This document contains 25 math word problems involving polynomial factorization and division. The problems ask the student to factor polynomials, divide polynomials, verify the quotient and remainder, determine if a polynomial is a factor, find values that make a polynomial divisible, and other related tasks. The document provides the questions but not the solutions.

1. Question 1.
5x3
– 15x2
+ 25x by 5x
Solution:
Question 2.
4z3
+ 6z2
-zby (frac { -1 }{ 2 }) z
Solution:
Question 3.
9x2
y – 6xy + 12xy2
by (frac { -3 }{ 2 }) xy
Solution:

2. Question 4.
3x2
y2
+ 2x2
y + 15xy by 3xy
Solution:
Question 5.
x2
+ 7x + 12 by x + 4
Solution:
Question 6.
4y2
4 + 3y + (frac { -1 }{ 2 }) by 2y + 1
Solution:

3. Question 7.
3x3
+ 4x2
+ 5x + 18 by x + 2
Solution:
Question 8.
14x2
– 53x + 45 by 7a – 9

4. Solution:
Question 9.
-21 + 71x – 31x2
– 24ax3
by 3 – 8ax
Solution:
Question 10.
3y4
– 3y3
– 4y2
– 4y by y2
– 2y

5. Solution:
Question 11.
2y5
+ 10y4
+ 6y3
+ y2
+ 5y + 3 by 2y3
+ 1
Solution:
Question 12.
x4
– 2x3
+ 2x2
+ x + 4 by x2
+ x + 1

6. Solution:
Question 13.
m3
– 14m2
+ 37m – 26 by m2
– 12m + 13
Solution:
Question 14.
x4
+ x2
+ 1 by x2
+ x + 1
Solution:

7. Question 15.
x5
+ x4
+ x3
+x2
+ x+ 1 by x3
+ 1
Solution:
Divide each of the following and find the quotient and remainder :
Question 16.
14x3
– 5x2
+ 9x -1 by 2x – 1

8. Solution:
Question 17.
6x3
– x2
– 10x – 3 by 2x – 3
Solution:
Question 18.
6x3
+ 11x2
– 39x – 65 by 3x2
+ 13x + 13

9. Solution:
Question 19.
30a4
+ 11a3
-82a2
– 12a + 48 by 3a2
+ 2a- 4
Solution:
Question 20.
9x4
– 4x2
+ 4 by 3x2
– 4x + 2

10. Solution:
Question 21.
Verify division algorithm i.e., Dividend = Divisor * Quotient + Remainder, in
each of the following. Also, write the quotient and remainder :
Solution:

15. Question 22.
Divide 15y4
+ 16y3
+ (frac { 10 }{ 3 }) y – 9y2
– 6 by 3y – 2
Write down the co-efficients of the terms in the quotient.
Solution:

16. Question 23.
Using division of polynomials state whether.
(i) x + 6 is a factor of x2
– x – 42
(ii) 4x – 1 is a factor of 4x2
– 13x – 12
(iii) 2y – 5 is a factor of 4y4
– 10y3
– 10y2
+ 30y -15
(iv) 3y + 5 is a factor of 6y5
+ 15y + 16y + 4y+ 10y – 35
(v) z2
+ 3 is a factor of z5
– 9z
(vi) 2x2
– x + 3 is a factor of 60x5
-x4
+ 4x3
– 5x2
-x- 15
Solution:

20. Question 24.
Find the value of ‘a’, if x + 2 is a factor of 4x4
+ 2x3
– 3x2
+ 8x + 5a.
Solution:

21. Question 25.
What must be added to x4
+ 2x3
— 2x2
+ x – 1 so that the resulting polynomial is
exactly divisible by x2
+ 2x – 3.

22. Solution: