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Answer :
To simplify the expression [tex]\(45x^3 - 10x^2 + 15\)[/tex], we can follow these steps:
1. Identify Common Factors:
The expression given is [tex]\(45x^3 - 10x^2 + 15\)[/tex]. We should first look for any common factors in the coefficients (45, -10, and 15).
2. Greatest Common Factor (GCF):
The GCF of 45, 10, and 15 is 5. This is the largest number that divides all these numbers without leaving a remainder.
3. Factor Out the GCF:
Let's factor 5 out of each term in the expression:
- Factor 5 out of 45x^3: [tex]\(45x^3 = 5 \times 9x^3\)[/tex]
- Factor 5 out of -10x^2: [tex]\(-10x^2 = 5 \times -2x^2\)[/tex]
- Factor 5 out of 15: [tex]\(15 = 5 \times 3\)[/tex]
So, the expression becomes:
[tex]\[
5(9x^3 - 2x^2 + 3)
\][/tex]
4. Simplify Further if Possible:
Check if there's anything else to simplify inside the parentheses. In this case, [tex]\(9x^3 - 2x^2 + 3\)[/tex] does not have any further factors that we can simplify.
Therefore, the simplified form of the expression [tex]\(45x^3 - 10x^2 + 15\)[/tex] is:
[tex]\[
5(9x^3 - 2x^2 + 3)
\][/tex]
That's how the expression can be simplified by factoring out the greatest common factor.
1. Identify Common Factors:
The expression given is [tex]\(45x^3 - 10x^2 + 15\)[/tex]. We should first look for any common factors in the coefficients (45, -10, and 15).
2. Greatest Common Factor (GCF):
The GCF of 45, 10, and 15 is 5. This is the largest number that divides all these numbers without leaving a remainder.
3. Factor Out the GCF:
Let's factor 5 out of each term in the expression:
- Factor 5 out of 45x^3: [tex]\(45x^3 = 5 \times 9x^3\)[/tex]
- Factor 5 out of -10x^2: [tex]\(-10x^2 = 5 \times -2x^2\)[/tex]
- Factor 5 out of 15: [tex]\(15 = 5 \times 3\)[/tex]
So, the expression becomes:
[tex]\[
5(9x^3 - 2x^2 + 3)
\][/tex]
4. Simplify Further if Possible:
Check if there's anything else to simplify inside the parentheses. In this case, [tex]\(9x^3 - 2x^2 + 3\)[/tex] does not have any further factors that we can simplify.
Therefore, the simplified form of the expression [tex]\(45x^3 - 10x^2 + 15\)[/tex] is:
[tex]\[
5(9x^3 - 2x^2 + 3)
\][/tex]
That's how the expression can be simplified by factoring out the greatest common factor.
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