Question

Factoring
5x^2-37x + 42​

Answer 1

`=\left(5x-7\right)\left(x-6\right)`

Explanation:

`5x^2-37x + 42\\Break\:the\:expression\:into\:groups\\=\left(5x^2-7x\right)+\left(-30x+42\right)\\\mathrm{Factor\:out\:}x\mathrm{\:from\:}5x^2-7x\mathrm{:\quad }x\left(5x-7\right)\\5x^2-7x\\\mathrm{Apply\:exponent\:rule}:\quad \:a^(b+c)=a^ba^c\\x^2=xx\\=5xx-7x\\\mathrm{Factor\:out\:common\:term\:}x\\=x\left(5x-7\right)`

`\mathrm{Factor\:out\:}-6\mathrm{\:from\:}-30x+42\mathrm{:\quad }-6\left(5x-7\right)\\-30x+42\\\mathrm{Rewrite\:}42\mathrm{\:as\:}6\cdot \:7\\\mathrm{Rewrite\:}30\mathrm{\:as\:}6\cdot \:5\\=-6\cdot \:5x+6\cdot \:7\\\mathrm{Factor\:out\:common\:term\:}-6\\=-6\left(5x-7\right)\\=x\left(5x-7\right)-6\left(5x-7\right)\\\mathrm{Factor\:out\:common\:term\:}5x-7\\=\left(5x-7\right)\left(x-6\right)`