Question

Factorise
x2 + 3x -40​

Answer 1

Answer:

( x + 8 ) ( x - 5 )

Step-by-step explanation:

$\large \text{Given p(x)= x^2+3x-40 }\\\\\\\large \text{we have to factorise it }\\\\\\\large \text{By splitting mid term method ac = +-b }\\\\\\\large \text{Here -40 = 8 \times- 5 }\\\\\\\large p(x)= x^2+3x-40$

$\large p(x)= x^2+8x-5x-40\\\\\\\large p(x)= x(x+8)-5(x+8)\\\\\\\large p(x)= (x+8)(x-5)\\\\\\\large \text{Zeroes of p(x)}$

$\large x+8=0 \ or \ x-5=0\\\\\\\large x=-8 \ or \ x=5$

Thus we factorise the p(x) and also get zeroes of it.

Answer 2

Answer:

$\mathrm{Factor}\:x^2+3x-40:\quad \left(x-5\right)\left(x+8\right)$

Step-by-step explanation:

$x^2+3x-40$

$\rule{250}{1}$

$\mathrm{Break\:the\:expression\:into\:groups}$

$\mathrm{Use\:Middle\:term\:splitting}$

$=\left(x^2-5x\right)+\left(8x-40\right)$

$\rule{250}{1}$

$\mathrm{Factor\:out\:}x\mathrm{\:from\:}x^2-5x$

$x^2-5x$

$\rule{250}{0.3}$

$\mathrm{Apply\:exponent\:rule}:\quad \:a^{b+c}=a^ba^c$

$x^2=xx$

$\rule{250}{0.3}$

$\mathrm{Factor\:out\:common\:term\:}x$

$=x\left(x-5\right)$

$\rule{250}{1}$

$\mathrm{Factor\:out\:}8\mathrm{\:from\:}8x-40$

$8x-40$

$\rule{250}{0.3}$

$\mathrm{Rewrite\:}40\mathrm{\:as\:}8\cdot \:5$

$=8x-8\cdot \:5$

$\rule{250}{0.3}$

$\mathrm{Factor\:out\:common\:term\:}8$

$=8\left(x-5\right)$

$\rule{250}{1}$

$=x\left(x-5\right)+8\left(x-5\right)$

$\rule{250}{1}$

$\mathrm{Factor\:out\:common\:term\:}x-5$

$=\left(x-5\right)\left(x+8\right)$