x3 + 6x2 - 4x - 24
= (x + 6)(x2 - 4)
= (x + 6)(x + 2)(x - 2)
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X + 4 is a factor of x^3 + 3x^2 - 10x - 24 along with (x + 2) and (x - 3)
2z+6z+24=0 8z+24=0 8z= -24 z= - 3
x^(2) - 10x + 24 Since the coefficient of 'x^(2)' is '1', ; number not shownl we look at the constant '24'. Write down all the factors of '24'. They are 1,2,3,4,6,8,12,& 24. From this list we need to select two numbers that add to '10' and multiply to '24'. The possibilities of addition ARE 4 + 6, 2+ 8 , & 12 -2. However, only 4 + 6 = 10 & -4 x -6 = 24 , but -12 X 2 = -24 (Not +24). So the only pair are '4' & '6'. Set up factor brackets;) (x 4)(x 6) Since ;24; is positive (+) then the signs in the brackets are both the same. They can be either '+' or '-' . Since the coefficient of 'x' is '-10' , then the signs are negative(-). So fully factored it is ( x - 4)(x - 6)
-5x + 6y = 24 6y = 5x + 24 y = 5/6 x + 4 the slope is 5 6
8x + 6 = 2x + 24 To solve, collect like terms on each side; collect the x's on the left, the numbers on the right: 8X + 6 = 2x + 24 8x - 2x = 24 - 6 6x = 18 6x / 6 = 18 / 6 x = 3