Question

if x ^4-3x^3-7x^2+27x-18 divided by x+3 the quotient is​

Answer 1

Answer:

see the above mentioned attachment .

• The quotient is x³ - 7x + 48

Answer 2

Solution:-

p(x) = x⁴ - 3x³ - 7x² + 27x - 18

q(x) = x + 3

Now,

zeroes of polynomial

=> x + 3 = 0

=> x = (-3)

Now,

p(-3) = (-3)⁴ - 3(-3)³ - 7(-3)² + 27(-3) - 18

p(-3) = 243 - 81 - 63 - 81 - 18

p(-3) = 243 - 81 - 162

p(-3) = 243 - 243

p(-3) = 0

So, it proves that p(x) is divisible by q(x).

Now, divide it to get quotient,

p(x) = x⁴ - 3x³ - 7x² + 27x - 18

q(x) = x + 3

=> x⁴ - 3x³ - 7x² + 27x - 18 ÷ ( x + 3 )

=> x³ - 7x + 6

.°. Quotient = x³ - 7x + 6