 -67 - -68. Let q be ((-1)/3)/(-1*v/4). Find l such that 2/9*l**4 + 10/9*l**3 - 8/9*l + q*l**2 - 16/9 = 0.
-2, 1
Let d(h) be the third derivative of -h**6/600 + 11*h**5/300 - 293*h**2. Determine y so that d(y) = 0.
0, 11
Let s(i) = -i**4. Let v(k) = -5*k**4 + 6*k**3. Let f(j) = 2*s(j) - v(j). Suppose f(c) = 0. What is c?
0, 2
Factor 8/3*t**2 + 0 - 2/3*t**3 - 8/3*t.
-2*t*(t - 2)**2/3
Let r be -1*(-2496)/(-252) - -10. Factor -r*d - 2/21*d**2 + 0.
-2*d*(d + 1)/21
Suppose -4*o - 5 - 263 = -4*h, -5*h + 2*o + 332 = 0. Solve -20 - 115*d**2 - 34*d - 15*d**4 + 20*d - h*d - 70*d**3 = 0.
-2, -1, -2/3
Let r(d) = 3 + 3*d - 3 + d**3 - 1 + 3*d**2. Let z = -22 - -27. Let v(l) = 3*l**3 + 7*l**2 + 7*l - 2. Let x(q) = z*r(q) - 2*v(q). Factor x(a).
-(a - 1)**2*(a + 1)
Let v(h) be the first derivative of -h**3/6 - 37*h**2/2 - 1369*h/2 + 257. Factor v(s).
-(s + 37)**2/2
Let u(m) = 4*m**2 - 2*m - 4. Let h(c) = 8*c**2 - 5*c - 8. Let a be -2 + 2 - (-7 + 5). Let b(d) = a*h(d) - 5*u(d). Factor b(y).
-4*(y - 1)*(y + 1)
Factor 77 - 8 - 26 - u - 18*u**2 + 2*u - u**3 - 25.
-(u - 1)*(u + 1)*(u + 18)
Factor -5*r - 38*r**3 + 10*r**2 - 10 + 123*r**3 - 42*r**3 - 38*r**3.
5*(r - 1)*(r + 1)*(r + 2)
Let k(s) = s**2 - s + 1. Let o(j) = -j**2 - 2*j + 2. Let t(z) = -z**2 + 2. Let n be t(2). Let y(g) = n*k(g) - o(g). Factor y(m).
-(m - 2)**2
Let h be (17 + -19)*2/(-2). Let u(w) be the first derivative of 0*w + 0*w**3 - 1 + 0*w**5 - 1/15*w**6 - 1/5*w**h + 1/5*w**4. Suppose u(q) = 0. Calculate q.
-1, 0, 1
Find y, given that 107 - 1178 + 2848*y - 81 - 52*y**4 + 1112*y**3 + 30*y**4 + 50*y**4 + 3824*y**2 = 0.
-36, -2, 2/7
Let d = -1042 - -5222/5. Let o(z) be the first derivative of 0*z + d*z**5 - 1 - 3*z**4 + 0*z**2 - 2/3*z**6 + 4/3*z**3. Factor o(p).
-4*p**2*(p - 1)**3
Find s, given that -246*s**2 + 120*s**2 + 18*s**3 + 68*s**2 + 48*s - 8 = 0.
2/9, 1, 2
Factor -88*i + 105*i**2 + 4*i**4 - 12*i**3 - 9*i**2 + 28 - 28*i**3.
4*(i - 7)*(i - 1)**3
What is t in 22/3*t**3 + 50/3*t + 70/3*t**2 + 2/3*t**4 + 0 = 0?
-5, -1, 0
Let z = 208/11 + -3032/165. Let o(y) be the first derivative of -8/5*y - 1/5*y**4 + z*y**3 + 2/5*y**2 - 11. Factor o(q).
-4*(q - 2)*(q - 1)*(q + 1)/5
Let y = -203 - -204. Suppose f = -1, -2*g + f = 2*g - y. Factor 3/2*z**2 + g - 3/4*z + 3/4*z**5 + 0*z**3 - 3/2*z**4.
3*z*(z - 1)**3*(z + 1)/4
Let v(l) = l + 11 - 9 + l + 2*l**2 - 6*l. Let t be v(2). Let -2*o - 54/13*o**t - 46/13*o**3 - 4/13 - 14/13*o**4 = 0. What is o?
-1, -2/7
Let j = 26 - 59. Let v = -22 - j. Suppose 25*q**2 - v*q**3 - q - 14*q + 2 - q**2 = 0. What is q?
2/11, 1
Let r(s) be the first derivative of 2*s**3/21 - 2*s**2/7 + 9. Determine h, given that r(h) = 0.
0, 2
Let k = -24 - -38. Let r = -12 + k. Suppose -9 - 2*a**r + 4 + 12*a - 13 = 0. Calculate a.
