Factor the trinomial. $$ b^{6}+17 b^{3}+70 $$ Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. $$ b^{6}+17 b^{3}+70=\square $$ B. The trinomial is not factorable.

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UpStudy AI · Accepted Answer

Let $$ u = b^3 $$. Then the expression becomes

$$
u^2 + 17u + 70.
$$

We now look for two numbers that add up to 17 and multiply to 70. Since $$7 + 10 = 17$$ and $$7 \times 10 = 70$$, we can factor the quadratic as

$$
u^2 + 17u + 70 = (u+7)(u+10).
$$

Substituting back $$ u = b^3 $$, we obtain

$$
b^6 + 17b^3 + 70 = (b^3 + 7)(b^3 + 10).
$$

Thus, the correct choice is:

A. $$ b^6 + 17 b^3 + 70 = (b^3 + 7)(b^3 + 10) $$.
$$ b^6 + 17b^3 + 70 = (b^3 + 7)(b^3 + 10) $$.

Factor the trinomial.

Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A.
B. The trinomial is not factorable.

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Factor the trinomial. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. B. The trinomial is not factorable.