Question

Write as a product of two polynomials 3(a–2)^2–(2–a)

Answer 1

Answer:

(3a + 10)(a + 1)

Step-by-step explanation:

$3 {(a - 2)}^{2} - (2 - a)$

$= 3( {a}^{2} + {(2)}^{2} + 2(a)(2)) - (2 - a)$

$= 3( {a}^{2} + 4 + 4a) - (2 - a)$

$= (3 {a}^{2} + 12 + 12a) - (2 - a)$

$= 3 {a}^{2} + 12 + 12a - 2 + a$

$= 3 {a}^{2} + 13a+ 10$

Splitting the middle term

$= 3 {a}^{2} + 3a + 10a + 10$

$= 3a(a + 1) + 10(a + 1)$

$= (3a + 10)(a + 1)$

Answer 2

Answer:

(a-2)(3a-5)

Step-by-step explanation:

(a-2)(3(a-2)+1)

(a-2)(3a-6+1)

(a-2)(3a-5)