Question

p(x) = x^3 + 8x^2 – 7x + 12 and g(x) = x - 1. if p(x)
divided by g(x), it gives q(X)and r(X)
as quotient and
remainder respectively. If a is the degree of
q(x) and b is
the degree of r(x), (a - b) =?
a. 1
b. 2
C. 3
d. 4​

Answer 1

Answer:

The correct answer is option (b) 2.

Step-by-step explanation:

Given :

$p(x)=x^{3}+8 x^{2}-7 x+12$ and $g(x)=(x-1)$.

To find if a is the degree of q(x) and b is the degree of r(x), (a - b) =?

Step 1

The degree of a polynomial exists at the highest degree of its terms when the polynomial exists expressed in its canonical form consisting of a linear combination of monomials.

So, the Degree of $r(x)=b=0$

$q(x)=\frac{p(x)}{g(x)}$

$p(x)=x^{3}+8 x^{2}-7 x+12$

$g(x)=(x-1)$

Step 2

Performing long division

By dividing the equation $x^{3}+8 x^{2}-7 x+12$ throughout by $x-1$, we get

$&x-1) \frac{x^{2}+9 x+2}{x^{3}+8 x^{2}-7 x+12}$

$&x^{3}-x^{2}$

$&\text { (-) (+) }$

$&9 x^{2}-7 x$

$&9 x^{2}-9 x$

$&\text { (-) }(+)$

$&+2 x+12$

$&2 x-2$

$&\text { (-) } \quad(+)$

$&14$.

Step 3

Then, $q(x)=\frac{p(x)}{g(x)}$

$=x^{2}+9 x+2$

$q(x)=a=2$

$a-b=2-0=2$

If a is the degree of q(x) and b is the degree of r(x), (a - b) = 2.