Question

Solve the factorization: a2x2-(a2b2+1)x + b2 = 0.

Answer 1

hope it helps you and clear your doubts

Answer 2

Given,

• The polynomial $a^2x^2 -(a^2b^2 +1)x +b^2 = 0$ is given.

To find,

• We have to find the factors of the given polynomial.

Solution,

The factors of $a^2x^2 -(a^2b^2 +1)x +b^2 = 0$ are $(x-b^2) (a^2x-1)$.

We can simply find the factors of the given polynomial by taking out the common terms.

                   $a^2x^2 -(a^2b^2 +1)x +b^2 = 0$

                  $a^2x^2-a^2b^2x-x +b^2$

Taking $a^2x$ common from the first two terms and -1 common from the last two terms, we get

                   $a^2x(x-b^2)-1(x-b^2)$

Now, taking $(x-b^2)$ common, we get

                   $(x-b^2) (a^2x-1)$

So, the factors of $a^2x^2 -(a^2b^2 +1)x +b^2 = 0$ are  $(x-b^2) (a^2x-1)$.

                    $x-b^2 = 0$        $a^2x-1 =0$

                          $x = b^2$                  $x = 1/a^2$

Hence, the factors of $a^2x^2 -(a^2b^2 +1)x +b^2 = 0$ are $(x-b^2) (a^2x-1)$.