Find the values of a, b, and c for which the quadratic equation ax2 + bx + c = 0 has the given numbers as solutions. Then
use those values to write a quadratic equation.
-$$( 7 p - 1 ) \left( 49 p ^ { 2 } + 7 p + 1 \right)$$
A) $343 p ^ { 3 } + 1$
B) $343 p ^ { 3 } + 56 p ^ { 2 } - 1$
C) $49 p ^ { 3 } - 1$
D) $343 p ^ { 3 } - 1$

Question

Quizplus · Accepted Answer

The given expression can be simplified by multiplying the two factors: $(7p - 1)(49p^2 + 7p + 1)$. First, distribute $7p$ across the second polynomial: $7p \times 49p^2 + 7p \times 7p + 7p \times 1$, which simplifies to $343p^3 + 49p^2 + 7p$. Then, distribute $-1$ across the second polynomial: $-1 \times 49p^2 - 1 \times 7p - 1 \times 1$, which simplifies to $-49p^2 - 7p - 1$. Adding these results together gives $343p^3 + 49p^2 + 7p - 49p^2 - 7p - 1$, where $49p^2$ and $-49p^2$, and $7p$ and $-7p$ cancel out, leaving $343p^3 - 1$.

Find the Values of A, B, and C for Which (7p−1)(49p2+7p+1)( 7 p - 1 ) \left( 49 p ^ { 2 } + 7 p + 1 \right)(7p−1)(49p2+7p+1)

Find the Values of A, B, and C for Which $( 7 p - 1 ) \left( 49 p ^ { 2 } + 7 p + 1 \right)$