Answer:
(u - 1)(4u + 3)
Step-by-step explanation:
Given
4u² - u - 3
Consider the factors of the product of the coefficient of the u² term and the constant term which sum to give the coefficient of the u- term.
product = 4 × - 3 = - 12 and sum = - 1
The factors are - 4 and + 3
Use these factors to split the u- term
4u² - 4u + 3u - 3 ( factor the first/second and third/fourth terms )
= 4u(u - 1) + 3(u - 1) ← factor out (u - 1) from each term
= (u - 1)(4u + 3)
Thus
4u² - u - 3 = (u - 1)(4u + 3) ← in factored form
