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UNIT 1 : ALGEBRA PREP

LESSON 4: OPERATIONS WITH POLYNOMIALS HOMEWORK QUESTIONS

 

 

HOMEWORK QUESTIONS:

 

1. Expand and simplify:

a) (x2 3x + 4) + (4x2 2x + 5) b) (x2 2x 3) (5x2 + 3x 2)

c) (-3x2 + 2x 5) 2x(3x 4) + 3(x 5) d) 3x2(2x3 6x 2) x(5x3 3x2 + 1)

 

2. Expand and simplify:

a) 3[2x (x 5)] 2x[5x (3x 2)] b) (2x 1)(3x2 5x 2)

c) (x2 + 2)(x2 5x + 3) d) 5(3 2x)(4x 1) 2x(3x + 2)2

e) (2a 3)2(a 2) 3a(a 1)(4a + 2) f) (5a 1)(2a3 3a2 + a 5)

g) (2a 3b + c)3

 

3. Expand and simplify:

 

4. Factor Fully:

 

 

Solutions:

 

1. Expand and simplify:

a) (x2 3x + 4) + (4x2 2x + 5) b) (x2 2x 3) (5x2 + 3x 2)

c) (-3x2 + 2x 5) 2x(3x 4) + 3(x 5) d) 3x2(2x3 6x 2) x(5x3 3x2 + 1)

Solutions:

a) (x2 3x + 4) + (4x2 2x + 5) = x2 3x + 4 + 4x2 2x + 5

= 5x2 5x + 9

 

b) (x2 2x 3) (5x2 + 3x 2) = (x2 2x 3) 1(5x2 + 3x 2)

= x2 2x 3 5x2 3x + 2

= -4x2 5x 1

 

c) (-3x2 + 2x 5) 2x(3x 4) + 3(x 5) = -3x2 + 2x 5 6x2 + 8x + 3x 15

= -9x2 + 13x - 20

 

d) 3x2(2x3 6x 2) x(5x3 3x2 + 1) = 6x5 18x3 6x2 5x4 + 3x3 x

= 6x5 5x4 15x3 6x2 x

 

2. Expand and simplify:

a) 3[2x (x 5)] 2x[5x (3x 2)] b) (2x 1)(3x2 5x 2)

c) (x2 + 2)(x2 5x + 3) d) 5(3 2x)(4x 1) 2x(3x + 2)2

e) (2a 3)2(a 2) 3a(a 1)(4a + 2) f) (5a 1)(2a3 3a2 + a 5)

g) (2a 3b + c)3

Solutions:

a) 3[2x (x 5)] 2x[5x (3x 2)] = 3(2x x + 5) 2x(5x 3x + 2)

= 3(x + 5) 2x(2x + 2)

= 3x + 15 4x2 4x

= - 4x2 x + 15

 

b) (2x 1)(3x2 5x 2) = 2x(3x2 5x 2) 1(3x2 5x 2)

= 6x3 10x2 4x 3x2 + 5x + 2

= 6x3 13x2 + x + 2

 

c) (x2 + 2)(x2 5x + 3) = x2(x2 5x + 3) + 2(x2 5x + 3)

= x4 5x3 + 3x2 + 2x2 10x + 6

= x4 5x3 + 5x2 10x + 6

 

d) 5(3 2x)(4x 1) 2x(3x + 2)2 = 5(12x 3 8x2 + 2x) 2x(3x + 2)(3x + 2)

= 5(-8x2 + 14x 3) 2x(9x2 + 6x + 6x + 4)

= -40x2 + 70x 15 18x3 12x2 12x2 8x

= - 18x3 64x2 + 62x 15

 

e) (2a 3)2(a 2) 3a(a 1)(4a + 2) = (4a2 12a + 9)(a 2) 3a(4a2 2a 2)

= 4a3 8a2 12a2 + 24a + 9a 18 12a3 + 6a2 + 6a

= -8a3 14a2 + 39a 18

 

f) (5a 1)(2a3 3a2 + a 5) = 5a(2a3 3a2 + a 5) 1(2a3 3a2 + a 5)

= 10a4 15a3 + 5a2 25a 2a3 + 3a2 a + 5

= 10a4 17a3 + 8a2 26a + 5

 

g) (2a 3b + c)3 = (2a 3b + c) (2a 3b + c) (2a 3b + c)

= (2a - 3b + c)(4a2 6ab + 2ac 6ab +9b2 3bc +2ac 3bc +c2)

= (2a 3b + c)(4a2 + 9b2 + c2 12ab + 4ac 6bc)

= 8a3 + 18ab2 +2ac2 24a2b +8a2c 12abc 12a2b 27b3 3bc2 +36ab2 12abc + 18b2c + 4a2c +9b2c +c3 12abc + 4ac2 6bc2

= 8a3 27b3 + c3 + 54ab2 +6ac2 36a2b + 12 a2c 9bc2 + 27b2c 36abc

 

3. Expand and simplify:

 

4. Factor Fully:

 

 

 

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