Question

Find the rcmaindcr when the polynomial p(t) = 2t⁴ - 7t³ - 13t² + 63t - 45 is divided by the following polynomials.(I) (t - I)
(2) t - 3
(3) 2t - 5
(4) t + 3
(5) 2t + 3

Answer 1

Answer:

1)-100

2)54

3)0

4)0

5)-135

Answer 2

Answer:

In the question :

(1)p(t)=$2t^4-7t^3-13t^{2} +63t-45$

put t-1=0

t=1

p(t)=$2(1)^4-7(1)^3-13(1)^2+63(1)-45$

p(t)=2-7-13+63-45

p(t)=-5+50-45=0

p(t)=0  

Polynomial is completely divisible .Therefore remainder will be zero.                                                                       

(2) put t-3=0

t=3

$p(3)=2(3)^4-7(3)^3-13(t)^2+63(t)-45$

162-189-117+189-45

=0

Polynomial is completely divisible.Therefore remainder is zero.

(3)put 2t-5=0

$t=\frac{5}{2}$

$2(\frac{5}{2})^4-7(\frac{5}{2})^3-13(\frac{5}{2})^2+63(\frac{5}{2})-45$

625-875-650+1260-360

=0

Polynomial is  completely divisible. Therefore remainder will be zero.

(4)put t+3=0

t=-3

$2(-3)^4-7(-3)^3-13(-3)^2+63(-3)-45$

=162+189-117-189-45

=0

Polynomial is completely divisible.Therefore remainder will be zero.

(5)Put 2t+3=0

t=-$\frac{3}{2}$

$=2(-\frac{3}{2} )^4-7(-\frac{3}{2} )^3-13(-\frac{3}{2})^2+63(-\frac{3}{2})-45$

=0

Polynomial is completely divisible . Therefore remainder will be  zero.