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Factor the expression:
[tex]\[ 3x^2 - 11x - 20 \][/tex]


Sagot :

To factor the quadratic expression [tex]\(3x^2 - 11x - 20\)[/tex], follow these steps:

1. Identify the coefficients:
The given quadratic expression is in the form [tex]\(ax^2 + bx + c\)[/tex], where:
- [tex]\(a = 3\)[/tex]
- [tex]\(b = -11\)[/tex]
- [tex]\(c = -20\)[/tex]

2. Look for factors:
We need to find two numbers that multiply to [tex]\(a \cdot c = 3 \cdot (-20) = -60\)[/tex] and add up to [tex]\(b = -11\)[/tex].

3. Find factor pairs:
The pairs of factors of -60 that add up to -11 are:
[tex]\((-15) \cdot 4 = -60\)[/tex] and [tex]\((-15) + 4 = -11\)[/tex].

4. Rewrite the middle term:
Rewrite [tex]\(-11x\)[/tex] using these two numbers:
[tex]\[ 3x^2 - 15x + 4x - 20 \][/tex]

5. Group terms:
Group the terms to factor by grouping:
[tex]\[ (3x^2 - 15x) + (4x - 20) \][/tex]

6. Factor out the greatest common factor (GCF) from each group:
[tex]\[ 3x(x - 5) + 4(x - 5) \][/tex]

7. Factor by grouping:
Notice that [tex]\((x - 5)\)[/tex] is a common factor:
[tex]\[ (3x + 4)(x - 5) \][/tex]

We've factored the quadratic expression [tex]\(3x^2 - 11x - 20\)[/tex] into [tex]\((3x + 4)(x - 5)\)[/tex].

Thus, the factored form of the expression is:
[tex]\[ (3x + 4)(x - 5) \][/tex]
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