Question

Find f(x) + g(x), f(x) − g(x), f(x) · g(x), and f(x)/g(x). f(x) = x2 + 13x + 42 g(x) = x + 6 (a) f(x) + g(x) (b) f(x) − g(x) (c) f(x) · g(x) (d) f(x)/g(x)

Answer 1

Answer:

(a) The value of f (x) + g (x) is $x^{2}+4x+48$.

(b) The value of f (x) - g (x) is $x^{2} +12x+36$.

(c) The value of f (x) · g (x) is $x^{3}+19x^{2}+120x+252$.

(d) The value of f (x)/g (x) is$(x+6)$.

Step-by-step explanation:

The two polynomials provided are:

$f(x)=x^{2} + 13x + 42\\\\g(x)=x+6$

(a)

Compute the value of f (x) + g (x) as follows:

$f(x)+g(x)=(x^{2} + 13x + 42)+(x+6)$

                   $=x^{2} + 13x + 42+x+6\\\\=x^{2} + (13x+x)+(42+6)\\\\=x^{2} +14x+48$

Thus, the value of f (x) + g (x) is $x^{2}+4x+48$.

(b)

Compute the value of f (x) - g (x) as follows:

$f(x)-g(x)=(x^{2} + 13x + 42)-(x+6)$

                   $=x^{2} + 13x + 42-x-6\\\\=x^{2} + (13x-x)+(42-6)\\\\=x^{2} +12x+36$

Thus, the value of f (x) - g (x) is $x^{2} +12x+36$.

(c)

Compute the value of f (x) · g (x) as follows:

$f(x)\cdot\ g(x)=(x^{2} + 13x + 42)\cdot(x+6)$

                 $=x^{2}\cdot(x+6)+13x\cdot(x+6)+42\cdot(x+6)\\\\=x^{3}+6x^{2}+13x^{2}+78x+42x+252\\\\=x^{3}+(6x^{2}+13x^{2})+(78x+42x)+252\\\\=x^{3}+19x^{2}+120x+252$

Thus, the value of f (x) · g (x) is $x^{3}+19x^{2}+120x+252$.

(d)

Compute the value of f (x)/g (x) as follows:

$f(x)/ g(x)=\frac{(x^{2} + 13x + 42)}{(x+6)}$

                $=\frac{(x^{2} + 7x + 6x + 42)}{(x+6)}\\\\=\frac{x(x+7)+6(x+7)}{(x+6)}\\\\=\frac{(x+6)(x+7)}{(x+6)}\\\\=(x+6)$

Thus, the value of f (x)/g (x) is$(x+6)$.