10x^2 – 43x + 28
(5x - 4)(2x - 7) <====
10x^2 - 35x - 8x + 28
10x^2 - 43x + 28
notes as written 10x2 = 20x
however i think you meant x squared which is written as 10x^2
whence faced with ax^2 + bx + c find the factors of the product ac than sums to b then fact via grouping
ac = 10 * 28 = 280
-8 * - 35 = 280
-8 + -35 = -43
=> 10x^2 - 35x - 8x + 28
=> 5x(2x - 7) - 4(2x - 7)
=> (2x -7)(5x - 4)
find factors of (10 * 28 = 280) that sum to (- 43)
(- 35) * (- 8)
split the middle term, then factor by grouping...
10x^2 - 35x - 8x + 28 = 5x(2x - 7) - 4(2x - 7) = (2x - 7)(5x - 4)
check by multiplying
socrates
10 factors as 5 and 2 , 28 as 7 and 4
5*7 +4*2 is 43, so use that.
(2x - 7)(5x - 4)
x=7/2, x=4/5
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Verified answer
10x^2 – 43x + 28
(5x - 4)(2x - 7) <====
10x^2 - 35x - 8x + 28
10x^2 - 43x + 28
notes as written 10x2 = 20x
however i think you meant x squared which is written as 10x^2
10x^2 - 43x + 28
whence faced with ax^2 + bx + c find the factors of the product ac than sums to b then fact via grouping
ac = 10 * 28 = 280
-8 * - 35 = 280
-8 + -35 = -43
=> 10x^2 - 35x - 8x + 28
=> 5x(2x - 7) - 4(2x - 7)
=> (2x -7)(5x - 4)
10x^2 - 43x + 28
find factors of (10 * 28 = 280) that sum to (- 43)
(- 35) * (- 8)
split the middle term, then factor by grouping...
10x^2 - 35x - 8x + 28 = 5x(2x - 7) - 4(2x - 7) = (2x - 7)(5x - 4)
check by multiplying
socrates
10 factors as 5 and 2 , 28 as 7 and 4
5*7 +4*2 is 43, so use that.
(2x - 7)(5x - 4)
x=7/2, x=4/5