Question

factor 2x2-x-21=0

Answer 1

here is an easy method that works every time

if you have a quadratic

\[ax^2 + bx + c \]

multiply a and c

so in your question 2 * -21 = -42

find the factors of -42 that add to -1

hint: the larger factor is negative

then write it as

(ax + factor 1)(ax + factor 2) Yor question (2x + factor 1)(2x + factor 2)
-------------------------- --------------------------
a 2


the binomials may have a common factor like (3x + 12)

which can be written as 3(x + 4)

and you'll find the common factor removed from the binomial will cancel with

the denominator

so in your question its

(2x + 6)(2x - 7)
--------------
2

factor a binomial

2(x + 3)(2x - 7)
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2

cancel the common factor, whats left is the answer

Answer 2

(2x-7)(x+3)