Question

Given f(x) =$2x^3–3x^2+1$ and g(x) = $x^3+5x–3$ are two polynomials. If f(x) and g(x) both are divided by (x – 2), then the obtained remainders are $r_1$ and $r_2$ respectively. The value of $(r_1{r}_2–r_1–r_2)$ is

• A. 69
• B. 55
• C. 65
• D. 74

Answer 1

The correct option is B 55

Given: f(x) = $2x^3–3x^2+1$ and g(x) =$x^3+5x–3$
We know that if polynomial p(x) is divided by (x – a), then the remainder is p(a).
$\therefore r_1=f\left(2\right)$
$=2(2{)}^3–3(2{)}^2+1$
$=16–12+1=5$
Similarly, $r_2=g\left(2\right)$
$=(2{)}^3+5(2)–3$
$=8+10–3=15$
$\therefore r_1{r}_2–r_1–r_2$
$=5\times 15–5–15$
$=75–20=55$
Hence, the correct answer is option (2).