C2 (Polynomials, Factor Theorem, Completing the Square)

Question 1

2.1 (full)

Answer 1

Question 2

Answer 2

Question 3

the factor theorem
for polynomial f(x) = (x-a)(x-b) what are roots, what are factors

Answer 3

if (x-a) is a factor of polynomial f(x):
f(a) = 0
x = a is a root of the equation f(x) = 0
the converse is true - if f(a) = 0, (x-a) is a factor of f(x)

Question 4

2.2

Answer 4

2.2

Question 5

factorise fully (into 3 brackets)

Answer 5

Question 6

the discriminant

Answer 6

b² - 4ac

if > 0 then 2 roots (crosses x axis)
if = 0 then 1 root - but this is a double root (tangent to x axis)
if < 0 then no roots (doesnt cross x axis)

Question 7

finding the turning point:
y=a(x+p)²+q

Answer 7

(-p,q)

Question 8

solve by completing the square (and find the turning point)

Answer 8