What is a factor of 6x² + x - 7?

Solution:

The factors of any quadratic equation can be found by factorization method

The factorization means multiply the coefficient of x² with constant term

⇒ x² coefficient is 6 and constant term is -7,on multiplying -42.

Now need to find the factors of - 42 such that the sum is 1

⇒ The factors are +7 and -6 so that the product is - 42 and sum is +1

According to this x term needs to be rearranged.

⇒ 6x² +7x − 6x - 7 = 0

Separating common terms as underlined

⇒x ( 6x + 7) - 1 ( 6x + 7) = 0

Again 6x + 7 is common term and on separating

⇒ (x - 1) (6x + 7) = 0

⇒ x = 1 and x = -7 / 6.

Hence, the values of x are 1 and -7 / 6.

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What is a factor of 6x² + x - 7 ?

Summary:

The factors of 6x² + x - 7 are 1 and (-7 / 6)