How do you factor #5x^2 - 17x+ 6#?

1 Answer
Richard G.
Mar 6, 2016

#(5x-2)(x-3)#

Explanation:

Open two sets of brackets.

The factors of #5x^2# are #5x, x#. Put them in the brackets.#(5x)(x)#.

Multiply the first and last coefficients, 5 x 6= 30. The factors of +30 are: +1, +30; +2, +15; +3, +10; +5, +6; -5, -6; -3, -10; -2, -15; and -1, -30.

Add each of these. The sum of -2, -15 is -17, the middle coefficient, so these are the right ones.

But you started by multiplying by 5, so now you must divide by 5, which goes into the -15, leaving the factor as -3.

#(5x -2)(x -3)#

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