Question

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Answer 1

Solution :-

↪ x³ + 13x² + 32x + 20

↪ x³ + x² + 12x² + 12x + 20x + 20

↪x²(x + 1) + 12x(x + 1) + 20(x + 1)

↪(x + 1) (x² + 12x + 20)

↪(x + 1) (x² + 10x + 2x + 20)

↪(x + 1) [x(x + 10) + 2(x + 10)]

↪(x + 1) (x + 10) (x + 2)

Some algebraic identities:-

• (a + b)² = a² + 2ab + b²

• (a² - b²) = (a + b) (a - b)

• (a + b)³ = a³ + 3a²b + 3ab²+ b³

• (a - b)³ = a³ - 3a²b + 3ab² - b³

• (a + b + c)² = a²+b²+c²+2ab+2bc+2ac

• (x + a) (x + b) = x² + (a+b)x + ab

Answer 2

x³+13x²+32x+20

=(x+1)(x²+12x+20)

  [∵, for x = -1, x³+13x²+32x+20

= -1+13-32+20

= 0. ]

=(x+1)(x²+10x+2x+20)

=(x+1){x(x+10)+2(x+10)}

=(x+1){(x+10)(x+2)}

=(x+1)(x+2)(x+10)