=2

x=3

34
Q
A

x = 3

x = 3/2

x = -3

35
Q
A

p = 3

36
Q
A

a = 5, b = -22

37
Q

Factorise 2x^2 - 3x - 2

A

(2x + 1) (x - 2)

38
Q

Factorise 3x^2 + 8x - 3

A

(x + 3) (3x - 1)

39
Q

Solve 4x^2 - 4x - 3

A

(2x - 3) (2x + 1)