Question

Factor 15x3 – 5x2 + 6x – 2 by grouping. What is the resulting expression?

Answer 1

The resulting expression of $15 x^{3}-5 x^{2}+6 x-2$ is $(3 x-1)\left(5 x^{2}+2\right)$

Solution:

Given, expression is $15 x^{3}-5 x^{2}+6 x-2$

We have to factor the given expression by grouping

$\text { Now, } 15 x^{3}-5 x^{2}+6 x-2$

Making the expression into two groups,

$=\left(15 x^{3}-5 x^{2}\right)+(6 x-2)$  

Taking the common terms out,

$=5 x^{2}(3 x-1)+2(3 x-1)$

Taking (3x – 1) as common,

$=(3 x-1)\left(5 x^{2}+2\right)$

As we can’t factorize further, the above expression is final

Hence, the resulting expression is $=(3 x-1)\left(5 x^{2}+2\right)$

Answer 2

Answer:

$\red { Factors \: of \: 15x^{3}-5x^{2} +6x-2}$

$\green {= (3x-1)(5x^{2} + 2)}$

Step-by-step explanation:

$Given \: polynomial : 15x^{3}-5x^{2} +6x-2$

$= 5x^{2}\times 3x - 5x^{2} \times 1+ 2\times 3x - 2\times 1 \\= 5x^{2} (3x-1) + 2(3x-1)\\= (3x-1)(5x^{2} + 2)$

Therefore.,

$\red { Factors \: of \: 15x^{3}-5x^{2} +6x-2}$

$\green {= (3x-1)(5x^{2} + 2)}$

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