
Let i be 15/4 + 12/(-16). Let x(u) = u**4 + 4*u**3 + u**2. Let o(p) = 2*p**4 + 12*p**3 + 2*p**2. Let v(y) = i*o(y) - 8*x(y). Factor v(z).
-2*z**2*(z - 1)**2
Suppose 27 = -11*o + 14*o. Solve -4*c - 7*c**2 + 33*c**3 - o*c**2 - 24*c**3 = 0 for c.
-2/9, 0, 2
Let u = 283/3 + -563/6. Factor m**3 + 0*m**2 - m - 1/2*m**4 + u.
-(m - 1)**3*(m + 1)/2
Let k be (-24)/14*14/(-4). Let m be 2 - (6/k)/2. Factor -3/2*y**2 + 3/2*y**4 + 0*y - 3/2*y**3 + m*y**5 + 0.
3*y**2*(y - 1)*(y + 1)**2/2
Let t be (-4)/(-6)*(0 - -3). Suppose -6*y = -11*y + 10. Factor z - 3*z**4 + t*z**3 - z**5 + 2*z**2 - 2*z + 2 - 3 + y*z**4.
-(z - 1)**2*(z + 1)**3
Let l(o) be the third derivative of -o**8/1680 + o**6/300 - o**4/120 - 53*o**2 - o. Factor l(y).
-y*(y - 1)**2*(y + 1)**2/5
Let p(z) be the first derivative of 11*z**7/210 - 3*z**6/50 - z**5/50 + 20*z + 11. Let a(m) be the first derivative of p(m). Factor a(v).
v**3*(v - 1)*(11*v + 2)/5
Let i be (0 - (-4)/8)*10. Let l(t) = 3*t**2 + t + 4*t**3 - i*t**3 - 2*t**2. Let q(u) = 8*u**3 - 14*u**2 - 12*u. Let j(d) = -10*l(d) - q(d). Factor j(m).
2*m*(m + 1)**2
Let c(f) = 12*f**2 + 648*f + 8748. Let s(z) = 3*z**2 + 162*z + 2187. Let u(o) = -5*c(o) + 21*s(o). Suppose u(r) = 0. What is r?
-27
Let h(z) be the third derivative of -z**6/360 - 29*z**5/30 - 841*z**4/6 - 97556*z**3/9 - 164*z**2. Factor h(c).
-(c + 58)**3/3
Let d = 119 + -115. Suppose -55*g**5 + 4*g + 38*g**d + 117*g**4 + 6*g - 167*g**3 + 32*g**3 + 25*g**2 = 0. What is g?
-2/11, 0, 1
Let i = 107429/15 + -7159. Let c = i + -7/3. Factor c*f**3 - 3/5*f**5 + 0 + 0*f + 3/5*f**2 - 3/5*f**4.
-3*f**2*(f - 1)*(f + 1)**2/5
Suppose -2*s - s + 3 = 0. Let x be (s + -1)/(4 + (-15)/5). Factor -1/4*t**3 + x - t - t**2.
-t*(t + 2)**2/4
Let j(q) = q - 10. Let o be j(12). Suppose l = -o*l + 4*g + 28, -5*g = 4*l + 4. Find f, given that -43 - 2*f + 42 + l*f**2 - 5*f**2 = 0.
-1
Let u(l) be the first derivative of -5 - 8/21*l**3 + 4/7*l**2 + 0*l + 1/14*l**4. Factor u(k).
2*k*(k - 2)**2/7
Let c(j) be the second derivative of 864*j**6/5 - 324*j**5/5 + 9*j**4 - j**3/2 + j + 113. Let c(z) = 0. Calculate z.
0, 1/12
Let b(n) = -n**5 + 2*n**4 + 12*n**3 + 3*n**2 - 3*n - 6. Let w(r) = r**4 + r**2 - r - 2. Let t(d) = 5*b(d) - 15*w(d). Factor t(p).
-5*p**3*(p - 3)*(p + 4)
Let z(u) be the third derivative of -u**5/360 - 7*u**4/72 - 49*u**3/36 + 79*u**2. Factor z(v).
-(v + 7)**2/6
Let x(h) = 2*h**3 + 2*h**2 - 6*h + 2. Let z = -60 + 62. Let o(q) = -2*q**3 - q**2 + 6*q - 3. Let p(j) = z*o(j) + 3*x(j). Factor p(t).
2*t*(t - 1)*(t + 3)
Let r = 44 + -40. Let -17*d**2 - 26*d**2 + d**r + 39*d**2 = 0. What is d?
-2, 0, 2
Suppose 9 - 21 = -4*k. Let b(c) be the second derivative of -3*c**2 + 0 + 1/4*c**4 + k*c - 1/2*c**3. Factor b(x).
