To factor the given expression completely, we can look for pairs of numbers that multiply to 45 and add up to 9. The factors of 45 are 1, 3, 5, 9, 15, and 45. Among these factors, only 5 and 9 add up to 9.
Therefore, we can rewrite the expression as follows:
x^3 + 5x^2 + 9x + 45 = x^2(x + 5) + 9(x + 5)
Next, we can see that both terms contain (x + 5). We can factor this common binomial out:
x^2(x + 5) + 9(x + 5) = (x^2 + 9)(x + 5)
So, the expression is factored completely as (x^2 + 9)(x + 5).
Factor completely.
x, cubed, plus, 5, x, squared, plus, 9, x, plus, 45
x
3
+5x
2
+9x+45
1 answer
1 answer