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Class 9 Exam  >  Class 9 Questions  >  Find if (-2x-5) is a factor of p(x)=3x^4+5x^3... Start Learning for Free
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Find if (-2x-5) is a factor of p(x)=3x^4+5x^3-2x^2-4 or not.?
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Find if (-2x-5) is a factor of p(x)=3x^4+5x^3-2x^2-4 or not.?
Answer:


Introduction:

To check whether (-2x-5) is a factor of p(x)=3x^4+5x^3-2x^2-4 or not, we will be using the factor theorem and synthetic division method.


Factor Theorem:

The Factor Theorem states that, if a polynomial p(x) is exactly divisible by a linear factor (x-a), then p(a) = 0.

So, to check whether (-2x-5) is a factor of p(x), we need to check whether p(-5/2) = 0 or not.


Synthetic Division:

Synthetic division is a shorthand method of polynomial division in which only coefficients are used.

Let's use synthetic division to divide p(x) by (-2x-5).

First, we will set up the synthetic division table:


```
-5/2 | 3 5 -2 0 -4
|_____|_____|_____|_____
```

Then, we bring down the first coefficient:


```
-5/2 | 3 5 -2 0 -4
|_____|_____|_____|_____
3
```

Next, we multiply -5/2 by 3 and write the result under the next coefficient:


```
-5/2 | 3 5 -2 0 -4
|_____|_____|_____|_____
3 -45/2
```

Then, we add the two coefficients:


```
-5/2 | 3 5 -2 0 -4
|_____|_____|_____|_____
3 -45/2 65/4
```

We continue this process until we reach the last coefficient:


```
-5/2 | 3 5 -2 0 -4
|_____|_____|_____|_____
3 -45/2 65/4 0 0
```

The last two coefficients are both 0, which means (-2x-5) is a factor of p(x).


Conclusion:

Using the factor theorem and synthetic division method, we have shown that (-2x-5) is a factor of p(x)=3x^4+5x^3-2x^2-4.
Community Answer
Find if (-2x-5) is a factor of p(x)=3x^4+5x^3-2x^2-4 or not.?
Let x=5/2given,p (x)=3x^4+5x^3-2x^2-4p (5/2) = 3 (5/2)^4+5 (5/2)^3-2 (5/2)^2-4=3 (625/16)+5 (125/8)-2 (25/4)-4=1275/16+625/8-25/2-4=1275/16+1250/16-200/16-64/16=2261/16...therefore (-2x-5) is not the factor of p(x)...
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