Question

Q3.Factorise the following polynomials.
(a) 6p(p – 3) + 1 (p – 3)
(b) 14(3y – 5z)3 + 7(3y – 5z)2

Answer 1

Answer:

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Answer 2

Question ❶ :

›»› 6p(p - 3) + 1(p - 3).

Answer :

›»› The factorization of 6p(p - 3) + 1(p - 3) is

Given :

• 6p(p - 3) + 1(p - 3).

To Find :

• Factorize the expression.

Solution :

→ 6p(p - 3) + 1(p - 3)

Any expression multiplied by 1 remains the same,

→ 6p(p - 3) + (p - 3)

Factor out p - 3 from the expression,

→ (p - 3) (6p - 1)

Hence, the factorization of 6p(p - 3) + 1(p - 3) is (p - 3) (6p - 1).

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Question ❷ :

›»› 14(3y - 5z)³ + 7(3y - 5z)².

Given :

• 14(3y - 5z)³ + 7(3y - 5z)².

To Find :

• Factorize the expression.

Solution :

→ 14(3y - 5z)³ + 7(3y - 5z)²

Bind the expression with the common factor 7(3y - 5z)²,

→ 7(3y - 5z)² (2(3y - 5z) + 1)

Expand the binomial expression,

→ 7(9y² - 30yz + 24z²) (2(3y - 5z) + 1)

Organize the expression with the distributive law,

→ 7(9y² - 30yz + 24z²) (6y - 10z + 1)

Sort the factors,

→ 7(3y - 5z)² (6y - 10z + 1)

Hence, the factorization of 14(3y - 5z)³ + 7(3y - 5z)² is 7(3y - 5z)² (6y - 10z + 1).

Additional Information :

✒ Factozisation :

Factorizing is to make a single term: try to write everything as products (multiplication), for example:

→ 6x² - 9x + 10 = (2x - 5) (3x - 2)

Step ① :

Find a common factor

Example:

→ 4xy + x⁴ + x = x(4x + x³ + 1)

Step ② :

Count the number of terms

(terms are separated by + or −)

If none of these methods work, re-arrange the terms, or remove brackets and start again.