(<span>4x2</span><span> – </span><span>4x</span><span> – </span>7)(x<span> + </span>3)<span>
</span> = (<span>4x2</span><span> – </span><span>4x</span><span> – </span>7)(x) + (<span>4x2</span><span> – </span><span>4x</span><span> – </span>7)(3)<span>
</span><span> = </span><span>4x2</span>(x<span>) – </span><span>4x</span>(x<span>) – </span>7(x<span>) + </span><span>4x2</span>(3<span>) – </span><span>4x</span>(3<span>) – </span>7(3)<span>
</span><span> = 4x3 – 4x2 – 7x + 12x2 – 12x – 21</span><span>
</span><span> = 4x3 – 4x2 + 12x2 – 7x – 12x – 21</span><span>
</span><span> = 4x3 + 8x2 – 19x – 21</span>
Answer:
The cubic polynomial is: x³ - x² - 6x.
Step-by-step explanation:
Given the degree and the roots of the polynomial we can find it.
An n - degree polynomial has n roots.
Here, given that the degree of the polynomial is 3 and three roots are given. Also, if (x - a) is a factor of a polynomial then x = a is a root of the polynomial. The converse is also true.
Since, the roots of the polynomial are given to -2, 0, 3 then it should have had the following factors.
(x + 2)(x - 0)(x - 3) = 0
Multiplying them we get:
⇒ 

which is the required cubic polynomial.
Hence, the answer.