Expanding and factorising quadratics

problem
Poly fibs

Age

16 to 18

Challenge level

A sequence of polynomials starts 0, 1 and each poly is given by combining the two polys in the sequence just before it. Investigate and prove results about the roots of the polys.
problem
Leftovers

Age

14 to 16

Challenge level

Weekly Problem 26 - 2008
If $n$ is a positive integer, how many different values for the remainder are obtained when $n^2$ is divided by $n+4$?
problem
How old am I?

Age

14 to 16

Challenge level

In 15 years' time my age will be the square of my age 15 years ago. Can you work out my age, and when I had other special birthdays?
problem
Pair products

Age

14 to 16

Challenge level

Choose four consecutive whole numbers. Multiply the first and last numbers together. Multiply the middle pair together. What do you notice?
problem
Finding factors

Age

14 to 16

Challenge level

Can you find the hidden factors which multiply together to produce each quadratic expression?
problem
Factorising with multilink

Age

14 to 16

Challenge level

Can you find out what is special about the dimensions of rectangles you can make with squares, sticks and units?
problem
Hollow squares

Age

14 to 16

Challenge level

Which armies can be arranged in hollow square fighting formations?
problem
Quadratic patterns

Age

14 to 16

Challenge level

Surprising numerical patterns can be explained using algebra and diagrams...
problem
Plus minus

Age

14 to 16

Challenge level

Can you explain the surprising results Jo found when she calculated the difference between square numbers?
problem
Fair shares?

Age

14 to 16

Challenge level

A mother wants to share some money by giving each child in turn a lump sum plus a fraction of the remainder. How can she do this to share the money out equally?