1. The problem is to factor the expression $35x^3 + 14x$ using the greatest common factor (GCF). 2. The formula for factoring by GCF is: $$a b + a c = a(b + c)$$ where $a$ is the GCF. 3. Identify the GCF of $35x^3$ and $14x$: - The GCF of 35 and 14 is 7. - The GCF of $x^3$ and $x$ is $x$. 4. Factor out the GCF $7x$: $$35x^3 + 14x = 7x(\cancel{5x^3} + \cancel{2x})$$ 5. Simplify inside the parentheses by dividing each term by $7x$: $$= 7x(5x^2 + 2)$$ 6. The correct factorization is: $$35x^3 + 14x = 7x(5x^2 + 2)$$ 7. The original provided factorization $7x(5x^3 + 2)$ is incorrect because factoring out $7x$ reduces the power of $x$ inside the parentheses by one. Final answer: $$35x^3 + 14x = 7x(5x^2 + 2)$$