Question

Find the factors of the following quadratic polynomial.6x^2-3-7x

Answer 1

Answer:

hey mate ...... here is your answer

6x^2-3-7x

=6x^2-7x-3

=6x^2+2x-9x-3

=2x(3x+1)-3(3x+1)

=(2x-3)(3x+1)

Step-by-step explanation:

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Answer 2

Answer: (3x + 1) (2x - 3)

Step-by-step explanation:

We are told to find the factors of a quadratic polynomial.

We usually solve such problems using splitting the middle term method.

Given: p(x) = 6x² -3 -7x

Let me swap the position of the terms such that:

p(x) = 6x² - 7x - 3

Now we have to split the middle term that is -7x

We have to split it in such a way that the 2 numbers should add up to -7x and when multiplied it should be -18x² (first term multiplied to constant)

So what would be the two numbers?

-9x and 2x looks to be the suitable numbers.

(-9x + 2x = -7x and -9x*2x = -18x²)

So we rewrite the Polynomial as:

6x² + 2x - 9x - 3

Take out the common term for 6x² + 2x and -9x - 3

∴ 2x (3x + 1) -3 (3x + 1)

∴ (3x + 1) (2x -3)  are the factors of the polynomials.