Express the polynomial as a product of linear factors.

Mathematics

1 answer:

inessss [21]3 years ago

4 0

Answer:

Step-by-step explanation:

Given

3x³ + 12x² + 3x - 18

The sum of the coefficients = 3 + 12 + 3 - 18 = 0

Thus x = 1 is a root and (x - 1) is a factor

Divide 3x³ + 12x² + 3x - 18 by (x - 1) using Synthetic division

1 | 3 12 3 - 18

↓ 3 15 18

-----------------------------

3 15 18 0 ← remainder

Quotient = 3x² + 15x + 18 = 3(x² + 5x + 6)

Thus

3x³ + 12x² + 3x - 18 = 3(x - 1)(x² + 5x + 6) = 3(x - 1(x + 3)(x + 2) → C

You might be interested in

What is the answer to -1/3 - -9/4

dangina [55]

Answer:

$\frac{23}{12}$

Step-by-step explanation:

Start by making a common denominator. In this case, it would be 12.

Multiply -1/3 by 4 to get -4/12

Multiply -9/4 by 3 to get -27/12

Then subtract

- $\frac{4}{12}$ - (- $\frac{27}{12}$ ) =23/12

You can also visualize this on a number line. Once you've made the denominator the same, start at -4/12 and move 27 units to the left to land on 23/12.

3 0

3 years ago

Evaluate the difference quotient<br> f(x)-f(1)/X-1, where f(x)=X +5/x+1

Arisa [49]

Answer:

C) $\displaystyle\frac{-2}{(x+1)}$

Step-by-step explanation:

$\displaystyle \frac{f(x)-f(1)}{x-1}\\ \\\frac{\frac{x+5}{x+1}-\frac{1+5}{1+1}}{x-1}\\ \\\frac{\frac{x+5}{x+1}-\frac{6}{2}}{x-1}\\\\\frac{\frac{2(x+5)}{2(x+1)}-\frac{6(x+1)}{2(x+1)}}{x-1}\\\\\frac{\frac{2(x+5)-6(x+1)}{2(x+1)}}{x-1}\\\\\frac{\frac{2x+10-6x-6}{2(x+1)}}{x-1}\\\\\frac{\frac{-4x+4}{2(x+1)}}{x-1}\\\\\frac{\frac{-4(x-1)}{2(x+1)}}{x-1}\\\\\frac{-4}{2(x+1)}\\ \\\frac{-2}{(x+1)}$