Questions: Add or subtract as indicated. Express the answer as a single polynomial in standard form. 10) (2 x^2-8 x+8)+(7 x^2-4 x-2) A) 9 x^2-12 x-6 B) 15 x^2-2 x-10 C) 9 x^2+12 x+6 D) 9 x^2-12 x+6 11) (6 x^2-12 x+20)-(3 x^2-2 x-18) A) 3 x^2-10 x-38 B) 3 x^2-10 x+2 C) 3 x^2-9 x+2 D) 3 x^2-10 x+38 12) (-10 x^2+5)-(-x^3+2 x^2+1) A) x^3-8 x^2+6 B) -9 x^3+7 x^2-1 C) x^3-12 x^2+4 D) -9 x^3+2 x^2+4 13) (3 x^7+5 x^6+6 x)+(5 x^7-8 x^6+9 x) A) 8 x^7-3 x^6+15 x B) 20 x^14 C) 8 x-3 x^7+15 x^6 D) 11 x^7-5 x^6+14 x Perform the indicated operations. Express the answer as a single polynomial in standard form. 14) 3 x^5(-5 x^6-1) A) -15 x^6-3 B) -18 x^5 C) -15 x^11-3 x^5 D) -15 x^11-1 Multiply the polynomials using the FOIL method. Express the answer as a single polynomial in standard form. 15) (-4 x+5)(x+11) A) -4 x^2-39 x-39 B) -4 x^2-41 x+55 C) -4 x^2+55 x-39 D) -4 x^2-39 x+55 16) (5 x+6)(4 x+4) A) 9 x^2+44 x+24 B) 20 x^2+44 x+44 C) 20 x^2+44 x+24 D) 9 x^2+44 x+44

Add or subtract as indicated. Express the answer as a single polynomial in standard form. 10) (2 x^2-8 x+8)+(7 x^2-4 x-2) A) 9 x^2-12 x-6 B) 15 x^2-2 x-10 C) 9 x^2+12 x+6 D) 9 x^2-12 x+6 11) (6 x^2-12 x+20)-(3 x^2-2 x-18) A) 3 x^2-10 x-38 B) 3 x^2-10 x+2 C) 3 x^2-9 x+2 D) 3 x^2-10 x+38 12) (-10 x^2+5)-(-x^3+2 x^2+1) A) x^3-8 x^2+6 B) -9 x^3+7 x^2-1 C) x^3-12 x^2+4 D) -9 x^3+2 x^2+4 13) (3 x^7+5 x^6+6 x)+(5 x^7-8 x^6+9 x) A) 8 x^7-3 x^6+15 x B) 20 x^14 C) 8 x-3 x^7+15 x^6 D) 11 x^7-5 x^6+14 x Perform the indicated operations. Express the answer as a single polynomial in standard form. 14) 3 x^5(-5 x^6-1) A) -15 x^6-3 B) -18 x^5 C) -15 x^11-3 x^5 D) -15 x^11-1 Multiply the polynomials using the FOIL method. Express the answer as a single polynomial in standard form. 15) (-4 x+5)(x+11) A) -4 x^2-39 x-39 B) -4 x^2-41 x+55 C) -4 x^2+55 x-39 D) -4 x^2-39 x+55 16) (5 x+6)(4 x+4) A) 9 x^2+44 x+24 B) 20 x^2+44 x+44 C) 20 x^2+44 x+24 D) 9 x^2+44 x+44
Transcript text: Add or subtract as indicated. Express the answer as a single polynomial in standard form. 10) $\left(2 x^{2}-8 x+8\right)+\left(7 x^{2}-4 x-2\right)$ A) $9 x^{2}-12 x-6$ B) $15 x^{2}-2 x-10$ C) $9 x^{2}+12 x+6$ D) $9 x^{2}-12 x+6$ 11) $\left(6 x^{2}-12 x+20\right)-\left(3 x^{2}-2 x-18\right)$ A) $3 x^{2}-10 x-38$ B) $3 x^{2}-10 x+2$ C) $3 x^{2}-9 x+2$ D) $3 x^{2}-10 x+38$ 12) $\left(-10 x^{2}+5\right)-\left(-x^{3}+2 x^{2}+1\right)$ A) $x^{3}-8 x^{2}+6$ B) $-9 x^{3}+7 x^{2}-1$ C) $x^{3}-12 x^{2}+4$ D) $-9 x^{3}+2 x^{2}+4$ 13) $\left(3 x^{7}+5 x^{6}+6 x\right)+\left(5 x^{7}-8 x^{6}+9 x\right)$ A) $8 x^{7}-3 x^{6}+15 x$ B) $20 x^{14}$ C) $8 x-3 x^{7}+15 x^{6}$ D) $11 x^{7}-5 x^{6}+14 x$ Perform the indicated operations. Express the answer as a single polynomial in standard form. 14) $3 x^{5}\left(-5 x^{6}-1\right)$ A) $-15 x^{6}-3$ B) $-18 x^{5}$ C) $-15 x^{11}-3 x^{5}$ D) $-15 x^{11}-1$ Multiply the polynomials using the FOIL method. Express the answer as a single polynomial in standard form. 15) $(-4 x+5)(x+11)$ A) $-4 x^{2}-39 x-39$ B) $-4 x^{2}-41 x+55$ C) $-4 x^{2}+55 x-39$ D) $-4 x^{2}-39 x+55$ 16) $(5 x+6)(4 x+4)$ A) $9 x^{2}+44 x+24$ B) $20 x^{2}+44 x+44$ C) $20 x^{2}+44 x+24$ D) $9 x^{2}+44 x+44$
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Solution

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Solution Steps

Step 1: Combine like terms for question 10

\[ \left(2 x^{2}-8 x+8\right) + \left(7 x^{2}-4 x-2\right) \] Combine the \(x^2\) terms: \(2x^2 + 7x^2 = 9x^2\).
Combine the \(x\) terms: \(-8x - 4x = -12x\).
Combine the constant terms: \(8 - 2 = 6\).
The result is: \(9x^2 - 12x + 6\).

Step 2: Subtract polynomials for question 11

\[ \left(6 x^{2}-12 x+20\right) - \left(3 x^{2}-2 x-18\right) \] Distribute the negative sign: \(6x^2 - 12x + 20 - 3x^2 + 2x + 18\).
Combine the \(x^2\) terms: \(6x^2 - 3x^2 = 3x^2\).
Combine the \(x\) terms: \(-12x + 2x = -10x\).
Combine the constant terms: \(20 + 18 = 38\).
The result is: \(3x^2 - 10x + 38\).

Step 3: Subtract polynomials for question 12

\[ \left(-10 x^{2}+5\right) - \left(-x^{3}+2 x^{2}+1\right) \] Distribute the negative sign: \(-10x^2 + 5 + x^3 - 2x^2 - 1\).
Combine the \(x^3\) term: \(x^3\).
Combine the \(x^2\) terms: \(-10x^2 - 2x^2 = -12x^2\).
Combine the constant terms: \(5 - 1 = 4\).
The result is: \(x^3 - 12x^2 + 4\).

Final Answer

  1. The correct answer is D.
  2. The correct answer is D.
  3. The correct answer is C.
  4. The correct answer is A.
  5. The correct answer is C.
  6. The correct answer is D.
  7. The correct answer is C.
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