Question Factor the binomial $s^2 + 9$ completely. Select "Prime" if the polynomial cannot be factored.

Studdy Solution

STEP 1

Assumptions
1. We are given a binomial in the form $s^2 + 9$ .
2. We need to factor the binomial completely.
3. If the binomial cannot be factored, we will denote it as "Prime".

STEP 2

Identify the type of binomial.
The given binomial is a sum of squares, which is in the form $a^2 + b^2$ , where $a = s$ and $b = 3$ .

STEP 3

Recall the factoring rules for binomials.
The sum of squares $a^2 + b^2$ cannot be factored into real factors because it does not have real roots. It can only be factored over the complex numbers.

STEP 4

Determine if the binomial can be factored over the real numbers.
Since $s^2 + 9$ is a sum of squares and there are no real factors for such a binomial, it cannot be factored over the real numbers.

STEP 5

Conclude whether the binomial is factorable or prime.
Since $s^2 + 9$ cannot be factored over the real numbers, we denote the binomial as "Prime".
The binomial $s^2 + 9$ is Prime.

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Question Factor the binomial $s^2 + 9$ completely. Select "Prime" if the polynomial cannot be factored.

Studdy Solution

STEP 1

Assumptions
1. We are given a binomial in the form $s^2 + 9$ .
2. We need to factor the binomial completely.
3. If the binomial cannot be factored, we will denote it as "Prime".

STEP 2

Identify the type of binomial.
The given binomial is a sum of squares, which is in the form $a^2 + b^2$ , where $a = s$ and $b = 3$ .

STEP 3

Recall the factoring rules for binomials.
The sum of squares $a^2 + b^2$ cannot be factored into real factors because it does not have real roots. It can only be factored over the complex numbers.

STEP 4

Determine if the binomial can be factored over the real numbers.
Since $s^2 + 9$ is a sum of squares and there are no real factors for such a binomial, it cannot be factored over the real numbers.

STEP 5

Conclude whether the binomial is factorable or prime.
Since $s^2 + 9$ cannot be factored over the real numbers, we denote the binomial as "Prime".
The binomial $s^2 + 9$ is Prime.

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Question Factor the binomial s2+9s^2 + 9s2+9 completely. Select "Prime" if the polynomial cannot be factored.

Studdy Solution

STEP 1

Assumptions1. We are given a binomial in the form s2+9 s^2 + 9 s2+9.2. We need to factor the binomial completely.3. If the binomial cannot be factored, we will denote it as "Prime".

STEP 2

Identify the type of binomial.The given binomial is a sum of squares, which is in the form a2+b2 a^2 + b^2 a2+b2, where a=s a = s a=s and b=3 b = 3 b=3.

STEP 3

Recall the factoring rules for binomials.The sum of squares a2+b2 a^2 + b^2 a2+b2 cannot be factored into real factors because it does not have real roots. It can only be factored over the complex numbers.

STEP 4

Determine if the binomial can be factored over the real numbers.Since s2+9 s^2 + 9 s2+9 is a sum of squares and there are no real factors for such a binomial, it cannot be factored over the real numbers.

STEP 5

Conclude whether the binomial is factorable or prime.Since s2+9 s^2 + 9 s2+9 cannot be factored over the real numbers, we denote the binomial as "Prime".The binomial s2+9 s^2 + 9 s2+9 is Prime.

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Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Question Factor the binomial $s^2 + 9$ completely. Select "Prime" if the polynomial cannot be factored.

Assumptions
1. We are given a binomial in the form $s^2 + 9$ .
2. We need to factor the binomial completely.
3. If the binomial cannot be factored, we will denote it as "Prime".

Identify the type of binomial.
The given binomial is a sum of squares, which is in the form $a^2 + b^2$ , where $a = s$ and $b = 3$ .

Recall the factoring rules for binomials.
The sum of squares $a^2 + b^2$ cannot be factored into real factors because it does not have real roots. It can only be factored over the complex numbers.

Determine if the binomial can be factored over the real numbers.
Since $s^2 + 9$ is a sum of squares and there are no real factors for such a binomial, it cannot be factored over the real numbers.

Conclude whether the binomial is factorable or prime.
Since $s^2 + 9$ cannot be factored over the real numbers, we denote the binomial as "Prime".
The binomial $s^2 + 9$ is Prime.