Solve the following quadratic equation by factorization. Show your working.
4x2+20x+8=-16First add 16 to both sides of the equation, this gives 4x2+20x+24=0 We always want to set the equation =0 for a quadratic as we are unable to solve it otherwise.Then we look to see if there is a factor in common with all three coefficients ( the numbers in front of x) Here the terms are 4, 20 and 24 One common factor is 4 so we divide the equation by 4 to give... x2+5x+6=0Next we have to look for any two numbers that add together to give +5 (from the middle term 5x) and times together to give +6 (Multiplying the together the remaining coefficients: 1 x 6), If you are unsure, list all the factors of 6 and then see which pairs add to +5Here there is only one pair of numbers that work successfully which are +3 and +2 At first glance 1 and 6 appear to work however due to having to have a negative sign in order to had to +5, they then only multiply to -6We then split the 5x into +3x which gives x2+2x+ 3x+6=0We then look for the maximum number of factors for x2 and 2x- here the only factor in common with both terms is x So we set out the bracket like this... x(Then we look for the expression, that when multiplied by x, will give the first two terms.. there is is (x+2) Meaning we now have x(x+2)When then need to fine another number that, when multimpled to (x+2) gives the second two terms (3x+6) The answer is +3This means the equation we now have lookks like thisx(x+2) +3(x+2)=0We can then arrange the equation like this....(x+3)(x+2)=0We now know that for this equation to equal 0 we have to have either (x+2)=0 or (x+3)=0 Means our solutions are x=-3 and x=-2