3
Let 0*p**5 - 288 - 368*p**2 - p**5 - 644*p + 116*p - 18*p**4 - 120*p**3 = 0. Calculate p.
-6, -2
Factor 1/6*d - 1 + 1/6*d**2.
(d - 2)*(d + 3)/6
Let c(q) be the third derivative of 5*q**6/84 - q**5 + 27*q**4/28 - 8*q**3/21 + 287*q**2. Let c(i) = 0. Calculate i.
1/5, 8
Let y = -29699/60 + 495. Let i(a) be the third derivative of y*a**5 + 0*a + 2*a**2 + 1/24*a**4 + 0 - 1/3*a**3. What is c in i(c) = 0?
-2, 1
Suppose 5*z + 5*w = 25, 324*z + 1 = 321*z + 5*w. Factor 0*t - 4/3*t**4 - 4/3*t**2 + 0 - 8/3*t**z.
-4*t**2*(t + 1)**2/3
Let g(d) be the first derivative of 0*d - 11 - 3*d**3 + 3/4*d**4 + 3*d**2. Factor g(h).
3*h*(h - 2)*(h - 1)
Let q(f) be the second derivative of 0 - 1/2*f**3 - 3*f**2 + 1/2*f**4 + 3/20*f**5 - 10*f. Factor q(b).
3*(b - 1)*(b + 1)*(b + 2)
Let x(i) = i**3 + 2*i**2 - 26*i - 10. Let j be x(-6). Let a(m) be the first derivative of 2/3*m**3 - m - 1/5*m**5 + 0*m**4 + 4 + 0*m**j. Solve a(k) = 0 for k.
-1, 1
Let s(f) be the second derivative of 2/165*f**6 + 7/55*f**5 - 2/33*f**4 + 6*f - 1/33*f**7 + 0 - 7/33*f**3 + 2/11*f**2. Suppose s(u) = 0. Calculate u.
-1, 2/7, 1
Let u be (-138)/(-92) - (-1)/2. Let s(j) be the first derivative of 0*j + 0*j**u - 1/5*j**5 + 1/4*j**4 + 0*j**3 + 4. Factor s(t).
-t**3*(t - 1)
Factor -1/3*i + 1/3*i**2 + 0.
i*(i - 1)/3
Factor -2/7*f**2 + 10/7 + 8/7*f.
-2*(f - 5)*(f + 1)/7
Let h(v) be the second derivative of 26*v + 0 - 1/24*v**4 + 0*v**2 + 7/12*v**3. Factor h(x).
-x*(x - 7)/2
Let g(l) = -24*l**4 + 20*l**3 + 28*l**2 - 15*l - 4. Let b(j) = 2*j**4 - 2*j**3 - 2*j**2 + j. Let d(t) = -5*b(t) - g(t). Factor d(s).
2*(s - 1)**2*(s + 1)*(7*s + 2)
Suppose -v - 4*z - 8 = -0*v, -4*v = -5*z - 52. Let -2*i + 2*i**2 - 24 + v + 12 = 0. What is i?
-1, 2
Let x(r) be the third derivative of -r**6/160 - r**5/40 - 13*r**3/6 + 14*r**2. Let h(c) be the first derivative of x(c). Factor h(t).
-3*t*(3*t + 4)/4
Solve -62/7*y**2 + 2/7 + 4*y + 32/7*y**3 = 0.
-1/16, 1
Let x(i) = -i**2 - 56*i + 1336. Let q be x(18). Factor -6/7*d**2 + 2*d + 2/7*d**q - 6/7*d**3 + 12/7.
2*(d - 3)*(d - 2)*(d + 1)**2/7
Let d(a) be the first derivative of -a**5/150 - a**4/30 - a**3/15 + 21*a**2 + 20. Let r(m) be the second derivative of d(m). Let r(s) = 0. What is s?
-1
Solve -1456/9*n + 4/9*n**4 + 784/9 + 188/3*n**2 + 104/9*n**3 = 0 for n.
-14, 1
Let k(w) be the third derivative of -1/8*w**4 + 0*w**7 - 32*w**2 + 0*w + 1/30*w**6 - 1/30*w**5 + 1/3*w**3 - 1/336*w**8 + 0. Let k(u) = 0. Calculate u.
-2, -1, 1
Factor -2/11*u**2 + 0 - 3/11*u + 1/11*u**3.
u*(u - 3)*(u + 1)/11
Suppose 4*z = -4*l + 12, 4*l + 561 = z + 573. Find j, given that 20/7*j**2 - 4/7*j + 0 - 16/7*j**l = 0.
0, 1/4, 1
Let o(f) be the third derivative of 1/30*f**5 + 0*f**3 + 0*f**4 - 26*f**2 + 0 + 0*f. Factor o(s).
