Question

Factor the polynomial
t{2} + 8{t}

Answer 1

To factor the polynomial t^2 + 8t, we can look for common factors and then try to find two terms that, when multiplied, give the coefficient of the middle term (8) and add up to the coefficient of the squared term (0).

First, we can factor out the common factor "t" from both terms:
t(t + 8)

Now, we need to find two terms that, when multiplied, give 8 and add up to 0.
The only possibility is 4 and 2 (4 * 2 = 8, 4 + 2 = 6). Therefore, we can rewrite the polynomial as:
t(t + 4)(t + 2)

So, the factored form of the polynomial t^2 + 8t is t(t + 4)(t + 2).