Question

Q-8 If x+ 2a is a factor of a5 -4a²x³ + 2x+ 2a +3, find the value of a.

(4)

Answer 1

Step-by-step explanation:

Given: If x+ 2a is a factor of $x^5 -4a^2x^3 + 2x+ 2a +3$,

To find: Find the value of a.

Solution:

Tip: Apply factor theorem.

It states that,if (x-a) is a factor of polynomial f(x), then f(a)=0

Step 1: Put x+2a=0 and find the value of x

$x = - 2a \: ...eq1$

Step 2: Put the value of eq1 in polynomial and find a

${x}^{5} - 4 {a}^{2} {x}^{3} + 2x + 2a + 3 = 0 \\ \\ { (- 2a)}^{5} - 4 {a}^{2} {( - 2a)}^{3} + 2( - 2a)+ 2a + 3 = 0 \\ \\ - 32 {a}^{5} + 32 {a}^{2} {a}^{3} - 4a + 2a + 3 = 0$

because

$\boxed{\bold{ {x}^{n} . {x}^{m} = {x}^{n + m} }}$

Apply the formula

$- 32 {a}^{5} +32 {a}^{5}- 2a + 3 = 0$

Cancel same terms having opposite signs

$\cancel{- 32 {a}^{5}} +\cancel{ 32 {a}^{5}} - 2a + 3 = 0$

$- 2a + 3 = 0 \\ \\ - 2a = - 3 \\ \\ 2a = 3 \\ \\ a = \frac{3}{2}$

Final answer:

If x+ 2a is a factor of $x^5 -4a^2x^3 + 2x+ 2a +3$,then

$\boxed{\bold{\green{a = \frac{3}{2}} }}$

Hope it helps you.

To learn more on brainly:

1) Find the value of 'a' for which 2x³+ax²+11x+a+3 is exactly divisible by 2x-1

Please show the whole solution also because...

https://brainly.in/question/1194454

2) check whether 7+3x is a factor of 3x³+7x

https://brainly.in/question/1198290

Answer 2

Answer:

Step-by-step explanation:

Given: If x+ 2a is a factor of x^5 -4a^2x^3 + 2x+ 2a +3x

5

−4a

2

x

3

+2x+2a+3 ,

To find: Find the value of a.

Solution:

Tip: Apply factor theorem.

It states that,if (x-a) is a factor of polynomial f(x), then f(a)=0

Step 1: Put x+2a=0 and find the value of x

\begin{gathered}x = - 2a \: ...eq1 \\ \end{gathered}

x=−2a...eq1

Step 2: Put the value of eq1 in polynomial and find a

\begin{gathered} {x}^{5} - 4 {a}^{2} {x}^{3} + 2x + 2a + 3 = 0 \\ \\ { (- 2a)}^{5} - 4 {a}^{2} {( - 2a)}^{3} + 2( - 2a)+ 2a + 3 = 0 \\ \\ - 32 {a}^{5} + 32 {a}^{2} {a}^{3} - 4a + 2a + 3 = 0 \\ \\ \end{gathered}

x

5

−4a

2

x

3

+2x+2a+3=0

(−2a)

5

−4a

2

(−2a)

3

+2(−2a)+2a+3=0

−32a

5

+32a

2

a

3

−4a+2a+3=0

because

\begin{gathered}\boxed{\bold{ {x}^{n} . {x}^{m} = {x}^{n + m} }} \\ \\ \end{gathered}

x

n

.x

m

=x

n+m

Apply the formula

\begin{gathered}- 32 {a}^{5} +32 {a}^{5}- 2a + 3 = 0 \\ \\ \end{gathered}

−32a

5

+32a

5

−2a+3=0

Cancel same terms having opposite signs

\begin{gathered} \cancel{- 32 {a}^{5}} +\cancel{ 32 {a}^{5}} - 2a + 3 = 0 \\ \\ \end{gathered}

−32a

5

+

32a

5

−2a+3=0

\begin{gathered} - 2a + 3 = 0 \\ \\ - 2a = - 3 \\ \\ 2a = 3 \\ \\ a = \frac{3}{2} \\ \\ \end{gathered}

−2a+3=0

−2a=−3

2a=3

a=

2

3

Final answer:

If x+ 2a is a factor of x^5 -4a^2x^3 + 2x+ 2a +3x

5

−4a

2

x

3

+2x+2a+3 ,then

\begin{gathered}\boxed{\bold{\green{a = \frac{3}{2}} }} \\ \\ \end{gathered}

a=

2

3

Hope it helps you.

To learn more on brainly:

1) Find the value of 'a' for which 2x³+ax²+11x+a+3 is exactly divisible by 2x-1

Please show the whole solution also because...

https://brainly.in/question/1194454

2) check whether 7+3x is a factor of 3x³+7x

https://brainly.in/question/1198290