4 - polynomials

Question 1

polynomial

Answer 1

expression with powers of x

Question 2

degree of a polynomial

Answer 2

largest power

Question 3

11 / 4 = 2 rem 3 (names of parts of a division)

Answer 3

11 - dividend
4 - divisor
2 - quotient
3 - remainder

Question 4

dividing algebraically

Answer 4

• do long division
• take the first term of the dividend divide it by the first term of the divisor
• then times the divisor by the result
• subtract this from the first two terms of the dividend
• then repeat !

Question 5

remainder theorem

Answer 5

for a polynomial f(x) the remainder when f(x) is divided by (x-a) is f(a)

Question 6

factor theorem

Answer 6

if f(a) = 0 then by remainder theorem the remainder is 0 - thus (x-a) is a factor of f(x)

Question 7

how to find remainder in algebraic division

Answer 7

if you do f(x)/ (x-a) as the division the remainder is f(a) - substitute a into the equation as x

Question 8

sketch the graph of a polynomial

Answer 8

• decide on basic shape considering order and +/-
• set x=0 and find y intercept
• factorise/ find roots
• decide how curve meets with x axis at each intercept eg turns/crosses/turns twice
• draw curve

Question 9

linear

Answer 9

x
straight line

Question 10

quadratic

Answer 10

x^2
smile / hill

Question 11

cubic

Answer 11

x^3
updownup/ downupdown

Question 12

quartic

Answer 12

x^4
W/M

Question 13

how to find the equation of a polynomial from its graph

Answer 13

-uses shape and position of x intercepts to write down factors
- use any other points eg y intercept to find a constant factor