 1)*(y + 3)**4
Let w(n) = 2 - 4*n + n + 3*n**2 - 2*n. Let j(k) = -3 + 8 - 12*k**2 - 36*k + 10 + 33*k**2. Let q(l) = -4*j(l) + 27*w(l). Factor q(f).
-3*(f - 2)*(f - 1)
Let w = -20/17 + 219/85. Factor 2/5*a + 0 - w*a**2.
-a*(7*a - 2)/5
Let r be (-12)/10*(-125)/50. Factor 10/9*c + 2/9*c**r + 8/9*c**2 + 4/9.
2*(c + 1)**2*(c + 2)/9
Let m(h) be the first derivative of -4*h**6/21 - 8*h**5/35 + 3*h**4/14 + 4*h**3/21 - h**2/7 - 23. Factor m(n).
-2*n*(n + 1)**2*(2*n - 1)**2/7
Suppose -t - 11 = -p, 0 = 4*t - p - 30 + 71. Let k(i) = -i**3 - 11*i**2 - 11*i - 8. Let j be k(t). Solve l**j - 1 - 5/2*l**3 + 5/2*l = 0 for l.
-1, 2/5, 1
Let o = 17 - 12. Suppose -36 = -4*p - 0*p + 5*n, -16 = -p + 3*n. Factor -6*w**2 + o*w - p*w + 3*w**2.
-w*(3*w - 1)
Factor 54*k**2 + 12 - 28*k**3 - 52*k + 4*k**4 + 18*k**2 - 28*k + 20.
4*(k - 2)**3*(k - 1)
Let l be 16/10 - (-2)/5. Let s = -1 + 6. Factor 4*j - 2*j**4 + 3*j**4 - s*j - j**l + j**3.
j*(j - 1)*(j + 1)**2
Let g be 9/((-27)/5) + 3. Let k be (-2)/(-6)*(1 - -1). Let 8/9*o**4 - g*o**2 + 8/9*o**3 + 4/9 - k*o**5 - 2/9*o = 0. Calculate o.
-1, -2/3, 1
Let p(z) be the third derivative of 0*z - 1/120*z**5 + 0*z**3 + 0 + 0*z**4 + 3/160*z**6 + z**2 - 1/120*z**7. Factor p(w).
-w**2*(w - 1)*(7*w - 2)/4
Suppose -2*p + 6 = 0, 5*f + p = 1 + 2. Factor -6*t + 4 + f + 2*t + t**2.
(t - 2)**2
Suppose 4*b + 3 = 3. Let j(y) be the third derivative of 0*y + 1/90*y**5 + 1/90*y**6 + 1/315*y**7 + 0 + b*y**3 + 0*y**4 + y**2. Factor j(v).
2*v**2*(v + 1)**2/3
Suppose -12/5 + 1/5*w**2 - 4/5*w = 0. Calculate w.
-2, 6
Let f = 5713/5 - 1142. Suppose 1/5*h**2 + 3/5*h**3 + 0 + 1/5*h**5 + 0*h + f*h**4 = 0. Calculate h.
-1, 0
Suppose 0 + 0*q**2 + 1/2*q**5 + 0*q - 3*q**3 + 1/2*q**4 = 0. What is q?
-3, 0, 2
Let c be 247/520 - (-2)/16. Factor -3/5*u**3 + c*u + 6/5 - 9/5*u**2 + 3/5*u**4.
3*(u - 2)*(u - 1)*(u + 1)**2/5
Let z be (-28)/(-84)*(-27)/(-12). Suppose i**2 + 0*i + 2*i**3 + 0 - 9/4*i**5 - z*i**4 = 0. What is i?
-2/3, 0, 1
Suppose -3*p = p - 16. Factor 2*d**2 + 0*d**2 - 18 - p*d**2 - 12*d.
-2*(d + 3)**2
Suppose 0 = 2*v - 7 + 61. Let k be v/(-12) - (-6)/8. Determine n so that -1/2*n**k - 1/2 + 1/2*n + 1/2*n**2 = 0.
-1, 1
Let g = -25 + 49. Let p = g - 22. Factor -1/5 - 1/5*f**p + 2/5*f.
-(f - 1)**2/5
Suppose 2*t + 6 = 34. Suppose 0 = 4*b - 12, 4*f = b - 3*b + t. Solve -l**f - 1 - l**3 + l + 0 + 2 = 0.
-1, 1
Let j = 160 - 160. Factor k**3 + k**2 + j + 1/3*k + 1/3*k**4.
k*(k + 1)**3/3
Let w be (-16)/6 + 3 - 0. Let p(g) be the second derivative of 2*g - 1/12*g**4 - 1/18*g**3 + w*g**2 + 0. Factor p(h).