3*(x - 2)*(x + 1)
Find s such that -11*s**2 + 12*s + 249*s**3 - 207*s**3 + 68*s**2 + 9*s**4 - 12 = 0.
-2, -1, 1/3
Suppose -i + 726 = 10*i. Let t be -1 - 1 - (-154)/i. Factor 1/9*v**2 + 2/9*v - t.
(v - 1)*(v + 3)/9
Let s(p) be the second derivative of -p**6/20 - 19*p**5/40 + 29*p**4/24 + 215*p**3/12 - 75*p**2/2 + 495*p. Determine h so that s(h) = 0.
-5, 2/3, 3
Let r(h) = -3*h - 3 - 1 - 4 - 4. Let n be r(-4). Factor 3/2*f**4 - 3*f**3 + 0*f + n + 3/2*f**2.
3*f**2*(f - 1)**2/2
Let v = 5 + 0. Find x such that -44*x**2 - 4*x**4 + 10 - x**4 - 25*x + 59*x**2 + v*x**3 = 0.
-2, 1
Let h(i) be the second derivative of -1/6*i**6 + 5/12*i**4 + 0 - 4*i + 0*i**2 - 5/6*i**3 + 1/4*i**5. Solve h(v) = 0.
-1, 0, 1
Let b(z) = -5*z**4 + 15*z**2 + 5. Let v(s) = -10*s**4 + 33*s**2 + 11. Let x(i) = 11*b(i) - 5*v(i). Determine q, given that x(q) = 0.
0
Suppose 9*z - 5*z + 60 = -3*c, 0 = c. Let q = 15 + z. Let -2/7*o**4 + 0 + 6/7*o**3 - 4/7*o**2 + q*o = 0. What is o?
0, 1, 2
Let t = -53523/4 + 13221. Let g = t - -162. Determine r, given that -g - 3*r + r**3 + 1/2*r**2 - 1/4*r**4 = 0.
-1, 3
Suppose 62*d**2 - 12*d**2 + 45 - 6*d + 18*d + 28*d + 5*d**5 - 30*d**3 - 15*d**4 + 65*d = 0. What is d?
-1, 3
Let k(q) be the first derivative of q**5/5 + q**4 + q**3 - 2*q**2 - 4*q - 60. Factor k(x).
(x - 1)*(x + 1)*(x + 2)**2
Let a = -42884 + 215644/5. Let d = 246 - a. Factor -d*j**3 + 0 + 0*j - 24/5*j**4 - 14/5*j**5 + 4/5*j**2.
-2*j**2*(j + 1)**2*(7*j - 2)/5
Let v(t) be the first derivative of -t**3/4 + 9*t**2 - 108*t + 245. Find h such that v(h) = 0.
12
Let n(q) be the third derivative of -q**5/60 - q**4/8 - q**3/3 - q**2 - 67*q. Let n(a) = 0. Calculate a.
-2, -1
Solve 2332*w**2 + 309369*w - 28*w**3 + 33*w**3 + 130990365 + 113394*w + 900372*w + 2123*w**2 = 0.
-297
Let h be (0 - 12/8)*-4. Suppose -2*i - 48 = -h*i. Find o, given that -4*o - 22*o**2 + i*o**2 + 3 + 11*o**2 = 0.
1, 3
Let o = 3846/5 - 26672/35. Factor 8/7 + o*x**2 - 40/7*x.
2*(5*x - 2)**2/7
Let v(x) be the third derivative of -40*x**2 + 0 - 1/9*x**3 + 0*x - 1/24*x**4 - 1/180*x**5. Factor v(m).
-(m + 1)*(m + 2)/3
Let l(r) = 7*r**3 + 101*r**2 - 18*r - 123. Let u(s) = 2*s**3 + 25*s**2 - 5*s - 31. Let t(f) = 6*l(f) - 22*u(f). Solve t(n) = 0.
-1, 1, 28
Let p(v) be the first derivative of 0*v + 0*v**2 - 1/12*v**4 + 23 + 4/9*v**3. Find w, given that p(w) = 0.
0, 4
Let z be -3*(224/(-24))/(-14) + 2 + 0. Find c such that -2/17*c**4 + 0 + 6/17*c**3 - 4/17*c**2 + z*c = 0.
0, 1, 2
Let w(p) be the second derivative of -p**6/1260 + p**5/60 - p**4/14 - 9*p**3 - 55*p. Let j(g) be the second derivative of w(g). Let j(k) = 0. What is k?
1, 6
Let x(z) be the first derivative of 0*z**4 + 0*z + 38 + 3/8*z**2 - 1/8*z**6 - 3/10*z**5 + 1/2*z**3. Suppose x(g) = 0. What is g?
