How do you factor #v^2-7v+10#?

2 Answers
May 23, 2015

Notice that #10 = 5 xx 2# and #7 = 5 + 2#, so

#v^2-7v+10 = (v-5)(v-2)#

When you are faced with a quadratic like this whose first coefficient is #1#, look for factors of the constant term and see if their sum or difference is equal to the middle coefficient. This is often a quick way to find a factorisation.

May 23, 2015

#f(v) = v^2 - 7v + 10 = (v - p)(v - q)#

Find 2 numbers, sum (-7) and product (10). They are -2 and -5.

#f(v) = (v - 2)(v - 5)#