Write this (x )(x ) Think of two POSITIVE whole numbers which multiply to give this number, 24,................that subtract (because of this sign)...., .......to give this POSITIVE number, 2,....... So the only two POSITIVE integers that multiply to give 24 and subtract to give 2, are 6 and 4, because 6 times 4 is 24 and 6 minus 4 is 2. So we put 6 and 4 in the parentheses like this: (x 6)(x 4) All we need do is put the correct signs in the middle of each parentheses. The larger of these two numbers (which is 6 in this case).... will always get this sign (which is -): So we put a "-" sign before the 6 in the first parentheses: (x-6)(x 4) Now we need to decide what sign goes in the middle of the second parentheses: We look back at this sign: Since it is a "-" the second parentheses gets the OPPOSITE sign from the sign in the other parentheses (so it gets a + ): (x-6)(x+4) That's the answer. --------------------------------- Let's do another problem like that: x²-9x+14 Write this (x )(x ) Think of two POSITIVE whole numbers which multiply to give this number, 14,........ ........that add (because of this + sign)...., .......to give this POSITIVE number, 9,....... So the only two POSITIVE integers that multiply to give 14 and add to give 9, are 7 and 2, because 7 times 2 is 14 and 7 plus 2 is 9. So we put 7 and 2 in the parentheses like this: (x 7)(x 2) All we need do is put the correct signs in the middle of each parentheses. The larger of these two numbers (which is 7 in this case).... will always get this sign (which is -): So we put a "-" sign before the 7 in the first parentheses: (x-7)(x 2) Now we need to decide what sign goes in the middle of the second parentheses: We look back at this sign: Since it is a "+" the second parentheses gets the SAME sign as the sign in the other parentheses (so it also gets a - ): (x-7)(x-2) That's the answer. Edwin