Question

can anyone solve this 4 problems of plynominals u hve to find the remainder when p(x) Is divided by g(x)

Answer 1

⭐⭐Hello friend..Ur answer is here⤵⤵

⚫Q.7 p (x)=x^3-2x^2-8x-1 , g (x)=x+1

➡ put x= -1

➡ (-1)^3-2 (-1)^2-8 (-1)-1

➡ -1-2+8-1

➡4

⚫Q.8 p (x)=2x^3+x^2-15x-12 , g (x)=x+2

➡ put x= -2

➡ 2 (-2)^3+(-2)^2-15 (-2)-12

➡ -16+4+30-12

➡6

⚫Q.9 p (x)=6x^3+13x^2+3 , g (x)=3x+2

➡ put = -2/3

➡ 6 (-2/3)^3+13 (-2/3)^2+3

➡ 6×(-8/27)+13 (4/9)+3

➡-48+156+81 /27

➡7

⚫Q.10 x^3-6x^2+2x-4 , g (x)=1-3/2x

➡put x=2/3

➡ (2/3)^3-6 (2/3)^2+2 (2/3)-4

➡ 8/27-8/3+4/3-4

➡8-72+36-108/27

➡ -136/27

I HOPE IT IS HELPFUL TO YOU ☺

Answer 2

Hey dear !!
____________________________

==>> In the example

We have to find the remainder .

So, we will use factor theorem to find the remainder . Lets do it !!!

7.) p(x) = x³ - 2x² - 8x - 1, g(x) = x + 1

==> Answer
taking x + 1 = 0 ∴ x = - 1

Now putting the value of x = -1 in the equation we get ,

p(-1) = (-1)³ - 2* ( -1)² - 8*(-1) -1

=> -1 -2*1 + 8 -1

=> -1 -2 + 8 - 1

=>-3 + 8 - 1

=> 5 - 1

=>4

∴ The Remainder is 4

___________________________

8.) p(x) = 2x³ + x² - 15x - 12 , g(x) = x +2

==>Answer

taking x + 2 = 0 ∴ x = -2

Now, putting the value of x = -2 in the equation we get ,

p(-2) = 2*(-2)³ + (-2)² -15*(-2) - 12

=> 2*(-8) + 4 + 30 - 12

=> -16 + 4 + 30 - 12

=> -12 + 30 - 12

=> 18 - 12

=> 6

∴ The Remainder is 6

___________________________

9.) p(x) = 6x³ + 13x² + 3 it can be written as p(x) = 6x³ + 13x² + 0x + 3 .., g(x) = 3x+2

==> Answer

taking 3x + 2 = 0

3x = -2

x = -2/3

Now, putting the value of x = -2/3 in equation we get,

$p( \frac{ - 2}{3} ) = 6( \frac{ - 2}{3} ) {}^{3} + 13( \frac{ - 2}{3} ) {}^{2} + 0( \frac{ - 2}{3} ) + 3 \\ \\ => 6( \frac{ - 8}{27} ) + 13( \frac{4}{9} ) + 0 + 3 \\ \\ =>\frac{ - 48}{27} + \frac{52}{9} + 3 \\ \\ => \frac{ - 48 + 156}{27} + 3 \\ \\ => \frac{108}{27} + \frac{81}{27} \\ \\ => \frac{189}{27} \\ \\ => 7$

∴ The Remainder is 7

___________________________

10.) p(x) = x³ - 6x² + 2x - 4 , g(x) = 1-3/2x

==> Answer

$taking \: \frac{1 - 3}{2} x = 0 \\ \\ \frac{ - 3x}{2} = - 1 \\ \\ - 3x = - 1 \times 2 \\ \\ - 3x = - 2 \: \: \: \: \: \: ......(multiply \: by \: - 1 \: both \: side) \\ \\ 3x = 2 \\ \\ x = \frac{2}{3}$
Now, putting x = 2/3 in equation we get,

$p( \frac{2}{3} ) = ( \frac{2}{3}) {}^{3} - 6( \frac{2}{3} ) {}^{2} + 2( \frac{2}{3} ) - 4 \\ \\ => \frac{8}{27} - 6( \frac{4}{3} )+ \frac{4}{3} - 4 \\ \\ => \frac{8}{27} - \frac{ 8}{3 } + \frac{4}{3} - 4 \\ \\ => \frac{8 - 72 + 36 - 108}{27} \\ \\ => \frac{ - 136}{27}$
∴ The remainder is -136/27

Thanks !!!!

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