Short Quiz

Question 1 of 5

Simplify \(\frac{x^{2}-25}{x^{2}-3x-10}\), assuming the original denominator is non-zero.

A \(\frac{x-5}{x-2}\) B \(\frac{x+5}{x+2}\) C \(\frac{x+5}{x-2}\) D \(\frac{x-5}{x+2}\)

Select one option. Answers are shown after the test.

Question 2 of 5

Factorise \(x^{2}+13x+40\).

A \((x+4)(x+10)\) B \((x+5)(x+8)\) C \((x-5)(x-8)\) D \((x+2)(x+20)\)

Select one option. Answers are shown after the test.

Question 3 of 5

Factorise \(8m^{3}-125n^{3}\).

A \((2m-5n)(4m^{2}+10mn+25n^{2})\) B \((2m-5n)(4m^{2}-10mn+25n^{2})\) C \((2m+5n)(4m^{2}-10mn+25n^{2})\) D \((8m-125n)(m^{2}+mn+n^{2})\)

Select one option. Answers are shown after the test.

Question 4 of 5

Factorise \(27x^{3}+64y^{3}\).

A \((3x+4y)(9x^{2}-12xy+16y^{2})\) B \((3x-4y)(9x^{2}+12xy+16y^{2})\) C \((3x+4y)(9x^{2}+12xy+16y^{2})\) D \((27x+64y)(x^{2}-xy+y^{2})\)

Select one option. Answers are shown after the test.

Question 5 of 5

Why is \(n^{3}-n\) divisible by \(6\) for every natural number \(n\)?

A Because \(n^{3}-n=n(n-1)(n+1)\), a product of three consecutive integers. B Because every cube is divisible by \(6\). C Because \(n^{3}-n=(n-1)^{3}\). D Because \(n^{3}\) and \(n\) are always even.

Select one option. Answers are shown after the test.

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