How do you factorise a quadratic equation where the coefficient of x² isn't 1?

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Using the formula ax2+bx+c, multiply the value of coefficient a, from your equation, with the value of c. Next, try to think of two factors of the number you just calculated, which also add together to make the value of coefficient b. Rewrite your equation with the x term split into two parts, where the new coefficients are the two factors you identified. Now you should think of your quadratic in two parts. Factorise the first two terms of the equation, followed by the second, then put them back together with the correct sign between them. You should notice that the two brackets in the new equation you have formed are identical, for example x(2x-1)+5(2x-1). We can now take out the bracket term as a factor (this will be the first bracket of your factorised quadratic) and the remaining terms will form the second factorised bracket, eg. for the example used before it would be (2x-1)(x+5). You have now successfully factorised your quadratic :)
In some cases, the quadratic you are given cannot be factorised, so we must use the quadratic formula if you are required to find its solutions

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Grace R. is an online Maths tutor with MyTutor studying at Cardiff University

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