2*s**2
Let f(c) = 16*c**2 + 78*c + 82. Let j(v) = -5*v**2 - 26*v - 27. Let o(i) = -3*f(i) - 10*j(i). Determine s, given that o(s) = 0.
-12, -1
Let w(z) be the first derivative of 2*z**5/85 + 2*z**4/17 + 4*z**3/17 + 4*z**2/17 + 2*z/17 + 85. Find o such that w(o) = 0.
-1
Let b(j) = j**3 + 4*j**2 - 7*j - 5. Suppose 4*x = 7 - 27. Let w be b(x). Determine g, given that 2*g - 8*g**2 + 4*g**3 + 7*g**w + 8*g**4 - 10*g**5 - 3*g**5 = 0.
-1, 0, 1/3, 1
Let p(c) = 4 - 17 - c**3 - 5*c**2 + 11. Let j(a) = -2*a**3 - 11*a**2 + a - 5. Let x(q) = -2*j(q) + 5*p(q). Suppose x(u) = 0. What is u?
-2, -1, 0
Let u(n) be the first derivative of -2*n**5/35 + 9*n**4/14 - 50*n**3/21 + 27*n**2/7 - 20*n/7 - 391. Solve u(a) = 0.
1, 2, 5
Factor 10*p + 30*p**2 + 0*p**3 + 3*p**3 - 10*p + 2*p**3.
5*p**2*(p + 6)
Let a be ((-16)/12)/(6/(-27)). Let n(k) = -4*k**3 - 4*k**2 + 4*k + 4. Let p(h) = 3*h**3 + 4*h**2 - 3*h - 4. Let b(u) = a*p(u) + 5*n(u). Factor b(w).
-2*(w - 2)*(w - 1)*(w + 1)
Suppose -42 = -3*o - 0*o. Let z(m) = m**2 + 23*m - 50. Let b(j) = 4*j**2 + 114*j - 250. Let p(l) = o*z(l) - 3*b(l). Factor p(i).
2*(i - 5)**2
Let y be 1 - -1 - 90/(-3). Let m = 35 - y. Suppose 5*w - 12*w - 5*w - 15*w**2 + m = 0. What is w?
-1, 1/5
Suppose 0 = -18*o + 22*o - 168. Let u be (-8)/(-14) - (-186)/o. Factor 15*n**4 - 5*n**3 + 5*n**2 - 45*n**u + 4*n**3 + 26*n**3.
-5*n**2*(n - 1)*(3*n + 1)**2
Suppose -84/19*s - 2/19*s**2 - 882/19 = 0. What is s?
-21
Let q(c) = 8*c + 36. Let v be q(-5). Let m be (-7)/252*v + (-34)/(-18). Let -4/3*f**m + 0 + 2/3*f + 2/3*f**3 = 0. Calculate f.
0, 1
Let m(n) = n**3 - 6*n**2 + 6*n - 8. Suppose 5*f = 21 + 9. Let a be m(f). Factor -29 + q + a + q**2 + 2*q**3 - 3*q**3.
-(q - 1)**2*(q + 1)
Let 2/7*y**2 - 2/7*y**3 + 0 + 0*y = 0. What is y?
0, 1
Let s(z) = -4*z**2 + 9*z**2 + 3 - 4*z + 0*z**3 - 1 - z**3. Let f be s(4). Solve 4*w - 5 - w**f + 2*w - 4 = 0.
3
Let j(l) be the third derivative of -4*l**2 + 0*l + 0*l**4 + 0 + 0*l**3 + 1/45*l**5 + 1/180*l**6. Solve j(f) = 0 for f.
-2, 0
Factor -6*v**3 + 12*v**2 - 7*v**3 - 223*v**4 + 110*v**4 + 114*v**4.
v**2*(v - 12)*(v - 1)
Let v(q) be the first derivative of 3 + 0*q + 1/15*q**6 - 6/25*q**5 + 1/5*q**4 + 0*q**2 + 0*q**3. Suppose v(j) = 0. Calculate j.
0, 1, 2
Let t(p) = -p + 13. Let x be t(11). Factor -10*i - 41*i**3 + 26*i**3 - 17*i**3 - 45*i**x - 25*i**4 - 28*i**3.
-5*i*(i + 1)**2*(5*i + 2)
Let -16/5*u**3 + 12/5*u**4 - 8/5 + 18/5*u - 4/5*u**2 - 2/5*u**5 = 0. Calculate u.
-1, 1, 4
Let l(m) be the second derivative of -m**7/105 + 11*m**6/75 - 22*m**5/25 + 38*m**4/15 - 16*m**3/5 - 224*m. Let l(c) = 0. Calculate c.
0, 2, 3, 4
Let a be (-221)/(-1156) - (-2)/34. Factor 0 + 1/4*w**3 + 0*w + a*w**2.
w**2*(w + 1)/4
Let q(b) be the second derivative of 5*b**4/4 - 197*b**3/2 + 117*b**2 - 169*b. Fact