Answer:
3y² + 7y + 4 = (3x + 4)(x + 1)
Step-by-step explanation:
* To factor a trinomial in the form ax² ± bx ± c:
- Look at the c term
# If the c term is positive
∵ c = r × s ⇒ r and s are the factors of c
∴ r and s will have the same sign (sign of b)
∵ a = h × k ⇒ h , k are the factors of a
∴ rk + hs = b
∴ (hx + r)(kx + s) ⇒ if b +ve OR (hx - r)(kx - s) ⇒ if b -ve
# If the c term is negative
∵ c = r × s ⇒ r and s are the factors of c
∴ r and s will not have the same sign
∵ a = h × k ⇒ h and k are the factors of a
∴ rk - hs = b OR hs - rk = b
(hx + r)(kx - s) OR (hx - r)(kx + s)
* Now lets solve the problem
∵ 3y² + 7y + 4
∵ ax² + bx + c
∴ a = 3 , b = 7 , c = 4
∵ a = h × k
∵ 3 = 3 × 1
∴ h = 3 , k = 1
∵ c = r × s
∵ 4 = 4 × 1
∴ r = 4 , s = 1
∵ c is positive
∴ hs + rk = b
∴ 3(1) + 4(1) = 7 ⇒ same value of b
∴ 3y² + 7y + 4 = (3x + 4)(x + 1)
