Question

Factorise the following expressions.

i) p^2+6p+8

ii) q^2-10q+21

iii) p^2+6p-16​

Answer 1

above your answer

plz thank

Answer 2

$\bold{\LARGE{\underline{\underline{Answer:–}}}}$

$i)\: p² \:+ 6p\: +\: 8$

$\longrightarrow\:\: p²\:+\:2p\:+\:4p\:+\:8$

$\longrightarrow\:\:(p²\:+\:2p)\:+\:(4p\:+\:8)$

$\longrightarrow\:\:p\:(p\:+\:2)\:+\:4\:(p\: -\:2$

Now , take (p + 2) as common

$\longrightarrow\:\:(p\:+\:2)\:(p\:+\:4)$

So, $i)\: p² \:+ 6p\: +\: 8\:=\:(p\:+\:2)\:(p\:+\:4)$

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$ii) \:q²\: -\:10q\:+\:21$

$\longrightarrow\:\:q²\: -\:3q\: -\:7q\:+\:21$

$\longrightarrow\:\:(q²\: -\:3q)\: -\:(7q\: -\:21)$

$\longrightarrow\:\:q\:(q \: -\:3)\: -\:7(q\: -\:3)$

$\longrightarrow\:\:(q\: -\:3)\:(q\: -\:7)$

Now, taking (q -3) as common

So, $q²\: -\:10q\:+\:21\:=\:(q\: -\:3)\:(q\: -\:7)$

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$iii)\: p²\:+\:6p\: -\: 16$

$\longrightarrow\:\:p²\: -\:2p\:+\:8p\: -\:16$

$\longrightarrow\:\:(p²\: -\:2p)\:+\:(8p\: -\:16$

$\longrightarrow\:\:p\:(p\: -\:2)\:+\:8\:(p\: -\:2)$

Now, taking (p - 2) as common

$\longrightarrow\:\:(p\: -\:2)\:(p\:+\:8)$

So, $p²\:+\:6p\: -\: 16\:=\:(p\: -\:2)\:(p\:+\:8)$