Question

what is the factored form of this expression?
$4t^2 - 27t + 18$
a. $(4t - 18)(t - 1)$
b. $(2t - 6)(2t - 3)$
c. $(2t - 9)(2t - 2)$
d. $(4t - 3)(t - 6)$

Explanation:

Step1: Test Option A via expansion

$(4t - 18)(t - 1) = 4t^2 -4t -18t +18 = 4t^2 -22t +18$

Step2: Test Option B via expansion

$(2t - 6)(2t - 3) = 4t^2 -6t -12t +18 = 4t^2 -18t +18$

Step3: Test Option C via expansion

$(2t - 9)(2t - 2) = 4t^2 -4t -18t +18 = 4t^2 -22t +18$

Step4: Test Option D via expansion

$(4t - 3)(t - 6) = 4t^2 -24t -3t +18 = 4t^2 -27t +18$

Answer:

D. $(4t - 3)(t - 6)$