Question

Factorizex^3+3x^2+3x+28​

Answer 1

Step-by-step explanation:

$\: \: \sf \: {x}^{3} + 3 {x}^{2} + 3x + 28 \\ \\ \: \: \sf \: {x}^{3} + 3 {x}^{2} + 3x + 1 + 27 \\ \\ \: \: \sf \: {(x + 1)}^{3} + 27 \\ \\ \: \sf \: {(x + 1)}^{3} + {3}^{3} \\ \\ \: \sf \: ((x + 1) + 3)( {( x + 1)}^{2} - 3(x + 1) + {3}^{2}) \: \: \: \: \: (using \: the \: identity \: {a}^{3} + {b}^{3} = (a + b)( {a}^{2} - ab + {b}^{2} )) \\ \\ \\ \: \: \sf \: (x + 4)( {x}^{2} + 1 + 2x - 3x - 3 + 9) \\ \\ \: \: \sf \dagger \therefore (x + 4)( {x}^{2} - x + 7)$

Hence, After factories we get (x+4)(x^2-x+7).

Additional Information:

• Factorization is only about splitting how much you split.
• Factorization by taking common factor.
• When each term of an expression has no common factor,we divide each term by this factor and take it out as a multiple.