To factor the quadratic expression \(12x^2 + 23x + 10\), we can use the method of factoring by grouping. 1. Multiply the coefficient of \(x^2\) (which is 12) by the constant term (which is 10): \[ 12 \times 10 = 120. \] 2. We need to find two numbers that multiply to 120 and add up to 23 (the coefficient of \(x\)). The two numbers that work are 15 and 8 because: \[ 15 \times 8 = 120 \quad \text{and} \quad 15 + 8 = 23. \] 3. Rewrite the middle term (23x) using 15 and 8: \[ 12x^2 + 15x + 8x + 10. \] 4. Now, group the terms: \[ (12x^2 + 15x) + (8x + 10). \] 5. Factor out the greatest common factor from each group: \[ 3x(4x + 5) + 2(4x + 5). \] 6. Now, we can factor out the common binomial factor \((4x + 5)\): \[ (4x + 5)(3x + 2). \] Thus, the factored form of \(12x^2 + 23x + 10\) is: \[ (4x + 5)(3x + 2). \]

12x^2+23x+10. Factor

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To factor the quadratic expression \(12x^2 + 23x + 10\), we can use the method of factoring by grouping.

Multiply the coefficient of \(x^2\) (which is 12) by the constant term (which is 10): \[ 12 \times 10 = 120. \]
We need to find two numbers that multiply to 120 and add up to 23 (the coefficient of \(x\)). The two numbers that work are 15 and 8 because: \[ 15 \times 8 = 120 \quad \text{and} \quad 15 + 8 = 23. \]
Rewrite the middle term (23x) using 15 and 8: \[ 12x^2 + 15x + 8x + 10. \]
Now, group the terms: \[ (12x^2 + 15x) + (8x + 10). \]
Factor out the greatest common factor from each group: \[ 3x(4x + 5) + 2(4x + 5). \]
Now, we can factor out the common binomial factor \((4x + 5)\): \[ (4x + 5)(3x + 2). \]

Thus, the factored form of \(12x^2 + 23x + 10\) is: \[ (4x + 5)(3x + 2). \]