Question

1.Factorize the following: ) x^3 + 5x^2 +7x + 3

Answer 1

x³+5x²+7x+3 = (x+3)(x²+2x+1)

= (x+3)(x+1)(x+1)

So, the three roots are : –3, –1 and –1

Answer 2

$\huge\purple{♡}\pink {Answer}\purple {♡}$

${x}^{3} + {5x}^{2} + 7x + 3$

Rewrite 5x^2 as a sum

${x}^{3} + ({x}^{2} + {4x}^{2} )+ 7x + 3$

Rewrite 7x as a sum

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

${x}^{2} (x + 1) + 4x(x + 1) + 3(x + 1)$

Factor out (x + 1)

$(x + 1)( {x}^{2} + 4x + 3)$

Rewrite 4x as a sum

$(x + 1)( {x}^{2} + 3x + x + 3)$

$(x + 1)(x(x + 3) + 1(x + 3))$

$(x + 1)(x + 3)(x + 1)$

${(x + 1)}^{2} (x + 3)$

hope it helps you........✌