Question

What will be the value of a , If y+2 is a factor of 4y^4+2y^3+8y+5a​

Answer 1

$\underline{\boxed{\bold{Question}}}$  

↠ What will be the value of a , If y+2 is a factor of 4y⁴ + 2y³ + 8y + 5a​ ?

$\; \; \; \;$  

━━━━━━━━━━━━━━━━━━━━━━━━━━━━━

$\; \; \; \;$  

$\underline{\boxed{\bold{Important\;Information}}}$  

❏ Remainder theorem : When we substitute the value of factor by equation it with zero , remainder will come out zero if it is a factor on that polynomial.

 $\; \; \; \;$  

━━━━━━━━━━━━━━━━━━━━━━━━━━━━━

 $\; \; \; \;$  

$\underline{\boxed{\bold{Given}}}$

↠ Polynomial = 4y⁴ + 2y³ + 8y + 5a​

↠ Factor = (y + 2)

 $\; \; \; \;$  

━━━━━━━━━━━━━━━━━━━━━━━━━━━━━

  $\; \; \; \;$  

$\underline{\boxed{\bold{Answer}}}$

Let's Start !

  $\; \; \; \;$  

━━━━━━━━━━━━━━━━━━━━━━━━━━━━━

  $\; \; \; \;$  

First of all let's find value of "y"

  $\; \; \; \;$  

$\bold { \red { :\implies (y+2)= 0 } }$

$\boxed { \bold { \blue { :\implies y = -2 } } }$

 $\; \; \; \;$  

Now let's substitute this value in given polynomial !

 $\; \; \; \;$  

$\bold { \red { :\implies 4y^{4}+2y^{3}+8y + 5a = 0 } }$

$\bold { \blue { :\implies 4(-2)^{4}+2(-2)^{3}+8(-2) + 5a = 0 } }$

$\bold { \red { :\implies (4 \times 16) + (2 \times -8) +(8 \times -2) + 5a = 0 } }$

$\bold { \blue { :\implies 64 - 16 -16 + 5a = 0 } }$

$\bold { \red { :\implies 32 + 5a = 0 } }$

$\bold { \blue { :\implies 5a = -32 } }$

$\boxed { \bold { \orange { :\implies a = \frac{-32}{5} } } }$

  $\; \; \; \;$  

━━━━━━━━━━━━━━━━━━━━━━━━━━━━━

  $\; \; \; \;$  

$\boxed{\boxed{\bold{\therefore Value \; of \; a = \frac{-32}{5} }}}$

  $\; \; \; \;$  

━━━━━━━━━━━━━━━━━━━━━━━━━━━━━

 $\; \; \; \;$  

Hope this helps u.../

【Brainly Advisor】

Answer 2

$\underline{\boxed{\bold\red{Question}}}$

What will be the value of a , If y+2 is a factor of 4y⁴+2y³+8y+5a

━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━

$\underline{\boxed{\bold\blue{Answer}}}$

⋆4y⁴+2y³+8y+5a--------eqn(1)

⋆First, let's find the value of Y

⇝Y+2=0

⇝Y=-2

━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━

Substituting the value of Y in the eqn (1)

⇝4(-2)⁴+2(-2)³+8(-2)+5a=0

⇝4(-16)+2(-8)+8(-2)+5a=0

⇝-64-16-16+5a=0

⇝-96+5a=0

⇝5a=96

$⇝a=\frac{96}{5}$

[Hope this helps you.../]