-(h + 1)*(3*h - 2)/3
Let s(c) be the second derivative of c**7/1680 - c**6/2160 + c**4/4 - 5*c. Let k(b) be the third derivative of s(b). What is a in k(a) = 0?
0, 2/9
Let s(n) be the first derivative of -n**6/9 - 8*n**5/45 - n**4/18 + 17. Find p, given that s(p) = 0.
-1, -1/3, 0
Let l(v) = 2*v**2 - 32*v - 16. Let s(y) = -y**2 + 21*y + 11. Let u = -3 + -2. Let m(z) = u*l(z) - 8*s(z). Determine x, given that m(x) = 0.
-2
Suppose y = 2*y + 7. Let h(n) = -5*n**4 - n**2 - 6*n. Let k(v) = -6*v**4 - v**2 - 7*v. Let w(r) = y*h(r) + 6*k(r). Factor w(s).
-s**2*(s - 1)*(s + 1)
Let i be (-3 + (-15)/(-6))*0. Suppose 2*f = 4 - i. Find v such that -1/2*v**f + 0 - v = 0.
-2, 0
Let o = 0 - -16. Let h = o + -47/3. Factor h*s + 1/3*s**2 - 2/3.
(s - 1)*(s + 2)/3
Let b = -32 + 34. Let j be ((-4)/30)/((-1)/24). Suppose -j + 2/5*m**3 - 12/5*m**b + 24/5*m = 0. What is m?
2
Suppose -4*q = -7*q + 228. Factor -5*x**2 + 69*x - x**3 - 3 + 0*x**3 - q*x.
-(x + 1)**2*(x + 3)
Let g(o) be the third derivative of -o**6/540 - o**5/90 - o**4/36 - o**3/6 - o**2. Let l(c) be the first derivative of g(c). Factor l(y).
-2*(y + 1)**2/3
Let d be (0 - 0) + (-2)/(-180). Let g(q) be the second derivative of -d*q**5 - 1/54*q**4 + 1/9*q**2 - q + 0 + 1/27*q**3. What is b in g(b) = 0?
-1, 1
Factor 1/7 - 1/7*s**2 - 1/7*s**3 + 1/7*s.
-(s - 1)*(s + 1)**2/7
Factor 12/7*j**2 + 4/7*j - 8/7.
4*(j + 1)*(3*j - 2)/7
Let u(d) be the first derivative of -2*d**5/5 + d**4/2 + 10*d**3/3 + 3*d**2 + 12. Factor u(m).
-2*m*(m - 3)*(m + 1)**2
Let g(p) be the second derivative of -p**9/30240 + p**7/5040 - p**4/12 + 9*p. Let f(x) be the third derivative of g(x). Suppose f(j) = 0. What is j?
-1, 0, 1
Let n(i) be the first derivative of -i**7/1260 - i**6/135 - i**5/45 + 5*i**3/3 + 6. Let u(a) be the third derivative of n(a). Factor u(v).
-2*v*(v + 2)**2/3
Let v = -14 - -17. Factor 3*j**v - 4*j**3 - j + 2*j.
-j*(j - 1)*(j + 1)
Let g = -11 - -15. Let a be (g/(-18))/((-20)/30). Factor -1/3*l + 0 - 2/3*l**2 - a*l**3.
-l*(l + 1)**2/3
Let j(v) = -v**2 + 2*v + 3. Let p be j(3). Let z(r) be the first derivative of 0*r**3 + 1 + p*r**2 - 1/14*r**4 + 0*r. Suppose z(c) = 0. What is c?
0
Let m(k) be the first derivative of -k**6/36 - 2*k**5/15 - k**4/4 - 2*k**3/9 - k**2/12 - 3. Factor m(s).
-s*(s + 1)**4/6
Let d be (-3)/6*13*-2. Suppose 5*v - d = 2. Factor s + 2*s**v - s + s**2 + 0*s.
s**2*(2*s + 1)
Let q(b) be the third derivative of -b**6/200 + b**5/75 - b**4/120 - 11*b**2 + 1. Let q(f) = 0. What is f?
0, 1/3, 1
Let o(z) be the third derivative of -2*z**5/5 - z**4/2 - z**3/4 + 48*z**2. Solve o(i) = 0 for i.
-1/4
Let f(q) = -q**2 + 4*q - 7. Let v(i) = 3*i - 3. Let t(z) = -2*z + 2. Let d(y) = 7*t(y) + 5*v(y). Let b(j) = -6*d(j) + f(j). Factor b(s).
-(s + 1)**2
Let d(p) be the third derivative of 1/15*p**5 + 13/360*p**6 + 0*p + 1/18*p**4 + 0 + 1/1008*p**8 + 1/105*p**7 + 0*p**3 - 3*p**2. Factor d(g).
g*(g + 1)**2*(g + 2)**2/3
Suppose -54/7 - 2/21*w**2 - 12/7*w = 0. What is w?
