Cubics

Question 1

Factorising cubics given one factor

Answer 1

1) write down the factor (x-k)( ).
2) put in the x2 term.
3) put in the constant.
4) put in the x term by comparing the numbers of x’s on both sides.
5) check there are the same number of x2’s and xs on both sides.
6) factorise the quadratic found if possible.

Question 2

Shape of cubic graphs

Answer 2

Looks like end of my signature.

Coefficient of x3 positive ‘bottom left to top right. Like signature

Question 3

The power of (x-a)^n affects what happens at x=a

Answer 3

Even power= The curve touches the X axis but does not cross it

Odd power= The curve crosses the X axis

Question 4

Sketching a cubic graph

Answer 4

Find where the function is 0

Example x(x-1)(2x+1)

Would be x= 0, 1, -1/2

Get better from practice ^^ is quite a bad flash card

Question 5

Factorising a cubic given no factors…

Answer 5

Use the factor theorem to find the first factor.

If f(x) is a polynomial, and f(k) = 0, then (x-k) is a factor of f(x)

Question 6

Polynomial

Answer 6

In mathematics, a polynomial is an expression consisting of variables and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponents of variables.