Question

factor -7x^2-34x+5

Answer 1

here is a method that works... for any quadratic

\[ax^2 + bx + c =0\]

multiply a and c

so in this question -7 + 5 = -35

find the factors of -35 that add to -34... the larger is negative and the smaller is positive.

can you give me the factors

Answer 2

Same technique I would use.

Answer 3

1 and -35 @campbell_st

Answer 4

so to help a little the factors you need are -35, 1

now write the quadratic as

\[\frac{ax + factor ~1)(ax + fractor~2)}{a}\]

so in your question it becomes

\[\frac{(-7x - 35)(-7x + 1)}{-7}\]

if you remove the common factor from the 1st binomial, you will find it cancels
with the denominator.

what is left is the factored from of your quadratic.

this method works every time... on some occassions you will have factors from both binomials that cancel with the denominator.

for some reason it's not a common textbook method...

hope it helps

Answer 5

great @candy, now see if you can find the common factor

Answer 6

Hmm.. I would solve it a little differently from there. \[-7x^2-34x+5\]\[=x^2-34x-35\]\[=(x-35)(x+1)\]Now because you multiplied a and c, you would divide by the value of a to fit your original equation.\[=\left(x-\frac{35}{-7}\right)\left(x+\frac{1}{-7}\right)\]Reduce whichever fraction you can and for the ones you cannot, multiply the denominator of the fraction to the variable \[=(x-5)(7x+1)\]

Answer 7

Well there you go... a new method .. and it works every time @Jhannybean

Answer 8

i figured it out i got (x-5)(-7x+1)

Answer 9

did i get it ?

Answer 10

Yep, I missed my negative sign.

Answer 11

almost -7x - 35 = -7(x + 5)

but great work otherwise