Answer:
a. – 4 or –3
b. –4 or –2
c. 4 or –3
d. 7 or 4
Step-by-step explanation:
To factorize the above expression, multiply the first and last term together, then find two factors of the result such that their sum will result to the middle term of the expression.
Now, we shall give the answers to the question.
a. x² + 7x + 12 = 0
x² + 3x + 4x + 12 = 0
Factorise
x(x + 3) + 4(x + 3) = 0
(x + 4)(x + 3) = 0
x + 4 = 0 or x + 3 = 0
x = 0 – 4 or x = 0 – 3
x = – 4 or –3
Therefore, the roots of the equation are – 4 or –3
b. t² + 6t + 8 = 0
t² + 2t + 4t + 8 = 0
Factorise
t(t + 2) + 4(t + 2) = 0
(t + 4)(t + 2) = 0
t + 4 = 0 or t + 2 = 0
t = 0 – 4 or t = 0 – 2
t = –4 or –2
Therefore, the roots of the equation are –4 or –2
c. 2n² – 2n – 24 = 0
Divide through by 2
n² – n – 12 = 0
n² + 3n – 4n – 12 = 0
Factorise
n(n + 3) – 4(n + 3) = 0
(n – 4)(n + 3) = 0
n – 4 = 0 or n + 3 = 0
n = 0 + 4 or n = 0 – 3
n = 4 or n = –3
Therefore, the roots of the equation are 4 or –3
d. y² – 11y + 28 = 0
y² – 4y – 7y + 28 = 0
Factorise
y(y – 4) – 7(y – 4) = 0
(y – 7)(y – 4) = 0
y – 7 = 0 or y – 4 = 0
y = 0 + 7 or y = 0 + 4
y = 7 or 4
Therefore, the roots of the equation are 7 or 4.
