How do you factor 6x2-19x+10

Question

How do you factor 6x²-19x+10

Answer 1

Another approach:  6x² - 19x + 10

 

Try to find 2 numbers whose product is 60  (the product of the coefficient of x² and 10, the constant), and whose sum is 19.  Try 15 and 4.

 

Rewrite to get 6x² - 15x - 4x + 10

 

Factor by grouping:  common factor of 6x² - 15x is 3x, and the common factor of -4x + 10 = -2.

 

Therefore:  6x² - 15x - 4 x + 10 = 3x(2x - 5) -2(2x - 5) = (3x-2)(2x-5).

 

 

Answer 2

Leah,

 

To factor the expression, we are looking to find values for A, B, C, and D in --

 

  (Ax + B) * (Cx + D) = 6x² - 19x + 10

 

Therefore, we know that A*C = 6 and B*D = 10. If we first try whole numbers, then there are not many choices - for A & C, just 6 & 1 or 3 & 2; for B & D, just 10 & 1 or 5 & 2. What combination will result in the -19 ? It looks like we can get 19 = 3 * 5 + 2 * 2, so our factoring ends up as

 

  (3x - 2) * (2x - 5)

 

To check ourselves, if we multiply it back -- 3*2 = 6, ok; -2 * 2 + -5 * 3 = -4 + -15 = -19, ok; -2 * -5 = 10, ok.

 

Looks like we have a solution!