## Algebra: A Combined Approach (4th Edition)

Appendix A - Ex. Set : 57 (Answer) $20x^2 + 23x + 6 = (5x + 2)(4x + 3)$
Appendix A - Ex. Set : 57 (Solution) Factorize : $20x^2 + 23x + 6$ Factors of $20x^2$ : $x\cdot20x$ or $2x\cdot10x$ or $4x\cdot5x$ or $5x\cdot4x$ or $10x\cdot2x$ or $20x\cdot x$ Factors of 6 : $1\cdot6$ or $2\cdot3$ or $3\cdot2$ or $6\cdot1$ Try combination of those factors $(x + 1)(20x + 6) = 20x^2 + 26x + 6$ (Incorrect middle term) $(x + 2)(20x + 3) = 20x^2 + 43x + 6$ (Incorrect middle term) $(2x + 1)(10x + 6) = 20x^2 + 22x + 6$ (Incorrect middle term) $(2x + 2)(10x + 3) = 20x^2 + 26x + 6$ (Incorrect middle term) $(4x + 1)(5x + 6) = 20x^2 + 29x + 6$ (Incorrect middle term) $(4x + 2)(5x + 3) = 20x^2 + 22x + 6$ (Incorrect middle term) $(5x + 1)(4x + 6) = 20x^2 + 34x + 6$ (Incorrect middle term) $(5x + 2)(4x + 3) = 20x^2 + 23x + 6$ (Correct middle term) As solution found, no need to try other options Thus, $20x^2 + 23x + 6 = (5x + 2)(4x + 3)$