Question

If the HCF of the polynomials f(x) and g(x) is 4x - 6, then f(x) and g(x) could be
(A) 2, 2x - 3
(B) 12x - 18,2
(C) 4x - 6, 2x - 3
(D) 2(2x - 3)², 4(2x - 3)​

Answer 1

f(x) and g(x) could be 2(2x - 3)², 4(2x - 3)​

Step-by-step explanation:

HCF of the polynomials f(x) and g(x) is 4x - 6,

=> f(x) = a (4x - 6)

& g(x) = b(4x - 6)

where a & b are co-prime

2(2x - 3)², 4(2x - 3)​  is the right answer

as

2(2x - 3)² = 2(2x - 3)(2x - 3) = (2x - 3)(4x - 6)

4(2x - 3)​ = 2 * 2 (2x - 3) = 2(4x - 6)

2 &  2x - 3 are a & b and also coprime

f(x) and g(x) could be 2(2x - 3)², 4(2x - 3)​

Learn more :

Find the H.C.F of 3/5 and 2/7

https://brainly.in/question/10134197

Answer 2

Answer:

(D) 2(2x - 3)², 4(2x - 3)

Step-by-step explanation:

Since, HCF stands for highest common factor,

2 = 1 × 2,

2x - 3 = 1 × (2x-3)

⇒ HCF(2, 2x-3) = 1,

12x - 18 = 6(2x-3) = 2 × 3 × (2x-3),

2 = 1 × 2

⇒ HCF(12x - 18, 2) = 2,

4x - 6 =  2 × (2x-3)

2x - 3 = 1 × (2x-3)

⇒ HCF(4x - 6, 2x - 3) = 2x - 3,

2(2x-3)² = 2 × (2x - 3) × (2x - 3)

4(2x - 3) = 2 × 2 × (2x - 3)

⇒ HCF(2(2x-3)², 4(2x - 3)) = 2 × (2x - 3) = 4x - 6

Hence, OPTION D is correct.

Learn more :

To find HCF :

https://brainly.in/question/11166779 ( answered by Dreamcatcher )