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Prove that (2*a^2 + 7a + 3)/(a + 3) is an odd number for any positive integer number, a.

We see that the numerator is a quadratic, so we factorise it to obtain:

(2a + 1)(a + 3)/(a + 3) = 2a + 1

Since a is a positive integer, we know that 2*a + 1 will always be an odd nu...

Answered by Nadia M. • Maths tutor

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Find the length of the hypotenuse if the right angled triangle's other two sides are of length 5cm and 12cm.

Use of a^2+b^2=c^2 must be included in the answer.

Furthermore the numbers must be put in the above equation to give: 5^2+12^2=c^2

This must then be solved to give: 169^0.5=c

The answ...

Answered by Sarah W. • Maths tutor

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4x^2 + 8x + 3 can be written in the form a(x + b)^2 + c where a, b and c are whole numbers. Work out the values of a, b and c.

Factorise 4x²+ 8x + 3 = 4(x²+ 2x + 3/4) divide the coefficient of x by 2: 2/2=1 Now x²+2x = (x+1)²-1² = (x+1)²-1 Hence, 4((x+1)²

Answered by Donny W. • Maths tutor

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Factorise x^2 - x - 6

You need 2 numbers that multiply together to make -6, and add together to make -1. The options to multiply to make -6 are: 6 and -1, -6 and 1, -3 and 2, 3 and -2. Looking at this list, the pair of numbers...

Answered by Charlotte G. • Maths tutor

5274 Views

Solve the equation 9x - 15 = 5 - x

This question is about rearranging the equation so that all the known variables are on one side and all the unknown variables are on the other side. To start with we can look at the x terms, remembering t...

Answered by Ella S. • Maths tutor

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