Can anyone factor completely 3x^2+15x-42 please?

Question

I know the answer is 3(x+3)(x-2) but how do I show the work?

Answer 1

3( x ² + 5 x - 14 )
3 ( x + 7 ) ( x - 2 )

Answer 2

First, find a the largest number that will divide evenly into all of the numbers (coefficients and constant) ) in your expression.

Three 'goes into' 3, one time---good, 3 goes into 15, let's see, five times---good! and 3 goes into 42, (this is why they pounded those times tables into us 10 years ago) oh yeah---14 times---good!

So we can factor a 3 out of all three numbers (the two coefficients [ 3 and 15] and the constant [-42] at the end)

Factoring out the three looks like so:

3(x^2 +5x - 14)

Now let's forget about the three for just a bit, and work on what is within the brackets. (but don't forget the three completely; we will bring it back later).

We look to see if we can factor the following:

(x^2 + 5x -14)

This factoring seems like a different procedure than the factoring we did with the 3 and all that in the beginning, doesn't it?---Factoring is sorta like reverse multiplying if you will. Don't worry!--Factoring is a skill that gets far better with practice.

There are a few ways to factor trinomials such as these (most trinomials can't be integer factored of course). Here is one way to factor:

build two bracket sets like so: Don't include the dots LOL
(.............) (..............)
Now, this one is relatively easy because there is no number (other than the invisible coefficient one) 'attached' to the x^2 term,
and so we can go ahead and put an 'x' in each bracket like so:
( x............) ( x............) You wouldn't get far using F.O.I.L. right now (if you had to--which you don't anyways) but you can see, that if you wanted to FOIL, and multiplied the x times the other x ,you would get your x^2....so we are doing the right thing---so far!

Next, (and this works if there is no number other than one stuck to the x^2) take the last number, the constant -14, and in your mind (here we go with times tables again!) think of two numbers that when multipled, equals this -14. (You can ignore the negative sign for a moment by the way.) Well that is easy: 1 times 14 = 14 good, but 2 times 7 also equals 14.

Pick the set that, when 'added or subtracted', equals the number in the middle (middle term's coefficient), the 5.

Hmmm...
Got it! Seven minus 2 equals five right? Cool!---Now we're getting somewhere! Just place +7 to the right of the 'x' in one of your brackets, and -2 to the right of the other 'x', within the other brackets. Our math is nearly finished and looks like this:

(x + 7) (x - 2) Didn't matter which bracket got what did it? Apples times oranges equals oranges times apples tee-hee.

Are we finished? NO!. We can't forget the poor forgotten 3, which we 'factored out' long ago! Put it in front like so, and we ARE indeed finished!!!

3 (x -2) (x +7) Notice I switched the brackets around? That is just to illustrate the apple orange thing I had just mentioned!
We call it a commutative thing! Also, you could just as well have expressed it like so: (-2+x)(7+x)3 but this looks ugly!

Now that we are done, it is always a good idea to check our work by 'going backwards' by multiplying and FOIL(ing) and all that wonderful stuff. I love math, can't you tell? And so will you if you practice really hard.

Answer 3

The answer that u have given is wrong...


any way the answer i got is :

3x^2 + 15x-42 = 3(x^2+5x-14)
3(x+7)(x-2)

Answer 4

The answer is (3x-6)(x+7) or 3(x-2)(x+7). They both equal the same thing. An easy way to do this is factor out a three to get 3(x^2+5x-14), then factor what's left using a reverse foil method.

Answer 5

First divide everything (whole equation by 3) = x^2+5x-14

If you equate x^2+5x-14 to 0 i.e. x^2+5x-14 = 0

This equation is in the form: AX^2 + BX - C = 0

1.) Find the factors for the A term which is just 1 and 1 since 1*1 =1.
2.) Find the factors for the C term. They are:

-1*14 = -14, 1*-14, = - 14, -2*7 =-14, or 2*-7 = - 14

3.) Find two factors of the "c" term that if one factor is multiplied by one factor of your "a" term, and the other factor is multiplied by the other factor of your a term, and then these two numbers are added together, will equal your "b" term.

For example:

1*(-2) + 1*7 = -2 + 7 = 5

Therefore the answer is: (X-2)(X+7). If you multiply this out

= x^2+5x-14

Answer 6

Factoring three is the easy first step.

3(x^2+5x-14)

When one has a quadratic of the form x^2+bx+c, there are two numbers, i,j which make up b and c so that:

b=i+j
c=i*j
and
x^2+bx+c=(x+i)(x+j)

since
5=7-2 and -14=7*-2, i=7 and j=-2

Therefore
3x^2+15x-42=3(x+7)(x-2)

Answer 7

1) factor completely 2x^2 - 16x + 30 2) Factor the expression completely. 4x2 + 12x + 9 4) Choose one of the factors of the expression 4x2 - 9 from the list below. (2x + 3) (x + 3) 4 (x - 3) 11) Solve the equation x2 + 9 = 0. ANSWER X = -4.5 12) Multiply and simplify (3x + 2)(x - 5). ANSWER 3X^2 +15X + 2X - 15 = 3X^2 + 17X - 15 15) Solve for the variable -3(x + 2) < -x - 10. 16) Solve the equation x^2 - 25 = 0. ANSWER X=25 25)Solve the equation 3x^2 - 15x = 0. 29) solve: 2(x - 4)< 8(x + 1/2) 33) simplify (6y^2+4y-3)+(3y^2+2) ANSWER 9y^4 + 4y -1 35)Choose one factor of the following expression from the list below. 3x2 - x - 10 (3x + 10) (3x+2) (3x + 5) (32) 42)Factor the expression x^2 - 8xy + 12y^2 completely. 45) simplify completely sqrt 8 46)Choose one factor of the following expression from the list below. 6x2 - 5x - 4 (3x + 4) (2x + 1) (6x + 1) (x - 4) 48)x^2-x-20=0 50)Solve the following quadratic by either factoring or using the quadratic formula: 6x2 - 5x = 6

Answer 8

3x^2+15x-42
=3(x^2+5x-14)
=3(x+7)(x-2)

Answer 9

pull out a common factor of 3:
3[x^2+5x-14]=
3[(x-2)(x+7)]

multiply this out to show it matches the original polynomial

Answer 10

3(x^2+5x-14)=3(x+7)(x-2)