Answer :
Let's factor the given quadratic expressions by pulling out the Greatest Common Factor (GCF) only.
11. For the quadratic [tex]\(6x^2 + 9\)[/tex]:
- Step 1: Identify the GCF of the terms in the expression.
- The terms are [tex]\(6x^2\)[/tex] and [tex]\(9\)[/tex].
- The GCF of [tex]\(6\)[/tex] and [tex]\(9\)[/tex] is [tex]\(3\)[/tex].
- Step 2: Factor out the GCF.
- Divide each term by the GCF, [tex]\(3\)[/tex].
- [tex]\(6x^2 \div 3 = 2x^2\)[/tex]
- [tex]\(9 \div 3 = 3\)[/tex]
- Step 3: Write the expression by factoring out the GCF.
- The expression becomes [tex]\(3(2x^2 + 3)\)[/tex].
So, the factored form by pulling out the GCF is [tex]\(3(2x^2 + 3)\)[/tex].
12. For the quadratic [tex]\(5x^2 + 25x + 20\)[/tex]:
- Step 1: Identify the GCF of the terms in the expression.
- The terms are [tex]\(5x^2\)[/tex], [tex]\(25x\)[/tex], and [tex]\(20\)[/tex].
- The GCF of [tex]\(5\)[/tex], [tex]\(25\)[/tex], and [tex]\(20\)[/tex] is [tex]\(5\)[/tex].
- Step 2: Factor out the GCF.
- Divide each term by the GCF, [tex]\(5\)[/tex].
- [tex]\(5x^2 \div 5 = 1x^2\)[/tex] or simply [tex]\(x^2\)[/tex]
- [tex]\(25x \div 5 = 5x\)[/tex]
- [tex]\(20 \div 5 = 4\)[/tex]
- Step 3: Write the expression by factoring out the GCF.
- The expression becomes [tex]\(5(x^2 + 5x + 4)\)[/tex].
So, the factored form by pulling out the GCF is [tex]\(5(x^2 + 5x + 4)\)[/tex].
In conclusion, the expressions factored by pulling out the GCF are:
- [tex]\(6x^2 + 9\)[/tex] is factored as [tex]\(3(2x^2 + 3)\)[/tex].
- [tex]\(5x^2 + 25x + 20\)[/tex] is factored as [tex]\(5(x^2 + 5x + 4)\)[/tex].
11. For the quadratic [tex]\(6x^2 + 9\)[/tex]:
- Step 1: Identify the GCF of the terms in the expression.
- The terms are [tex]\(6x^2\)[/tex] and [tex]\(9\)[/tex].
- The GCF of [tex]\(6\)[/tex] and [tex]\(9\)[/tex] is [tex]\(3\)[/tex].
- Step 2: Factor out the GCF.
- Divide each term by the GCF, [tex]\(3\)[/tex].
- [tex]\(6x^2 \div 3 = 2x^2\)[/tex]
- [tex]\(9 \div 3 = 3\)[/tex]
- Step 3: Write the expression by factoring out the GCF.
- The expression becomes [tex]\(3(2x^2 + 3)\)[/tex].
So, the factored form by pulling out the GCF is [tex]\(3(2x^2 + 3)\)[/tex].
12. For the quadratic [tex]\(5x^2 + 25x + 20\)[/tex]:
- Step 1: Identify the GCF of the terms in the expression.
- The terms are [tex]\(5x^2\)[/tex], [tex]\(25x\)[/tex], and [tex]\(20\)[/tex].
- The GCF of [tex]\(5\)[/tex], [tex]\(25\)[/tex], and [tex]\(20\)[/tex] is [tex]\(5\)[/tex].
- Step 2: Factor out the GCF.
- Divide each term by the GCF, [tex]\(5\)[/tex].
- [tex]\(5x^2 \div 5 = 1x^2\)[/tex] or simply [tex]\(x^2\)[/tex]
- [tex]\(25x \div 5 = 5x\)[/tex]
- [tex]\(20 \div 5 = 4\)[/tex]
- Step 3: Write the expression by factoring out the GCF.
- The expression becomes [tex]\(5(x^2 + 5x + 4)\)[/tex].
So, the factored form by pulling out the GCF is [tex]\(5(x^2 + 5x + 4)\)[/tex].
In conclusion, the expressions factored by pulling out the GCF are:
- [tex]\(6x^2 + 9\)[/tex] is factored as [tex]\(3(2x^2 + 3)\)[/tex].
- [tex]\(5x^2 + 25x + 20\)[/tex] is factored as [tex]\(5(x^2 + 5x + 4)\)[/tex].
