another algebra equation

Question

10x^2+17x+3.

 

neither of them have factors except 1 again.

factors of 10 are 5*2, 1*10

3 is 1*3

 

(10x+___) (x+____)

 

is this correct. The problem says to simplify but isn't factoring and simplifying the same thing.

Answer 1

10x²+17x+3

multiply 10 times 3

10*3=2*5*3=(2)*(5*3) and 15+2=17, the coefficient of the middle term

(5x     )(2x     ) so far

(5x     )(2x    3) so far

(5x   1)(2x   3) so far

(5x+1)(2x+3) is the answer

 

in your other problem I posted a comment but it didn't show up, so...

6x²+49x-45

6*45=270=2*3*3*3*5

group the factors so that the products subtract to 49

this is basically what Patrick did only he listed all products but when you get the hang of this you won't have to list so many

2*3*3*3*5=(2*3*3*3)*5=54*5 and 54-5=49

to get 54 multiply 6*9

(6x    )(x    9) so far

(6x   5)(x     9) so far

(6x-5)(x+9) is the answer

 

 

 

Answer 2

Danielle, let's look at what someone showed you before.

 

We first have to multiply 10 and 3. 10 x 3 = 30, right?

 

Now, what are the factors of 30? 1 x 30, 2 x 15, 3 x 10, 5 x 6.

 

What two of those factors add together to make 17, the middle number? 2 + 15 = 17, right?

 

So, we are going to break down 17x into 2x + 15x, because 2x + 15x = 17x.

 

Rewrite the expression as 10x² + 2x + 15x + 3

 

What is common among the first two terms? 2x, so we factor that out. 10x² + 2x = 2x(5x + 1)

 

What is common among the last two terms? 3.  15x + 3 = 3(5x + 1).

 

Notice how what is inside each set of parentheses is the same!

 

So, rewriting our equation yet again, we have 2x(5x + 1) + 3(5x + 1)

 

Just like 2x + 15x = 17x, if we are multiplying two things by the same "thing", we can add them together.  Since we can't add 2x + 3, we just put them together in their own parenteses.

 

10x² + 17x + 3 = (2x + 3)(5x + 1)

 

Hope that helps!

 

Answer 3

Again I advice quadratic equation..unfortunately my iPad cant write it out well for you to see but I guess you check your textbook or Google for formula

 

-b+-square root of b^2-4(a)(c)/2(a)

 

a=10, b=17,c=4

 

-17+-square root of 17^2-4(10)(3)/2(10)

17^2-4(10)(3)

289-4(30)

289-120=169

square root of 169=13

-17+13/20=-4/20=-1/5=-0.2

-17-13/20=-30/20=-3/2=-1.5

 

factors of x=-0.2,-1.5