Question

(2x3 + 3x2 + 10x)(8x4)

Answer 1

The simplified form of the given expression is $\left(2^{3} \times x^{5}\right)\left(2 x^{2}+3 x+10\right)$

Step-by-step explanation:

Given expression:

         $\left(2 x^{3}+3 x^{2}+10 x\right)\left(8 x^{4}\right)$

Now, we have to simplify the above so split into two term.

$\left(2 x^{3}+3 x^{2}+10 x\right)$ can be written as below, ‘x’ is taken out as it is common.

          $x\left(2 x^{2}+3 x+10\right)$ -----> eq. 1

$8 x^{4}$ can be written as below, ‘8’ is cube of 2

          $8 x^{4}=2^{3} \times x^{4}$ -----> eq 2

Now combine eq. 1 and 2, we get

         $x\left(2 x^{2}+3 x+10\right)\left(2^{3} \times x^{4}\right)$

When try to factoring $2 x^{2}+3 x+10$, trinomial cannot be factored. Because,

• Multiply the coefficient of the first term by the constant 2(10) = 20
• Find two factors of  20 whose sum equals the coefficient of the middle term, which is 3. But no two such factors can be found.

Hence,

         $\left(2^{3} \times x^{5}\right)\left(2 x^{2}+3 x+10\right)$