Polynomials

Question 1

Difference of two squares

Answer 1

(a+b)(a-b)=a^2-b^2

Question 2

Long brackets

Answer 2

(x+y+z)(a+b+c+d)

x(a+b+c+d) +y(a+b+c+d) +z(a+b+c+d)

Question 3

When simplifying expressions look for

Answer 3

Common factors which can be numbers, variables or even brackets. If you spot a common factor you can take it outside the bracket

Then check if what you have multiplies out to give the original expression

Question 4

When a=1 in a quadratic put it into two brackets

Answer 4

Find two numbers that multiply to give c and add/subtract to give b

Question 5

Factorising a quadratic when a is not 1

Answer 5

Factorise 3x^2 + 4x -15

(3x )(x )

Need to find two numbers that multiply together to make 15 but which will give you 4x when you multiply them by x and 3x and then add and subtract them…

Here they are 5 and 3 which give 9x and 5x which when you subtract they give 4x. So they are the numbers that go in the bracket.

Question 6

Simplifying algebraic fractions

Answer 6

Look for common factors in the numerator and denominator - factorise top + bottom and cancel.

Question 7

What to do if there is a fraction in the numerator or denominator?

Answer 7

Multiply the whole thing by the same factor to get rid of it.

Example on page 9

Question 8

Multiplying algebraic fractions.

Answer 8

Same as normal multiply top and bottom.

Question 9

Dividing algebraic fractions:

Just like normal fractions

Answer 9

Multiply by its reciprocal… (1 divides by the original thing)

For fractions you just turn fractions upside down and times

Question 10

Reciprocal =

Answer 10

1 divided by x

Question 11

Polynomials add and subtracting fractions

Answer 11

Find common denominator.