Question

FAN/Medal - Factor completely: 2x^3 + 6x^2 + 10x + 30

2(x^3 + 3x^2 + 5x + 15)

2[(x^2 + 5)(x + 3)]

(2x^2 + 10)(x + 3)

(x^2 + 5)(2x + 6)

Answer 1

i got x^2 +5 - 2x+3

Answer 2

Reformatting the input :

(1): "x2" was replaced by "x^2". 1 more similar replacement(s).
Step by step solution :
Step 1 :

Simplify 2x3+6x2+10x + 30

Pulling out like terms :

1.1 Pull out like factors :

2x3 + 6x2 + 10x + 30 =

2 • (x3 + 3x2 + 5x + 15)
Checking for a perfect cube :

1.2 x3 + 3x2 + 5x + 15 is not a perfect cube
Trying to factor by pulling out :

1.3 Factoring: x3 + 3x2 + 5x + 15

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

Group 1: 5x + 15
Group 2: x3 + 3x2

Pull out from each group separately :

Group 1: (x + 3) • (5)
Group 2: (x + 3) • (x2)
-------------------
Add up the two groups :
(x + 3) • (x2 + 5)
Which is the desired factorization
Polynomial Roots Calculator :

1.4 Find roots (zeroes) of F(x) = x2 + 5

Polynomial Roots Calculator is a set of methods aimed at finding values of x for which F(x)=0

Rational Roots Test is one of the above mentioned tools. It would only find Rational Roots that is numbers x 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 1 and the Trailing Constant is 5.

The factor(s) are:

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

Let us test ....
P Q P/Q F(P/Q) Divisor
-1 1 -1.00 6.00
-5 1 -5.00 30.00
1 1 1.00 6.00
5 1 5.00 30.00


Polynomial Roots Calculator found no rational roots
Final result :

2 • (x2 + 5) • (x + 3)

Answer 3

excuse me \[2 \times (x ^{2} + 5) \times (x+3)\]

Answer 4

so i get where we divide be 2 and get x3 + 3x2 + 5x + 15

Answer 5

then split to 2 groups x3 + 3x2 and 5x + 15

Answer 6

but got lost after that

Answer 7

its B, just saying

Answer 8

i replaced x^? to x? just to make it simple

Answer 9

Thoughtfully split the expression at hand into groups, each group having two terms : Group 1: 5x + 15
Group 2: x3 + 3x2
Pull out from each group separately :
Group 1: (x + 3) • (5)
Group 2: (x + 3) • (x2)
you have to make the y value equal to the other group

Answer 10

ok ty

Answer 11

yw :)

Answer 12

Suppose \(f(x)=2x^{3} + 6x^{2} + 10x + 30\)
Let \(f(x)=0\)
So, A root of equation is \(x=-3\) => \(f(x)\) has a factor is \((x+3)\)
dividing polynomial \(f(x)\) by \((x+3)\) we get \(2(x^{2}+5)\)

Thus, \(2x^{3} + 6x^{2} + 10x + 30\) = \(2(x+3)\)\((x^{2}+5)\)