Question

(15x^2+x -6) by (3x +2)​

Answer 1

Answer:

A common factor is an expression which can be divided into each term in a polynomial. For example, 3x is a common factor in the polynomial 9x3 - 15x2 + 3x, because 3x divides evenly into each of the three factors. To factor out the common factor we divide each term by that factor, and write the common factor out front; 3x (9x3 /3x - 15x2 /3x + 3x/3x) = 3x(3x2 - 5x + 1).

When a polynomial has a common factor, it is to our advantage to factor it out first. At the very least the remaining polynomial will involve smaller numbers.

Ex. It is possible to factor 15x2 + 45x + 30, without first factoring out the common factor of 15, but if we factor out the 15 first we get, 15(x2 + 3x + 2), a much easier polynomial to factor, 15(x + 2)(x + 1). If we do not factor out the 15 first we get, (15x + 30)(x + 1). This however is not completely factored. In order to have the correct answer we must factor the 15 out of (15x + 30), giving us 15(x +2)(x +1) again.

Sometimes it is impossible to factor the polynomial at all until the common factor is taken out.

Ex. Consider 8x2 - 200. Because this polynomial has only 2 terms, if it can be factored it must be a Difference of Squares, a Difference of Cubes or a Sum of Cubes. Because of the subtraction symbol we know it is not a Sum of Cubes. While 8 is a perfect cube, and x2 is a perfect square, 8x2  is neither. Similiarly, 200 is neither a perfect square or a perfect cube. BUT, if we factor out the common factor of 8, we get 8(x2 - 25). Now x2 is a perfect square and 25 is a perfect square and our answer is 8(x-5)(x+5).

Step-by-step explanation:

Answer 2

$\huge{ \tt{ \underline{♕︎sᴏℓᴜᴛɪᴏɴ ♕︎}}}$

$\tt{➨ \: \: \frac{( {15x}^{2} + x - 6)}{(3x + 2)}}$

$\tt{➨ \: \: \frac{({15x}^{2} + 10x - 9x - 6)}{(3x + 2)}}$

$\tt{➨ \: \: \frac{( {15x}^{2} + 10x)( - 9x - 6)}{(3x + 2)}}$

$\tt{➨ \: \: \frac{5x(3x + 2) - 3(3x + 2)}{(3x + 2)}}$

$\tt{➨ \: \: (5x - 3)(3x + 2)(3x + 2)}$

$\tt \pink{➨ \: \: (5x - 3) = 5x - 3}$