Factor the expression. x squared minus x minus 42?

x^2 - x - 42
= (x - 7)(x + 6)

A) (x - 7) (x + 6)

x² - x - 42 = 0
x² - 1/2x = 42 + (- 1/2)²
x² - 1/2x = 168/4 + 1/4
(x - 1/2)² = 169/4
x - 1/2 = 13/2

1st factor:
= x - 1/2 - 13/2
= x - 14/2
= x - 7

2nd factor:
= x - 1/2 + 13/2
= x + 12/2
= x + 6

Answer: A) (x - 7)(x + 6)

Proof (F.O.I.L.):
= (x - 7)(x + 6)
= x² + 6x - 7x - 42
= x² - x - 42

a million. x^2+13x+30=0 (x+10)(x+3)=0 x= -10,-3 2. x^2-19x+ninety 5=0 (x-12)(x-7)=0 x=12,7 3. x^2-34x+240=0 (x+6)(x-40)=0 x= -6, 40 4. 2x^2+15-108=0 (2x-9)(x+12)=0 x= 9/2, -12 5. 9x^2-9x-28=0 (3x-7)(3x+4)=0 x=7/3, -4/3 6. 18x^2-57x+35=0 (6x-5)(3x-7)=0 x= 5/6, 7/3 right here, we only only could locate the suited coefficients of x yet this may well be an ordeal and mistake technique. simply by fact the optimal exponent is two (it replace into consistently x^2), there could additionally be 2 aspects. the approach is easy. right it truly is an occasion of looking the suited coefficients. as an occasion, in no.6, we can call the aspects simply by fact here: (6x-5)(3x-7)=0 6x-a 5-b 3x-c 7-d We could locate somewhat that the version of a more desirable to d and d more desirable to c would be -57x. The final term interior the given subject (35) have aspects 5*7, 35*a million. for that reason, on account which you're given 18x^2 as your first term, there are opportunities that it might desire to be 6x*3x, 9x*2x or 18x*x. employing trial and mistake, the proper answer is (6x-5)(3x-7). take under consideration the indications. :)

x^2 - x - 42
= x^2 + 6x - 7x - 42
= (x^2 + 6x) - (7x + 42)
= x(x + 6) - 7(x + 6)
= (x + 6)(x - 7)
(answer A)

x ² - x - 42
(x - 7) (x + 6)

You have to see what two numbers multiplied by eachother are -42 and since the X is negative and doesn't have any coefficients. They have to add up to -1

So the answer will have -7 and 6. They are two numbers that multiply to -42 and add to -1.

So then you do (X-7)(X+6)

If you can't work it out normally, work it backwards... solve A, B, C, D.... to do that,

Think of the problem as 4 parts:

(A mumble B) (C mumble D)

you multiply A and C.... X times X = x-squared, right?
you multiply B and D.... 7x6 is 42... which of the answers gives you a minus 42 (-42)? That's your first clue.
you do the same multiply for pairs AD and BC... each time you get 6x or 7x, right? Which one is plus 6 and minus 7, because that gives you a minus 1 total...

first one gives you x squared. that last step gives you -1x (or minus X... same thing). Second step gives you minus 42.

Now whaddya do when you're flying without multiple-guess?

Treat this like two story problems: what times what =42? and what plus what = minus 1.

Any problem they give you, if you can think about the problem as a (what numbers add to give me the middle part and multiply to give me the end part), and you're done.

Last of all, some more clues that you can't really memorize as much as just try to understand so you'll see how they help you solve algebra problems:

Real small numbers (or negative ones) in the middle of the question (the minus X part) mean one term is plus and one is minus, usually.

A number that is pretty large (13) would make me I'm looking for two same-sign numbers.

And a minus sign on the end means one of each, too... a plus times a minus is the only way to get a negative product when they're multiplied. minus times minus = plus, plus times plus = minus.

A

x^2 - x - 42 ...[1]

Line [1] will factor into two terms of the form:

(x + a)(x + b) ...[2]

To factor line [1], you want to find values for "a" and "b" that will multiply to give you -42 and add to give you -1. Two numbers that will do this are -7 and 6. (NOTE: (-7)(6) = -42, and -7 + 6 = -1, so they satisfy both requirements.)

So, plug those values into the factored form in line [2]:

(x - 7)(x + 6) ...[sol'n]

The answer is choice (A).

Hope this helps!

x² – x – 42
= x² – 7x + 6x – 42
= x(x – 7) + 6(x – 7)
= (x + 6)(x – 7) ------------- option A
--------