Question

find the remainder when, (x^4+4x^2-9x+21)is divided by (2x-7)​

Answer 1

given :-

p(x) = x⁴ + 4x² - 9x + 21

g(x) = 2x - 7

here we have to find the remainder when p(x) is divided by g(x)

we can use two methods.

either divide the polynomial by g(x) or use remainder theorem.

remainder theorem is easier is we want to find only the remainder.

what we've to do is only find the value of x in g(x) and then put it's value in p(x)

➡ 2x - 7 = 0

➡ 2x = 7

➡ x = 7/2

therefore p(7/2) = (7/2)⁴ + 4(7/2)² - 9(7/2) + 21

= 2401/16 + 196/4 - 63/2 + 21/1

LCM of 16, 4, 2 and 1 = 2 × 2 × 2 × 2 = 16

= 2401/16 + (196 × 4)/(4 × 4) - (63 × 8)/(2 × 8) + (21 × 16)/(1 × 16)

= 2401/16 + 784/16 - 505/16 + 336/16

= 3016/16 or 188.5 FINAL ANSWER

Answer 2

$\huge\underline\textbf{Answer:-}$

$\underline\textbf{According to the given question:-}$

p(x) = x⁴ + 4x² - 9x + 21

$g(x) = 2x - 7$

• Let us Find the value of xin g(x) and also the value in p(x)

$=>2x - 7 = 0$

$=>2x = 7$

$=>x = 7/2$

=>p(7/2) = (7/2)⁴ + 4(7/2)² - 9(7/2) + 21

$=>2401/16 + 196/4 - 63/2 + 21/1$

• The answer we get from taking (LCM) of 16,4, 2 ans 1 = 2 × 2 × 2 × 2 = 16

=>2401/16 + (196 × 4)/(4 × 4) - (63 × 8)/(2 × 8) + (21 × 16)/(1 × 16)

=>2401/16 + 784/16 - 505/16 + 336/16

=>The reminder we get from (x^4+4x^2-9x+21)is divided by (2x-7) 3016/16 or 188.5