Factor Completely: x2 + 16 (x + 4)(x - 4) (x - 4)(x - 4) (x + 4)(x + 4) Prime

1 answer:

7 0

I think the correct answer from the choices listed above is the last option.The expression x^2 + 16 is a prime expression which cannot be further simplified over the real numbers. But when considering the complex numbers, the factor would be:

(x + 4i)(x - 4i)

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Multiply (3b 2+ 4b + 8)(-2b 2+ b + 10).

emmainna [20.7K]

Answer: -30b^2+76b+80
Explanation:
Multiply the second parenthesis by each term from the first parenthesis:
3b•2(-2•2+b+10)+4b•(-2b•2+b+10)+8(-2b•2+b+10)
Then distribute 3b•2 through the parenthesis
-24b^2+6b^2+60b+4b•(-2b•2+b+10)+8(-2b•2+b+10)
Then collect like terms
-30b^2+60b+40b-32b+8b+80
Collect like terms=
-30b+76b+80

4 0

3 years ago

What is the remainder of f(x)=x^4-2x^3-27x^2-9x+18 when divided by binomial x+4

givi [52]

Answer:

The remainder will be 6.

Step-by-step explanation:

We have the function:

$f(x)=x^4-2x^3-27x^2-9x+18$

And we want to find the remainder after it is divided by the binomial:

$x+4$

We can use the Polynomial Remainder Theorem. According to the PRT, if we have a polynomial P(x) being divided by a binomial in the form (x - a), then the remainder will be given by P(a).

Here, our divisor is (x + 4). We can rewrite this as (x - (-4)).

Therefore, a = -4.

Then according to the PRT, the remainder will be:

$f(-4)=(-4)^4-2(-4)^3-27(-4)^2-9(-4)+18=6$