Question

How do you solve $ 3{x^2} - 11x - 20 = 0 $ by factoring?

Answer 1

Hint: First we will reduce the equation further if possible. Then we will try to factorise the terms in the equation. Split the middle term and factorise the equation. Then equate the factors equal to zero and evaluate the value of the variable.

Complete step by step solution:
We will start off by reducing any reducible terms in the equation.
 $ 3{x^2} - 11x - 20 = 0 $
Now we will factorise the terms in the equation. bbbnm bvv vn hgvg jvh
 $
\Rightarrow 3{x^2} - 11x - 20 = 0 \\
\Rightarrow 3{x^2} - 15x + 4x - 20 = 0 \\
\Rightarrow (3{x^2} - 15x) + (4x - 20) = 0 \\
\Rightarrow 3x(x - 5) + 4(x - 5) = 0 \\
\Rightarrow (x - 5)(3x + 4) = 0 \;
  $
Now we will equate the factors with zero.
 $\Rightarrow (x - 5)(3x + 4) = 0 $
Here, either $ x = 5 $ or $ 3x + 4 = 0 $ .
If we solve further, we will get,
 $
\Rightarrow {3x + 4} = 0 \\
\Rightarrow {3x} = { - 4} \\
\Rightarrow x = {\dfrac{{ - 4}}{3}}
 $
Hence, the values of $ x $ are $ 5,\dfrac{{ - 4}}{3} $ .
So, the correct answer is “ $ 5,\dfrac{{ - 4}}{3} $ ”.

Note: While splitting the middle term be careful. After splitting the middle term, do not solve all the equations simultaneously. Solve all the equations separately, so that you don’t miss any term of the solution. Check if the solution satisfies the original equation completely. If any term of the solution doesn’t satisfy the equation, then that term will not be considered as a part of the solution.