sari is factoring the polynomial $2x^{2}+5x + 3$. if one factor is $(x + 1)$, what is the other…
sari is factoring the polynomial $2x^{2}+5x + 3$. if one factor is $(x + 1)$, what is the other factor?\n$2x-3$\n$2x + 3$\n$3x-2$\n$3x + 2$
Answer
Explanation:
Step1: Use polynomial long - division
Divide (2x^{2}+5x + 3) by (x + 1).
Step2: Divide the leading terms
The leading term of (2x^{2}+5x + 3) is (2x^{2}), and the leading term of (x + 1) is (x). (\frac{2x^{2}}{x}=2x).
Step3: Multiply and subtract
Multiply (x + 1) by (2x) to get (2x^{2}+2x). Subtract this from (2x^{2}+5x + 3): ((2x^{2}+5x + 3)-(2x^{2}+2x)=3x + 3).
Step4: Divide the new leading term
The leading term of (3x + 3) is (3x), and (\frac{3x}{x}=3).
Step5: Multiply and subtract again
Multiply (x + 1) by (3) to get (3x+3). Subtract this from (3x + 3), the remainder is (0). So the quotient is (2x + 3).
Answer:
B. (2x + 3)