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Factorize fully:

[tex]\[ 6x^2 + 9x - 10 \][/tex]

Sagot :

GinnyAnswer
To fully factorize the quadratic expression \(6x^2 + 9x - 10\), follow these detailed steps:

1. Identify coefficients:
- \(a = 6\)
- \(b = 9\)
- \(c = -10\)

2. Multiply \(a\) and \(c\):
- \(ac = 6 \times (-10) = -60\)

3. Find two numbers that multiply to \(ac\) and add to \(b\):
- We need two numbers that multiply to \(-60\) and add to \(9\).

These numbers are \(15\) and \(-4\):
- \(15 \times (-4) = -60\)
- \(15 + (-4) = 9\)

4. Rewrite the middle term \(9x\) using \(15\) and \(-4\):
- \(6x^2 + 15x - 4x - 10\)

5. Factor by grouping:
- Group the terms:
[tex]\[(6x^2 + 15x) + (-4x - 10)\][/tex]

- Factor out the greatest common factor (GCF) from each group:
[tex]\[3x(2x + 5) - 2(2x + 5)\][/tex]

6. Factor out the common binomial \((2x + 5)\):
- \((2x + 5)(3x - 2)\)

So, the fully factorized form of the expression \(6x^2 + 9x - 10\) is:
[tex]\[ (2x + 5)(3x - 2) \][/tex]
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