Question

x^3 + 13x^2 + 32x + 20
plz help me the person who answer fast i'll mark him/her brainlieast

Answer 1

SoluTion:

Given polynomial:

• x³ + 13x² + 32x + 20

To find :

• Factors of given polynomial

Explanation:

→ x³ + 13x² + 32x + 20

By hit and trial method,

→ put x = 0

→ (0)³ + 13(0)² + 32(0) + 20

→ 20 ≠ 0

Hence, it isn't a factor of given Polynomial.

→ put x = -1

→ (-1)³ + 13(-1)² + 32(-1) + 20

→ -1 + 13 - 32 + 20

→ 0 = 0

Hence, (x + 1) is a factor of given Polynomial.

Now, divide given Polynomial by (x + 1).

[ Refer to the attachment ]

For more factors, split the middle term of x² + 12x + 20.

→ x² + 10x + 2x + 20

→ x(x + 10) + 2(x + 10)

→ (x + 10) (x + 2)

Hence, all factors are (x + 10), (x + 2) and (x + 1).

Answer 2

✯✯ QUESTION ✯✯

${x}^{3}+{13x}^{2}+32x+{20}$..

━━━━━━━━━━━━━━━━━━━━

✰✰ ANSWER ✰✰

$\longmapsto\tt{Constant\:Term=20}$

$\longmapsto\tt{Factors\:of\:20=+-1,+-2,+-4}........$

☛Now ,

$\longmapsto\tt{x-1=0}$

$\longmapsto\tt{x=1}$

➙Putting x=1 : -

$\longmapsto\tt{{(1)}^{3}+13{(1)}^{2}+32(1)+20}$

$\longmapsto\tt{1+13+32+20}$

$\longmapsto\tt{66}$

No , x-1 is not a factor of x³ + 13x² + 32x + 20..

_______________________

$\longmapsto\tt{x+2=0}$

$\longmapsto\tt{x=-2}$

➙Putting x=-2 : -

$\longmapsto\tt{{-2}^{3}+13{(-2)}^{2}+32(-2)+20}$

$\longmapsto\tt{-8+13(4)-64+20}$

$\longmapsto\tt{-8+52-64+20}$

$\longmapsto\tt{-72+72}$

$\longmapsto\tt{0}$

Yes , x+2 is a factor of x³ + 13x² + 32x + 20..

➜So , Divide the polynomial x³ + 13x² + 32x + 20 by x + 2..

(See the attachment)

➥Now ,

By Splitting Middle Term : -

$\longmapsto\tt{{x}^{2}+11x+10}$

$\longmapsto\tt{{x}^{2}+10x+1x+10}$

$\longmapsto\tt{x(x+10)+1(x+10)}$

$\longmapsto\tt{(x+1)(x+10)}$

☛Three Factors are (x+2) , (x+1) , (x+10)..