-9
Let q be (-8 + 8)/(1*-1). Suppose 2*x - x = q. Factor -2/13*c + x + 2/13*c**3 - 2/13*c**2 + 2/13*c**4.
2*c*(c - 1)*(c + 1)**2/13
Let b(v) be the third derivative of -441*v**5/20 - 21*v**4/2 - 2*v**3 + v**2 + 2. Factor b(i).
-3*(21*i + 2)**2
Let d(o) be the first derivative of 4*o**5/5 - o**4 - 4*o**3/3 + 2*o**2 + 30. Find h, given that d(h) = 0.
-1, 0, 1
Let u(i) be the first derivative of -2*i**3/33 + 2*i/11 + 3. Find c, given that u(c) = 0.
-1, 1
Let m(v) be the third derivative of 0*v - 3*v**2 + 2/525*v**7 + 1/60*v**6 - 1/168*v**8 + 0 + 0*v**3 - 1/75*v**5 + 0*v**4. Determine k, given that m(k) = 0.
-1, 0, 2/5, 1
Suppose c - 6*c = 10. Let z = 2 + c. Determine a so that -1/2*a**4 - 3/2*a**3 - 1/2*a + z - 3/2*a**2 = 0.
-1, 0
Let a(q) = 3*q**3 + 3*q**2 - 2*q - 2. Let p(x) = 7*x**3 + 6*x**2 - 5*x - 3. Suppose c = -2*c + 6. Let b(z) = c*p(z) - 5*a(z). Factor b(w).
-(w - 1)*(w + 2)**2
Let c = 173/255 - 1/85. Let 0 + 0*i + c*i**2 = 0. What is i?
0
Let g(l) be the second derivative of l + 1/3*l**3 - 1/10*l**5 + 0*l**4 + 0*l**2 + 0. Factor g(j).
-2*j*(j - 1)*(j + 1)
Let o be (3 + -2 + -1)/(1 - 0). Let p(j) be the second derivative of o*j**3 - 1/70*j**5 - 1/14*j**4 + 0 - j + 4/7*j**2. Factor p(n).
-2*(n - 1)*(n + 2)**2/7
Factor 0 + 0*k**2 + 0*k + 2*k**4 + 6*k**3 + 1/6*k**5.
k**3*(k + 6)**2/6
Let i be 28/(-126) - (-2)/9. Let h(w) be the first derivative of i*w**3 + 0*w**5 + 2 + 0*w + 0*w**2 - 1/12*w**4 + 1/18*w**6. Determine m, given that h(m) = 0.
-1, 0, 1
Let a(q) be the first derivative of 2*q**3/3 + 24*q**2 + 288*q - 28. Factor a(g).
2*(g + 12)**2
Let h = -16 + 22. Factor 5 - h + 2 - j**2.
-(j - 1)*(j + 1)
Let 0 + 4/3*x**2 + 0*x - 2/3*x**3 = 0. Calculate x.
0, 2
Suppose 0 = -3*j - 5*t + 2192, 0*j - 5*t - 744 = -j. Let b = j - 6584/9. Suppose 50/9*q**5 - 20/3*q**4 + 8/9*q + 0 - b*q**3 + 8/3*q**2 = 0. Calculate q.
-2/5, 0, 1
Let l(h) be the first derivative of -h**7/105 + h**6/20 - h**5/10 + h**4/12 - h**2 - 3. Let o(m) be the second derivative of l(m). What is c in o(c) = 0?
0, 1
Suppose 0 = 16*g + 3*g - 95. Factor 1/4*p**4 - 1/4*p**2 + 0 + 1/4*p**3 - 1/4*p**g + 0*p.
-p**2*(p - 1)**2*(p + 1)/4
Let v = 1/2 + 29/6. Factor 16/9*c**4 + 0 - v*c**3 - 2/9*c**5 - 32/9*c + 64/9*c**2.
-2*c*(c - 2)**4/9
Let w be (-1 - 1)*(-9)/6. Suppose 0 = -k + h + w, -4 = 5*h + 1. Factor 2 + 2 + 2*t**4 - 4 - k*t**2.
2*t**2*(t - 1)*(t + 1)
Let c = -4 + 4. Suppose -4*w**2 + w**3 - 1 + w**2 + 3*w + c*w = 0. Calculate w.
1
Let w(o) be the third derivative of -27*o**8/224 - 99*o**7/140 - 9*o**6/5 - 13*o**5/5 - 7*o**4/3 - 4*o**3/3 + 4*o**2. Factor w(k).
-(k + 1)*(3*k + 2)**4/2
Suppose 0 = -3*m - 12 - 0. Let z be (m/(-12))/((-2)/(-60)). Factor z*q**2 - 2 - 6*q - 1 - 13*q**2.
-3*(q + 1)**2
Let x(v) be the firs