Let p=x^(2)+6. Which equation is equivalent to (x^(2)+6)^(2)-21=4x^(2)+24 in terms of p ? Choose 1 answer: (A) p^(2)+4p-21=0 (B) p^(2)-4p-21=0 (C) p^(2)+4p-45=0 (D) p^(2)-4p-45=0

Expand left side using substitution: Let's first expand the left side of the equation using the given substitution p = x^2 + 6. We have (x^2 + 6)^2 - 21, which can be written as (p)^2 - 21.Expand right side using substitution: Now let's expand the right side of the equation, which is 4x^2 + 24. Since p = x^2 + 6, we can replace x^2 with p - 6 to get 4(p - 6) + 24.Distribute and simplify: Next, we distribute the 4 into the parentheses: 4(p - 6) + 24 becomes 4p - 24 + 24.Set equation to zero: Now, we simplify the expression 4p - 24 + 24 by combining like terms, which results in 4p.Match equation to answer choices: We now have the equation (p)^2 - 21 = 4p. To find the equivalent equation in terms of p, we need to set the equation to zero by moving all terms to one side.Subtract 4p from both sides to get (p)^2 - 4p - 21 = 0.We can now match our resulting equation to the answer choices. The equation (p)^2 - 4p - 21 = 0 corresponds to choice (B) p^(2) - 4p - 21 = 0.

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Let
p=x^(2)+6.
Which equation is equivalent to
(x^(2)+6)^(2)-21=4x^(2)+24 in terms of
p ?
Choose 1 answer:
(A)
p^(2)+4p-21=0
(B)
p^(2)-4p-21=0
(C)
p^(2)+4p-45=0
(D)
p^(2)-4p-45=0

Let $p = x^{2} + 6$ . Which equation is equivalent to $(x^{2} + 6)^{2} - 21 = 4x^{2} + 24$ in terms of $p$ ? Choose $1$ answer: $\newline$ (A) $p^{2} + 4p - 21 = 0$ $\newline$ (B) $p^{2} - 4p - 21 = 0$ $\newline$ (C) $p^{2} + 4p - 45 = 0$ $\newline$ (D) $p^{2} - 4p - 45 = 0$

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Math Problems

Algebra 1

Solve a quadratic equation by factoring

Full solution

Q. Let

p = x^{2} + 6

. Which equation is equivalent to

(x^{2} + 6)^{2} - 21 = 4x^{2} + 24

in terms of

p

? Choose

1

answer:

\newline

(A)

p^{2} + 4p - 21 = 0

\newline

(B)

p^{2} - 4p - 21 = 0

\newline

(C)

p^{2} + 4p - 45 = 0

\newline

(D)

p^{2} - 4p - 45 = 0

Expand left side using substitution: Let's first expand the left side of the equation using the given substitution $p = x^2 + 6$ . $\newline$ We have $(x^2 + 6)^2 - 21$ , which can be written as $(p)^2 - 21$ .
Expand right side using substitution: Now let's expand the right side of the equation, which is $4x^2 + 24$ . $\newline$ Since $p = x^2 + 6$ , we can replace $x^2$ with $p - 6$ to get $4(p - 6) + 24$ .
Distribute and simplify: Next, we distribute the $4$ into the parentheses: $4(p - 6) + 24$ becomes $4p - 24 + 24$ .
Set equation to zero: Now, we simplify the expression $4p - 24 + 24$ by combining like terms, which results in $4p$ .
Match equation to answer choices: We now have the equation $(p)^2 - 21 = 4p$ . $\newline$ To find the equivalent equation in terms of $p$ , we need to set the equation to zero by moving all terms to one side.
Match equation to answer choices: We now have the equation $(p)^2 - 21 = 4p$ . $\newline$ To find the equivalent equation in terms of $p$ , we need to set the equation to zero by moving all terms to one side.Subtract $4p$ from both sides to get $(p)^2 - 4p - 21 = 0$ .
Match equation to answer choices: We now have the equation $(p)^2 - 21 = 4p$ . $\newline$ To find the equivalent equation in terms of $p$ , we need to set the equation to zero by moving all terms to one side. Subtract $4p$ from both sides to get $(p)^2 - 4p - 21 = 0$ . We can now match our resulting equation to the answer choices. The equation $(p)^2 - 4p - 21 = 0$ corresponds to choice (B) $p^{2} - 4p - 21 = 0$ .