Question

find the remainder when x^4 + 4x^2 - 5x^2- 6x+ 7 is divided by 3x+2. divide and show

Answer 1

Solution:-

p(x) = x⁴ + 4x² - 5x² - 6x + 7

p(x) = x⁴ - x² - 6x + 7

Using factor theorem

p(x) is divide by 3x + 2

So,

p(-2/3) = 0

$\bf \: ( \frac{ - 2}{3} ) {}^{4} - ( \frac{ - 2}{3}) {}^{2} - 6 \times \frac{ - 2}{3} + 7$

$\bf \: \frac{16}{81} - \frac{4}{9} + 4 + 7$

$\bf \: \frac{16}{81} - \frac{4}{9} + 11$

Taking lcm = 81

$\bf \: \frac{16 - 4 \times 9 + 11 \times 81}{81}$

$\bf \: \frac{16 - 36 + 891}{81}$

$\bf \: \frac{907 - 36}{81}$

$\bf \: \frac{871}{81}$

$\bf \: remainder = \frac{871}{81}$

approx value is 11