Answer
$5(x-2)(x-7)$
Work Step by Step
In order to factor $5x^{2}-45x+70$, we must first factor out a 5 (which is the greatest common factor of each term) from all three terms.
$5(x^{2}-9x+14)$
Next, we must find a pair of negative numbers whose product is equal to 14 (or the constant term) and whose sum is equal to -9 (or the coefficient on the middle term).
We know that the pairs of negative numbers whose product is 14 are -1,-14 and -2,-7.
Out of these pairs, the sum of -2 and -7 is equal to -9.
Therefore, $5x^{2}-45x+70=5(x-2)(x-7)$.
