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In this lesson, we will learn how to find the quotient and remainder when polynomials are divided, including the case when the divisor is irreducible.

Q1:

Use polynomial division to simplify 2 π₯ + 5 π₯ + 7 π₯ + 4 π₯ + 1 3 2 .

Q2:

Find the quotient when 2 π₯ + 7 π₯ β 8 π₯ β 2 1 3 2 is divided by 2 π₯ + 3 .

Q3:

Find the quotient when π₯ β 1 0 π₯ + 1 6 π₯ β 9 π₯ β 4 π₯ + 1 4 6 4 3 2 is divided by π₯ + 2 π₯ β 7 2 .

Q4:

Find the quotient when π₯ β 8 π₯ + 2 0 π₯ β 2 1 4 2 is divided by π₯ + 2 π₯ β 7 2 .

Q5:

Find the quotient when 1 6 π₯ + 1 2 π₯ β 1 4 π₯ + 6 π₯ 4 3 2 is divided by 4 π₯ + 6 π₯ 2 .

Q6:

We want to factor 3 2 π₯ + 1 0 0 π₯ + 3 5 π₯ β 6 3 π₯ 4 3 2 into two factors. Given that one of these factors is 4 π₯ + 9 π₯ 2 , what is the other?

Q7:

Given that 2 π₯ + 9 π₯ β 2 3 π₯ β 3 0 = οΉ π π₯ + π π₯ + π ο ( π₯ + 6 ) 3 2 2 , by comparing coefficients, find π , π , and π .

Q8:

The volume of a box is 1 0 π₯ + 2 7 π₯ + 2 π₯ β 2 4 3 2 . Given that its length is 5 π₯ β 4 and its width is 2 π₯ + 3 , express the height of the box algebraically.

Q9:

The volume of a cylinder is π οΉ 2 5 π₯ β 6 5 π₯ β 2 9 π₯ β 3 ο 3 2 . Given that its radius is 5 π₯ + 1 , find an expression for its height.

Q10:

Use polynomial division to simplify 6 π₯ + 5 π₯ β 2 0 π₯ β 2 1 2 π₯ + 3 3 2 .

Q11:

What must be added to 2 1 π₯ + 7 1 π₯ + 2 3 2 to give an expression that is divisible by 7 π₯ + 5 ?

Q12:

Write π₯ β 2 π₯ β 1 7 π₯ β 3 π₯ + 4 π₯ β 2 π₯ + 3 π₯ 5 4 3 2 2 in the form π ( π₯ ) + π ( π₯ ) π ( π₯ ) .

Q13:

Find the remainder π ( π₯ ) , and the quotient π ( π₯ ) when 4 π₯ + 2 π₯ β π₯ β 6 4 3 is divided by 2 π₯ β 4 π₯ + 1 2 .

Q14:

Find the quotient when 7 2 π₯ + 5 4 π₯ + 1 8 π₯ 4 2 6 is divided by 6 π₯ + 2 π₯ 3 .

Q15:

What is the width of a rectangle whose area is οΉ β 2 4 π₯ β 7 8 π₯ β 1 2 π₯ + 1 8 π₯ ο 4 3 2 cm^{2} and whose length is οΉ 3 π₯ + 9 π₯ ο 2 cm?

Q16:

The volume of a cylinder is π οΉ 3 π₯ + 2 4 π₯ + 4 6 π₯ β 1 6 π₯ β 3 2 ο 4 3 2 and its radius is π₯ + 4 . Write, in its simplest form, a polynomial for the height of the cylinder.

Q17:

Write π₯ β 2 π₯ β 2 1 π₯ β 7 π₯ + 6 π₯ + 3 π₯ β 2 4 3 2 2 in the form π ( π₯ ) + π ( π₯ ) π ( π₯ ) .

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