Polynomials and Fundamental Theorem of Calculus

Question

Question 1

 

Question 2

Question 3

 

Answer 1

(2).

The solution as shown below.

Answer 2

(1).

The solution as shown below.

Answer 3

(2).(c).

Write the expression in long division form [ p(x) = x² + 6x + 3 ] / [ s(x) = x + 3 ].

Divide the first term of the dividend [ p(x) ] by the first term of the divisor [ s(x) ] :  x²/x = x.

So,the first term of the quotient [ q(x) ]  is x. Multiply (x + 3) by x and subtract.

Divide the first term of the last row by first term of the divisor : 3x/x = 3.

So,the second term of the quotient is 3. Multiply (x + 3) by 3 and subtract.

The remainder is the last entry in the last row.There fore, r = 5.

The number along the bottom row are the coefficients of the quotient.

The result of the division is

The solution q(x) = x + 3 and r = 5.

Answer 4

(3). (a).

The solution as shown below.