Question

factorise x^3+13x^2+32x+20
dear friend I want this question to be explained very easily and short ​

Answer 1

Answer:

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)

Step-by-step explanation:

Let p(x) = x3 + 13x2 + 32x + 20

p(-1) = -1 + 13 - 32 + 20 = -33 + 33 = 0

Therefore (x + 1) is a factor of p(x).

On dividing p(x) by (x + 1) we get

p(x)  (x + 1) = x2 + 12x + 20

Thus,

x3 + 13x2 + 32x + 20 = (x + 1)(x2 + 12x + 20)

= (x + 1) (x2 + 10x + 2x + 20)

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

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

Hence, x3 + 13x2 + 32x + 20

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

Answer 2

Answer:

The final answer is,

factors of p(x) = (x+1) (x+2) (x+10)

Step-by-step explanation:

• Take the given polynomial as p(x).
• Take the given polynomial as p(x).Try to get the value of the polynomial 0 by putting different value for x.
• Take the given polynomial as p(x).Try to get the value of the polynomial 0 by putting different value for x.By factor theorem if p(a) gives 0 then (x -a) is the factor of the polynomial.
• Take the given polynomial as p(x).Try to get the value of the polynomial 0 by putting different value for x.By factor theorem if p(a) gives 0 then (x -a) is the factor of the polynomial.Divide the polynomial with the factor so obtained using long division method.
• Take the given polynomial as p(x).Try to get the value of the polynomial 0 by putting different value for x.By factor theorem if p(a) gives 0 then (x -a) is the factor of the polynomial.Divide the polynomial with the factor so obtained using long division method.Factorise the quotient (it will be a quadratic polynomial).
• Take the given polynomial as p(x).Try to get the value of the polynomial 0 by putting different value for x.By factor theorem if p(a) gives 0 then (x -a) is the factor of the polynomial.Divide the polynomial with the factor so obtained using long division method.Factorise the quotient (it will be a quadratic polynomial).The factors of the quotient and the first quotient we obtained will be the factors of the given polynomial.

hope this answer helps you.