Question 4 Factor $$ 25 y^{4}+5 y^{3}+30 y^{2}+6 y $$. $$ \left(5 y^{3}+6 y\right)(6 y+1) $$ $$ y\left(25 y^{3}+5 y^{2}+30 y+6\right) $$ $$ y\left(5 y^{2}+6\right)(5 y+1)^{2} $$ $$ y\left(5 y^{2}+6\right)(5 y+1) $$

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UpStudy AI · Accepted Answer

Factor the expression by following steps:
- step0: Factor:
  $$25y^{4}+5y^{3}+30y^{2}+6y$$
- step1: Evaluate:
  $$25y^{4}+30y^{2}+5y^{3}+6y$$
- step2: Rewrite the expression:
  $$y\times 25y^{3}+y\times 30y+y\times 5y^{2}+y\times 6$$
- step3: Factor the expression:
  $$y\left(25y^{3}+30y+5y^{2}+6\right)$$
- step4: Factor the expression:
  $$y\left(5y+1\right)\left(5y^{2}+6\right)$$
To factor the expression $$ 25 y^{4}+5 y^{3}+30 y^{2}+6 y $$, we can follow these steps:

1. **Identify the common factor**: 
   The terms $$ 25 y^{4}, 5 y^{3}, 30 y^{2}, $$ and $$ 6 y $$ all have a common factor of $$ y $$.

2. **Factor out the common factor**:
   When we factor out $$ y $$, we get:
   $$
   y(25 y^{3} + 5 y^{2} + 30 y + 6)
   $$

3. **Factor the remaining polynomial**:
   Now we need to factor the polynomial $$ 25 y^{3} + 5 y^{2} + 30 y + 6 $$. This can be factored further:
   $$
   25 y^{3} + 5 y^{2} + 30 y + 6 = (5y + 1)(5y^{2} + 6)
   $$

4. **Combine the factors**:
   Therefore, the complete factorization of the original expression is:
   $$
   y(5y + 1)(5y^{2} + 6)
   $$

Thus, the final factored form of $$ 25 y^{4}+5 y^{3}+30 y^{2}+6 y $$ is:
$$
y(5y + 1)(5y^{2} + 6)
$$

Among the options provided, the correct factorization is:
$$
y(5y + 1)(5y^{2} + 6)
$$
The factored form of $$ 25 y^{4}+5 y^{3}+30 y^{2}+6 y $$ is $$ y(5y + 1)(5y^{2} + 6) $$.

Question 4 Factor \( 25 y^{4}+5 y^{3}+30 y^{2}+6 y \). \( \left(5 y^{3}+6 y\right)(6 y+1) \) \( y\left(25 y^{3}+5 y^{2}+30 y+6\right) \) \( y\left(5 y^{2}+6\right)(5 y+1)^{2} \) \( y\left(5 y^{2}+6\right)(5 y+1) \)

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