factor completely 5x^2 −14x+9
To factor the expression 5x^2 - 14x + 9, we need to find two numbers that multiply to 5*9=45 and add up to -14 (the coefficient of the middle term).
The two numbers that fit these conditions are -9 and -5. We can then rewrite the middle term as -9x - 5x and factor by grouping:
5x^2 - 14x + 9
= 5x^2 - 9x - 5x + 9
= (5x^2 - 9x) - (5x - 9)
= x(5x - 9) - 1(5x - 9)
= (x - 1)(5x - 9)
Therefore, the factored form of 5x^2 - 14x + 9 is (x - 1)(5x - 9).