Question

Factor the cubic polynomial
15q^3+40q^2+3q+8

Answer 1

15q3+40q2+3q+8

Final result :

(5q2 + 1) • (3q + 8)
Step by step solution :

Step 1 :

Raise q to the 2nd power
Exponentiaion :

Equation at the end of step 1 :

(((15•(q3))+(40•q2))+3q)+8
Step 2 :

Raise q to the 3rd power
Exponentiaion :

Equation at the end of step 2 :

(((15 • q3) + (23•5q2)) + 3q) + 8
Step 3 :

Simplify 15q3+40q2+3q + 8
Checking for a perfect cube :

3.1 15q3+40q2+3q+8 is not a perfect cube

Trying to factor by pulling out :

3.2 Factoring: 15q3+40q2+3q+8

Thoughtfully split the expression at hand into groups, each group having two terms :

Group 1: 3q+8
Group 2: 40q2+15q3

Pull out from each group separately :

Group 1: (3q+8) • (1)
Group 2: (3q+8) • (5q2)
-------------------
Add up the two groups :
(3q+8) • (5q2+1)
Which is the desired factorization

Polynomial Roots Calculator :

3.3 Find roots (zeroes) of : F(q) = 5q2+1
Polynomial Roots Calculator is a set of methods aimed at finding values of q for which F(q)=0

Rational Roots Test is one of the above mentioned tools. It would only find Rational Roots that is numbers q which can be expressed as the quotient of two integers

The Rational Root Theorem states that if a polynomial zeroes for a rational number P/Q then P is a factor of the Trailing Constant and Q is a factor of the Leading Coefficient

In this case, the Leading Coefficient is 5 and the Trailing Constant is 1.

The factor(s) are:

of the Leading Coefficient : 1,5
of the Trailing Constant : 1

Let us test ....

P Q P/Q F(P/Q) Divisor
-1 1 -1.00 6.00
-1 5 -0.20 1.20
1 1 1.00 6.00
1 5 0.20 1.20

Polynomial Roots Calculator found no rational roots

Final result :

(5q2 + 1) • (3q + 8)

Answer 2

did this help?

Answer 3

uh kind of confusing.

Answer 4

awww lol what grade u in?

Answer 5

so i can translate in your grade...lol

Answer 6

omg just factor by grouping. what is this trash?

Answer 7

-.- its called rea fkin math

Answer 8

so why did you make this problem so difficult can't you just factor out common terms in the first two terms then in the last two terms. which whould be 5q2(3q+8)+(3q+8). then factor out the common term? 3q+8? Is that right?

Answer 9

k nvm that was effed....

Answer 10

what Greta said is right. lol slept late last night finishing code

Answer 11

lol idk...i just put my input in helping u but i see by confused u are so i didnt help much so i will leave now young one

Answer 12

so (3q+8)(5q^2+1) is right then?

Answer 13

^ YES

Answer 14

-sighs- see u didnt need any help u just needed to think it through

Answer 15

factor 5q^2 out you will have
5q^2(3q+8)+3q+8
then since 3q+8 is common
(3q+8)(5q^2+1)

Answer 16

there was a way easier way to do it then... all that stuff

Answer 17

thank you @UsukiDoll !!!

Answer 18

the super long way was nonsense really. just factor by grouping and it shows when you compare the first two portions of the equation with the LAST TWO PORTIONS OF THE EQUATION.

Answer 19

and yet again i am useless....

Answer 20

because whatever you typed was ... what the .. really. was that necessary?

Answer 21

we didnt say that I just said that the site you got that from was making it harder than it really is

Answer 22

lol well sorry then >.<

Answer 23

yeah

Answer 24

dont listen to me im a newbe since today

Answer 25

the question just says to factor not factor and find all 0s.

Answer 26

like i said just dont listen to me

Answer 27

*throws a twix bar*

Answer 28

hahaha

Answer 29

-dodges and runs away with dark cloak trailing behind me-

Answer 30

Hersheys banned uk chocolates boo!

Answer 31

Im in 8th grade by the way.

Answer 32

lol im 7th

Answer 33

wow I feel old x.x

Answer 34

lol how ld r u?

Answer 35

26

Answer 36

lol oh im fourteen