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The factor theorem is used to determine factors of large polynomials so that we can split large polynomials into a product of linear polynomials. Say we have a cubic polynomial of the form f(x)=x^3+bx^2+c...

Firstly multiply through by (x+1)(2x+1) to get rid of the fractions and then expand the brackets. Then gather the terms on one side to get a quadratic equation (ie 3x^2 - x -2=0) and then simply solve thi...

To integrate we increase the power by one, then divide by the new power.
Therefore the power (^2) increases to (^3), and the 6 is divided by the new power (^3), making the first number a 2.
2x^3...

Rearrange the second equation (or first) in terms of y (or x) y = 2-xthen subsitute into the other equation 3x + (2-x) = 4The solve for x : 2x = 2 x = 1then subsitute that value for x into any equation an...

x² + 4x + 3 is a quadratic equation. We're looking for a pair of numbers that add to make 4, and multiply together to make 3. Students should be encouraged to try options (e.g. 2 and 2).
T...