sari is factoring the polynomial $2x^2+5x+3$. if one factor is $(x+1)$, what is the other factor?\n\n$2x-3$\n…
sari is factoring the polynomial $2x^2+5x+3$. if one factor is $(x+1)$, what is the other factor?\n\n$2x-3$\n$2x+3$\n$3x-2$\n$3x+2$
Answer
Explanation:
Step1: Identify the polynomial and the given factor
The polynomial is $P(x) = 2x^2 + 5x + 3$ and one factor is $(x + 1)$.
Step2: Set up the division or factorization equation
Let the other factor be $(ax + b)$. Then: $$2x^2 + 5x + 3 = (x + 1)(ax + b)$$
Step3: Determine the first term of the second factor
Multiply $x$ by $ax$ to get $2x^2$. Thus, $a = 2$. $$2x^2 + 5x + 3 = (x + 1)(2x + b)$$
Step4: Determine the constant term of the second factor
Multiply $1$ by $b$ to get the constant term $3$. Thus, $b = 3$. $$2x^2 + 5x + 3 = (x + 1)(2x + 3)$$
Step5: Verify the middle term
Expand $(x + 1)(2x + 3)$: $$x(2x) + x(3) + 1(2x) + 1(3) = 2x^2 + 3x + 2x + 3 = 2x^2 + 5x + 3$$ The middle term matches.
Answer:
2x+3