-1, 0, 1
Let y = -13292 + 13300. Factor 22*v**2 - y + 32/3*v + 10/3*v**3.
2*(v + 1)*(v + 6)*(5*v - 2)/3
Let i(n) = -n**3. Let x(m) = 4*m**3 - 8*m**2 + 7*m. Let f(a) = -6*i(a) - 2*x(a). Factor f(q).
-2*q*(q - 7)*(q - 1)
Let v(t) be the first derivative of 4*t**5/25 + t**4 + 16*t**3/15 - 152. Factor v(l).
4*l**2*(l + 1)*(l + 4)/5
Factor 6 + 19/2*d + 4*d**2 + 1/2*d**3.
(d + 1)*(d + 3)*(d + 4)/2
Let v(r) be the first derivative of -r**4/3 - 8*r**3/3 - 8*r**2 - 11*r + 5. Let q(s) be the first derivative of v(s). Solve q(t) = 0.
-2
Let c(o) be the first derivative of -3/11*o**2 + 2/33*o**3 - 7 + 4/11*o. Suppose c(u) = 0. Calculate u.
1, 2
Let o(q) be the third derivative of -q**7/5880 + q**6/840 - q**5/420 - 8*q**3/3 + 22*q**2. Let j(x) be the first derivative of o(x). Factor j(d).
-d*(d - 2)*(d - 1)/7
Suppose -5*t + 4*s - s + 17 = 0, -s + 21 = 5*t. Suppose 0 = -9*i + i. Factor 2/3*p**3 + i + 2/9*p**t + 4/9*p**2 + 0*p.
2*p**2*(p + 1)*(p + 2)/9
Let f = -434 - -438. Let n(a) be the third derivative of 1/40*a**4 - 11/200*a**6 + 0*a + f*a**2 - 1/50*a**5 + 0 + 0*a**3 + 6/175*a**7. Solve n(l) = 0.
-1/3, 0, 1/4, 1
Suppose 2*o = -3*l + 9, -3*o + 0*l = 3*l - 12. Solve 9*i - 2*i**2 - 5*i**o + 8*i**3 + 11*i**2 + 3 = 0 for i.
-1
Let k(b) be the third derivative of b**8/2240 + 13*b**4/12 + 3*b**2. Let y(g) be the second derivative of k(g). What is o in y(o) = 0?
0
Let k = 8084/3 - 32327/12. Solve -1/4*q**2 - k*q - 1/2 = 0.
-2, -1
Let s(k) be the third derivative of -7*k**6/540 + 11*k**5/270 - k**4/108 - k**3/9 - 109*k**2. Factor s(q).
-2*(q - 1)**2*(7*q + 3)/9
Let x(p) be the second derivative of p**5/10 + 4*p**4 + 23*p**3/3 + 5*p - 22. Let x(i) = 0. What is i?
-23, -1, 0
What is r in -1/4*r**4 + 0*r - 400*r**2 - 20*r**3 + 0 = 0?
-40, 0
Let d(p) be the third derivative of p**5/20 + 5*p**3/6 - 88*p**2. Let f(x) = 3 + 0 - 2 + x**2. Let j(l) = -d(l) + 4*f(l). What is n in j(n) = 0?
-1, 1
Factor -68*w + 75*w - 3*w**3 + 1 - 2*w**3 + 4*w**3 + 5.
-(w - 3)*(w + 1)*(w + 2)
Let y(x) be the third derivative of 1/2*x**3 - 7/24*x**4 - 6*x**2 + 0*x + 1/315*x**7 + 1/180*x**5 + 0 + 1/40*x**6. Let y(q) = 0. What is q?
-3, 1/2, 1
Let r(q) be the third derivative of -q**5/480 - q**4/96 + q**3/6 + 197*q**2. Factor r(p).
-(p - 2)*(p + 4)/8
Let i(x) be the second derivative of x**6/105 - 3*x**5/10 + 20*x**4/7 - 100*x**3/21 + 32*x. Factor i(a).
2*a*(a - 10)**2*(a - 1)/7
Let s = -24/85 - -277/680. Let f(c) be the first derivative of s*c**4 + 0*c**2 - 3 + 0*c - 1/3*c**3. Let f(a) = 0. What is a?
0, 2
Let y = 1 + 1. Suppose 2*w - 2 = y. Factor -3*x**w + 8 + 84*x**2 + 36*x - 4.
(9*x + 2)**2
Let o(b) be the third derivative of -13/210*b**7 + 1/48*b**4 + 0*b - 2/15*b**5 - 17/120*b**6 + 1/6*b**3 - 1/96*b**8 - 6*b**2 + 0. Factor o(m).
-(m + 1)**4*(7*m - 2)/2
Let r = 1221 - 