FACTORING POLYNOMIALS WORKSHEET

(1) Factorize the following:

(i)  x² + 10x + 24

(ii)  z² + 4z - 12

(iii)  p² - 6p - 16

(iv)  t² + 72 - 17t

(v)  y² - 16y - 80

(vi)  a² + 10a - 600              Solution

(2)  Factorize the following:

(i)  2x² + 9a + 10

(ii)  5x² - 29xy - 42y²

(iii)  9 - 18x + 8x²

(iv)  6x² + 16xy + 8y²

(v)  12x² + 36x²y + 27y²x²

(vi)  (a + b)² + 9(a + b) + 18          Solution

(3)  Factorize the following:

(i)  (p - q)² - 6(p - q) - 16

(ii)  m² + 2mn - 24n²

(iii)  √5 a² + 2a - 3√5

(iv)  a⁴ - 3a² + 2

(v)  8m³ - 2m²n - 15mn²

(vi)  (1/x²) + (1/y²) + (2/xy)           Solution

Factorize the following cubic polynomials :

(1)  x³ - 2x² - 5 x + 6

(2)  4x³ - 7x + 3

(3)  x³-23x²+142x-120

(4)  4x³-5x²+7x-6

(5)  x³ - 7x + 6

(6)   x³ +13x²+32x+20         Solution

Factorize the following quadratic polynomial using box method :

(1)  3x² + 19x + 6

(2)  5y² - 29y + 20

(3)  2x² + 17x  - 30

(4)  18x² - x  - 4       Solution

Find least common multiple by factoring :

(1)  4x²y, 8x³y²

(2)  -9a³b², 12a²b²c

(3)  16m, -12m²n², 8n²

(4)   p² − 3p +2, p² - 4

(5)  2x² - 5x -3, 4x² -36

(6)  (2x² -3xy)², (4x -6y)³, 8x³ -27y³

Solution

Factor the following polynomial :

(1)  4x + 8

(2)  16a + 64b - 4c

(3)  36x - 16

(4)   35 + 21a

(5)  4a - 8b + 5ax - 10bx             Solution

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