Use the information provided to answer Part A and Part B.

Consider the equation (x² + 3)² + 21 = 10x² + 30.

Consider the equation (x² + 3)² + 21 = 10x² + 30.

Part ALet u = x² + 3. Which equation is equivalent to (x² + 3)² + 21 = 10x² + 30 in terms of u? A.) u² + 10u + 51 = 0 B.) u² - 10u + 51 = 0 C.) u² + 10u + 21 = 0 D.) u² - 10u + 21 = 0 |
Part BWhat are the solutions of the equation (x² + 3)² + 21 = 10x² + 30? Select all that apply.A.) -4 E.) 2 B.) -3 F.) 3 C.) -2 G.) 4 D.) 0 |

__Part A__**If u = x² + 3, then replace the x² + 3 with u**

(x² + 3)² + 21 = 10(x² + 3) {factored 10 out of right side}

u² + 21 = 10u {replaced (x² + 3) with u}

u² - 10u + 21 = 0 {subtracted 10u from each side}

**D.) u² - 10u + 21 = 0**

__Part B__**Solve the equation u² - 10u + 21 = 0 for u**

u² - 10u + 21 = 0

(u - 7)(u - 3) = 0 {factored into two binomials}

u - 7 = 0 or u - 3 = 0 {set each factor equal to 0}

u = 7 or u = 3 {solved each equation for u}

**If u = x² + 3, then**

x² + 3 = 7 or x² + 3 = 3 {substituted x² + 3 in for u}

x² = 4 or x² = 0 {subtracted 3 from each side of each equation}

x = 2 or -2 or 0 {took the square root of each side of each equation}

**C.) -2**

D.) 0

E.) 2

D.) 0

E.) 2

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