Question

factorise 9 x cube minus 27 x square - 100 x + 300 if 3 X + 10 is one of the factors​

Answer 1

Step-by-step explanation:

here is the answer hope this helps

Answer 2

Factorization of polynomials

• A polynomial can be written as the product of its factors having a degree less than or equal to the original polynomial.
• The process of factoring is called factorization of polynomials.

Let us first solve it using GCF (greatest common factor)

• To solve using GCF we first find factors common to all terms.

• That is, if ab+bc is given, clearly b is common here.

Therefore, we can write ab+bc=b(a+c)             [ reverse distributive law ]

Given,   $9x^{3}-27x^2-100x+300$

              $=9x^2(x-3)-100(x-3)$     (Taking out common factors)

              $=(9x^2-100)(x-3)$- - - - - (1)

Using the formula $(a^2-b^2)=(a+b)(a-b)$  on $(9x^2-100)$

    $9x^2-100 = (3x)^2-10^2$

                     $=(3x+10)(3x-10)$ - - - - - - - (2)

Substituting (2) into (1), we get,

                      $=(9x^2-100)(x-3)\\\\=(3x+10)(3x-10)(x-3)$

Given (3x+10) is a factor of $9x^{3}-27x^2-100x+300$

∴ The other factors are (3x-10)(x-3)

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