Enhanced Curriculum Support

Sec A

1. Factorised form of r2−10r+21 is:

(a) (r + 7)(r + 3) (b) (r - 7)(r - 3)

(c) (r - 7)(r + 3) (d) (r -1)(r - 4)

2. 9m2+12mn+4n2 is same as:

(a) 3m+2n2 (b) 3m−2n2

(c) (3m - 2n) (d) (3m + 2n)

3. Factorise: x2+8x+16:

(a) x+42 (b) x+22

(c) x+32 (d) x+52

4. The value of (3x3+9x2+27x) ÷ 3x is:

(a) x2+3x+9 (b) 3x3+9x2+9

(c) 3x2+3x2+27x (d) x2+9+27x

5. Factorise: xy + y + xz + z:

(a) (x - 1) (b) (y + z)

(c) (x + 1) (y + z) (d) (x + 1)

6. The factorisation of x2+x+xy+y+zx+z is:

(a) (x + y + z)(z + x) (b) (x + y + z)(x + y)

(c) (x + y + z)(y + z) (d) (x + y + z)(x + 1)

7. Factorise: 169a2−144b2

(a) (13a + 12b) (b) (13a - 12b) (c) (12a - 13b) (d) (13a + 12b) (13a - 12b)

8. Factorise: 4y2−12y+9:

(a) 5y−32 (b) 7y−52 (c) 2y−32 (d) 2y−52

9. One of the factors of 4(x + y) (3a - b) + 6(x + y) (2b - 3a) is:

(a) (4a - 3b) (b) (3a - b) (c) (2b - 3a) (d) (-3a + 4b)

Sec B

1. Work out the division: 96abc(3a – 12)(5b – 30) ÷ 144(a – 4)(b – 6)

2. Factorise: m4−256

3. Factorise: a4−2a2b2+b4

Sec C

1. Factorize 6x2−13x+6

(OR)

Factorise the expression and divide them as directed: (5p2−25p+20) ÷ (p-1)

2. Factorize 2x2+5x+3

3. Factorize 12x3y4+16x2y5−4x5y2

Problem 1

An old playground needs renovation, and the area available for sports activities is 10p2+15p square meters.

Factorize 10p2+15p to determine how the space can be arranged for different sports activities.

If students work together to plan the playground, discuss how collaboration in designing and sharing the space demonstrates teamwork.

How does creating shared spaces promote community, and why is it important for young people to be involved in such projects?

Problem 2

Rita’s class is designing an eco-friendly vegetable garden. The area designated for the garden is represented by 8z2+20z square meters.

Factorize 8z2+20z to determine possible layout dimensions for the garden.

The class decides to divide this area among themselves to plant various vegetables. How does working together on this project help foster a sense of responsibility toward sustainable practices?

Explain how growing their own food and engaging with nature teaches values like environmental stewardship and self-sufficiency.

Q1

The area of a rectangular field is given by 4x2−20x. Factorize the expression to find the possible dimensions of the field.

If x represents the width, what values of x would give the maximum and minimum possible area for the field?

How does changing x affect the factors, and what does this tell you about the area of the rectangle?

Q2

Given the expression 10p2+30p+20, factorize it into two binomial factors.

Now, modify the expression by adding 5p to it: 10p2+35p+20.

Factorize the new expression and compare the factors to the original factors. How did adding 5p change the factorization, and why?

Questions

1. Factorised form of 23xy – 46x + 54y – 108 is:

(a) (23x + 54) (y – 2) (b) (23x + 54y) (y – 2)

(c) (23xy + 54y) (– 46x – 108) (d) (23x + 54) (y + 2)

2. Factorised form of p2−17p−38 is:

(a) (p – 19)(p + 2) (b) (p – 19)(p – 2)

(c) (p + 19)(p + 2) (d) (p + 19)(p – 2)

3. The value of (3x3+9x2+27x) ÷ 3x is:

(a) x2+9+27x (b) 3x3+3x2+27x

(c) 3x3+9x2+9 (d) x2+3x+9

Questions

1. The factorisation of 2x + 4y is ?

2. Factorised form of 4y2−12y+9 is ?

Questions

1. Factorisation of −3a2+3ab+3ac is 3a(–a – b – c).

2. Factorised form of p2+30p+216 is (p + 18)(p – 12).

3. The factors of a2−2ab+b2 are (a + b) and (a + b).

4. (9x – 51) ÷ 9 is x – 51.

5. The value of a+1a−1a2+1 is a4−1.

Questions

1. Factorise the following.

(i) 21x2y3+27x3y2 (ii) a3−4a2+12−3a

(iii) 4x2−20x+25 (iv) y29 – 9

(v) x4−256

2. Divide 15y+3y2−16 by 5y2−y−12.

3. Factorise the following expressions.

(i) 6ab+12bc (ii) −xy−ay

(iii) ax3−bx2+cx (iv) l2m2n−lm2n2−l2mn2

(v) 3pqr−6p2q2r2−15r2 (vi) x3y2+x2y3−xy4+xy

(vii) 4xy2−10x2y+16x2y2+2xy

(viii) 2a3−3a2b+5ab2−ab

(ix) 63p2q2r2s−9pq2r2s2+15p2qr2s2−60p2q2rs2

(x) 24x2yz3−6xy3z2+15x2y2z−5xyz

(xi) a3+a2+a+1

(xii) lx+my+mx+ly

(xiii) a3x−x4+a2x2−ax3

(xiv) 2x2−2y+4xy−x

(xv) y2+8zx−2xy−4yz

(xvi) ax2y−bxyz−ax2z+bxy2

(xvii) a2b+a2c+ab+ac+b2c+c2b

(xviii) 2ax2+4axy+3bx2+2ay2+6bxy+3by2

4. Perform the following divisions:

(i) 3pqr−6p2q2r2÷3pq (ii) ax3−bx2+cx÷−dx

(iii) x3y3+x2y3−xy4+xy÷xy (iv) −qrxy+pryz−rxyz÷−xyz

5. Factorise the expressions and divide them as directed:

(i) x2−22x+117÷x−13

(ii) x3+x2−132x÷xx−11

(iii) 2x3−12x2+16x ÷ x−2x−4

(iv) 9x2−4 ÷ (3x + 2)

(v) 3x2−48 ÷ (x – 4)

(vi) x4−16 ÷ x3+2x2+4x+8

(vii) 3x4−1875 ÷ 3x2−75

Q1

A company packs its products in a box whose volume is given by 7x3−14x2+21x.

Factorize 7x3−14x2+21x to find the possible dimensions of the box.

If x = 4, calculate the actual volume of the box.

If the dimensions of the box need to be doubled (by increasing x), how does the volume change?

Q2

A toy manufacturer produces a type of toy whose production cost is given by the expression 6y2+15y. Another manufacturer produces a similar toy at a production cost given by 8y2+20y. They want to compare their costs by simplifying these expressions.

Factorize 6y2+15y and 8y2+20y to identify common factors in each expression.

If y = 3 rupees per unit material, find the cost for each manufacturer to produce a toy.

At y = 3, who has the lower production cost, and by how much?

Q3

Rahul’s family owns two rectangular fields. The area of the first field is represented by the expression 3x2+12x and the area of the second field by 4x2+8x. They want to put a fence around each field and need to know the dimensions.

Factorize the expressions 3x2+12x and 4x2+8x to find the dimensions (length and width) of each field.

If x = 5 meters, calculate the actual dimensions and areas of both fields.

Which field has a greater area when x = 5 ? Explain your answer.