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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
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