Factor 6x^2 – 13x + 5 = 0?

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Dr. Juanita Wolff · Accepted Answer

SOLUTION: (3x -5)(2x -1) = 0 EXPLANATION:First notice the highest term coefficient. it is 6.That means it can be either(2x+___)(3x+___) //* or could be negative signor (x+____)(6x+___)Those would make highest term 6x^2.Now focus on constant 5.It can be (2x__1)(3x___5) Where ___ indicates you have to do trial and error for sign.To get positive 5, it can be either both signs are positive or both are negative. But now look at the middle terms. It is -13So in order to get -13, you need both negative signs because the middle term in binomial is where outside product and inside product in nested form gets added in FOIL method.So it should be (3x -5 )(2x-1)The more you practice, you will be able to do it in your head. Otherwise you need to do many trials and errors.Now in case you have to solve for x, it should be obvious that 3x-5 = 0 and 2x -1 = 0x = 5/3, 1/2

Dr. Juanita Wolff · Answer

6x^2 – 13x +5 = 0x^2 – 13x + 30 = 0(x – 10) (x -3) = 0(x – 10/6) (x -3/6) = 0(x – 5/3) ( x – 1/2) = 0(3x – 5) ( 2x-1) = 0

Dr. Juanita Wolff · Answer

6x^2-13x+5=0(2x -1 )(3x -5 )=02x-1=0 or x-5=0 2x=1 or x=5x=1/2 or x=5the solution set ={1/2 , 5}

Dr. Juanita Wolff · Answer

=> 6x^2-13x+5 = 0=> 6x^2-3x-10x+5 = 0=> 3x(2x-1)-5(2x-1) = 0=> (3x-5)(2x-1) = 0Either, x = 5/3, or x = 1/2

Dr. Juanita Wolff · Answer

6x^2 – 13x + 5 = 0(3x-5)(2x-1) = 0

Dr. Juanita Wolff · Answer

6x² – 13x + 5 = 06x² – 3x – 10x + 5 = 03x(2x – 1) – 5(2x – 1) = 0(2x – 1)(3x – 5) = 0x = 1/2, 5/3

Dr. Juanita Wolff · Answer

6x^2-13x+5 if the second operation is +, then both operations in solution are the same if first operation determines the operations in the solution (-)6x^2-13x+5( – ) ( – )6x^2-13x+5possible solutions:(6x- ) (1x- )(1x- ) (6x- )(3x- ) (2x- )(2x- ) (3x- ) ^ and ^ must be 1 & 5 because they are factors of 5 in 6x^2-13x+5Possible solutions:(6x-1)(x-5)(x-1)(6x-5)(3x-1)(2x-5)(2x-1)(3x-5)Use FOIL (first, outside, inside, last) . “first” & “last” is done “outside” & “inside” added up must be -13xexplanation of FOIL: (a+b)(a+b)=aa+ab+ab+bb=a^2+2ab+b^2 aa(first) ab(outside) ab(inside) bb (last)(6x-1)(x-5)-30x-x nope(x-1)(6x-5)-6x-5x -11x nope(3x-1)(2x-5)-2x-15x nope(2x-1)(3x-5)-3x-10x = -13x correctThe answer is (2x-1)(3x-5)(2x-1)(3x-5)=0Solve for x2x-1=0 or 3x-5=0+, -, x, or / by both sides of the equation2x=1 or 3x=52/2x=1/2 or 3/3x=5/31x=1/2 or 1x=5/3x=1/2 or x=5/3x={1/2, 5/3}

Dr. Juanita Wolff · Answer

(3x-5)(2x-1)=0x = 5/3, 1/2

Dr. Juanita Wolff · Answer

use the quadratic formula (-B +/- sqrt(b^2 – 4AC))/2awhereA= 6B= -13C= 5(13 +/- sqrt(13^2 – 4(6)(5)))/2so you get two answersx = .5 and x = 1.6667

Dr. Juanita Wolff · Answer

(3x+1)(2x-5)=0x=-1/3x=5/2

Dr. Katlynn Swaniawski II

Factor 6x^2 – 13x + 5 = 0?

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