We can only solve it is equal to something if we assume that it eausl zero, then if we factor it we can assume the factors eqal zero xy=0, then assume x and y=0
so what we do is if we have ax^2+bx+c we factor a and take the factors closest together then place them with the x then factor c and chose the closest ones then try them and see if it works
so if we had 6x^2+20x+16 6=2 times 3 (2x+ )(3x+ ) we know that they are both + because the middle terms is positive and the end terms is positive 16=4 times 4 (2x+4)(3x+4)=6x^2+12x+8x+16=6x^2+20x+16
th easy way to check is we know that teh end terms will be right since we made them that way to check the middle terms if we have (ax+b)(cx+d) to check what the middle term is we do bcx+dax and see if that equals the middle term
so 2. 6x^2+20x+16 6=2 times 3 (2x+ )(3x+ ) we know that they are both + because the middle terms is positive and the end terms is positive 16=4 times 4 (2x+4)(3x+4)=6x^2+12x+8x+16=6x^2+20x+16 facored is (2x+4)(3x+4)=0 2x+4=0 x=-2 3x+4=0 x=-4/3
3. 5x^2+21x+4 5=1 times 5 prime is nice since we only have 1 option (x+ )(5x+ ) we know they are both pluss since middle and end term is positive 4=2 times 2 (x+2)(5x+2) (2 times 5x)+(x times 2)=10x+2x=12x, we need 21 so this wrong change end term (x+4)(5x+1) (4 times 5x)+(1 times x)=20x+x=21x correct factore form (x+4)(5x+1)=0 x+4=0 x=-4 5x+1=0 x=-1/5
4. -7x^2+59x-24 -7=-1 and 7 or -7 and 1 we pick -1 and 7 since we want the middle term to be positive (7x- )(-x+) signs are differenc since end term is negaive -24=8 and -3 (7x-3)(-x+8) (7x times 8)+(-3 times -x)=56x+3x=59x correct (7x-3)(-x+8)=0 7x-3=0 x=3/7 -x+8=0 x=8
OK, so I am getting tired of this so I will just do the rest in factored form isnce you probably shoud have figured out how to do it from the previous examples
5. (x-3)(3x-5) 6. (x-1)(2x+13) 7. (x-2)(3x+8) 8. 2x^2+17x-20 cannot be factored but 2x^2+18x-20 can maybe typing mistake 9. (x+3)(11x-8)
answers: 2.(2x+4)(3x+4) 3.(x+4)(5x+1) 4.(7x-3)(-x+8) 5. (x-3)(3x-5) 6. (x-1)(2x+13) 7. (x-2)(3x+8) 8. 2x^2+17x-20 cannot be factored but 2x^2+18x-20 can maybe typing mistake 9. (x+3)(11x-8)
The graph represents a function but the table does not. The reason for this is that one input value (70) in the table is associated with two output values (54.6 and 53.11), which is a sure sign that we do NOT have a function here.