Question

The diagram represents 6x2 – 7x 2 with a factor of 2x – 1. A 2-column table with 2 rows. First column is labeled 2 x with entries 6 x squared, negative 4 x. Second column is labeled negative 1 with entries negative 3 x, 2. Both rows are labeled with a question mark. What is the other factor of 6x2 – 7x 2? 3x – 2 3x – 1 3x 1 3x 2.

Answer 1

Factors of a polynomial can divide it without leaving remainder. The other factor of $6x^2 - 7x + 2$ is given by Option D :  $3x + 2$

How to factorize a polynomial?

Let the  polynomial A(x) has one factor f(x).

Then, it means, we have:

$\dfrac{A(x)}{f(x)} = g(x)$

Thus, A(x) can be written as $A(x) = f(x) \times g(x)$

Thus, the other factor of that polynomial is

$g(x) = \dfrac{A(x)}{f(x)}$

For given case, the polynomial $A(x)$ is

$A(x) = 6x^2 - 7x + 2$

Its one factor f(x) is given $f(x) = 2x - 1$

Thus, its second factor is obtained as:

$g(x) = \dfrac{A(x)}{f(x)} = \dfrac{6x^2 - 7x + 2}{(2x - 1)} = \dfrac{6x^2 -4x -3x - 2}{2x - 1}\\\\g(x) = \dfrac{2x(3x + 2) - 1(3x + 2)}{2x - 1} = \dfrac{(2x - 1)(3x + 2)}{2x - 1}\\\\g(x) = (3x + 2)$

Thus, the second factor of the given polynomial is

Option D :  $3x + 2$

Learn more about factors of polynomials here:

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