Question

FACTORISE
${x}^{4} + 3 {x}^{2} + 4$
​

Answer 1

Step-by-step explanation:

${x}^{4} + 3 {x}^{2} - 4 = 0 \\ = > {( {x}^{2} )}^{2} + 4 {x}^{2} - {x}^{2} - 4 = 0 \\ = > {x}^{2} ( {x}^{2} + 4) - 1( {x}^{2} + 4) = 0\\ = > ( {x}^{2} + 4)( {x}^{2} - 1)$

Answer 2

$\huge{ \bold{ \star{ \underline{ \red{ \: Question...}}}}}$

✳FACTORISE

${x}^{4} + 3 {x}^{2} + 4$

$\huge{ \bold{ \star{ \underline{ \red{ \: Answer...}}}}}$

✏(x2+4)(x+1)(x-1)

$\huge{ \bold{ \star{ \underline{ \red{ Solution...}}}}}$

$\large{ \sf{ \mapsto{ \: \:p(x) = {x}^{4} + 3 {x}^{2} - 4}}} \\ \\ \large{ \green{ \sf{let \: assume \: {x}^{2} \: be \: \red{a} }}}...... \\ \\ \large{ \sf{ \mapsto{ \: then \:p( {x}^{2}) \: = \: \: {a}^{2} + 3a - 4}}} \\ { \sf{ \purple{ \underline{(\: {x}^{2} = a)}}}} \\ \\ \large{ \sf{ \mapsto{ \: \: {a}^{2} + 4a - a - 4}}} \\ { \sf{ \underline{ \purple{by \: middle \: term \: factorization..}}}} \\ \\ \large{ \sf{ \mapsto{a(a + 4) - 1(a + 4)}}} \\ \\ \large{ \sf{ \mapsto{(a + 4)(a - 1)}}} \\ \\ \large{ \sf{ \mapsto{( {x}^{2} + 4)( {x}^{2} - 1)}}} \\ \\ \large{ \sf{ \mapsto{ \green{ \boxed{( {x}^{2} + 4)(x + 1)(x - 1)}}}}}$

▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃

$\large{ \bold{ \orange{ \underline{ required \: answer \: is \: ( {x}^{2} + 4)(x - 1)(x + 1)}}}}$