= 0.
0
Suppose -1/3*g**5 + 2 - 23/3*g - 8*g**3 + 34/3*g**2 + 8/3*g**4 = 0. Calculate g.
1, 2, 3
Let s(m) = 5*m**4 + 18*m**3 + 49*m**2 + 15*m - 7. Let k(w) = -2*w**4 - 9*w**3 - 24*w**2 - 8*w + 3. Let f(c) = 14*k(c) + 6*s(c). What is o in f(o) = 0?
-1, 0, 11
Suppose 4*q = c - 20, -2*c + 2 + 10 = -q. Suppose -g - 4*g + 3*h = -1, -4*g + c*h = 4. Factor 6*b**g + 6*b + 4 - 2*b**4 - 2*b**3 + 5*b - b.
-2*(b - 2)*(b + 1)**3
Let a(v) = 7*v**4 - 71*v**3 + 340*v**2 - 634*v + 410. Let o(y) = -23*y**4 + 214*y**3 - 1019*y**2 + 1901*y - 1231. Let u(n) = 7*a(n) + 2*o(n). Factor u(p).
3*(p - 17)*(p - 2)**3
Let v(z) be the first derivative of 2*z**3/21 + 23*z**2/7 + 152*z/7 - 269. Suppose v(b) = 0. Calculate b.
-19, -4
Let s(z) be the third derivative of z**9/60480 - z**8/13440 + z**7/10080 + 23*z**4/24 - 3*z**2. Let v(w) be the second derivative of s(w). Solve v(y) = 0 for y.
0, 1
Let u(f) = f + 1. Let z(r) = 2*r**3 - 6*r**2 + 2. Let h(c) = -6*u(c) + z(c). Let i(j) = 11*j**3 - 35*j**2 - 35*j - 23. Let n(b) = 34*h(b) - 6*i(b). Factor n(v).
2*(v + 1)**3
Let i(r) be the first derivative of -7*r**6/36 - 19*r**5/30 + 37*r**4/8 - 149*r**3/18 + 19*r**2/3 - 2*r + 432. Determine l so that i(l) = 0.
-6, 2/7, 1
Let b(l) be the third derivative of l**5/120 - l**4/6 + 7*l**3/12 - 8*l**2 + 1. Let b(i) = 0. Calculate i.
1, 7
Suppose 5*q = -4*b - 10, -8*b = -0*q - q + 42. Factor -1/5 - 1/5*y**q + 2/5*y.
-(y - 1)**2/5
Let i(t) be the third derivative of -1/1050*t**7 + 1/300*t**6 + 0*t**3 + 0*t - 1/60*t**4 + 1/300*t**5 + 0 + 9*t**2. Determine u so that i(u) = 0.
-1, 0, 1, 2
Let k(j) = -7*j**2 + 22*j - 27. Let c(v) = 6*v**2 - 21*v + 27. Let a(q) = 4*c(q) + 3*k(q). Determine b, given that a(b) = 0.
3
Let q(h) be the third derivative of -h**9/544320 - h**8/90720 + h**7/6480 - h**6/1620 + h**5/4 + 14*h**2. Let u(z) be the third derivative of q(z). Factor u(y).
-(y - 1)**2*(y + 4)/9
Let y(d) = -d**5 - d**2 - d. Let x(j) = 2*j**5 - 4*j**4 - 3*j**3 + 7*j**2 + 7*j. Let v = 9 + -15. Let l(q) = v*y(q) - 2*x(q). Solve l(c) = 0 for c.
-2, -1, 0, 1
Let l be (-2480)/(-155) + -11 + -2. Factor 33/7*p + 3/7*p**l + 3*p**2 + 15/7.
3*(p + 1)**2*(p + 5)/7
Let k = 73/143 + -3/286. Factor 0 - k*a**4 + 3/2*a**3 - a**2 + 0*a.
-a**2*(a - 2)*(a - 1)/2
Let s(z) = -2*z**4 - 78*z**3 - 1318*z**2 + 1674*z + 2916. Let n(d) = 2*d**3 + 2*d**2. Let l(p) = -28*n(p) + 2*s(p). Factor l(r).
-4*(r - 2)*(r + 1)*(r + 27)**2
Factor -187*d**2 + 3*d**3 + 2*d + 158*d**2 + 16*d.
d*(d - 9)*(3*d - 2)
Let t(y) be the third derivative of -y**6/40 - 3*y**5/4 - 3*y**4/2 + 14*y**3 - 3*y**2 + 129. Factor t(o).
-3*(o - 1)*(o + 2)*(o + 14)
Let y be (-66)/429*(3 - (-44)/(-6)). Find z such that -2*z**4 + 2*z**2 - y*z**5 + 0*z + 2/3*z**3 + 0 = 0.
-3, -1, 0, 1
Suppose -392*d - 9 = -395*d. Let w(g) be the second derivative of -5*g - g**2 - 2/3*g**d - 1/6*g**4 + 0. Factor w(t).
-2*(t + 1)**2
Let s(l) be the first derivative of -l**3/3 - 40. Factor s(z).
-z**2
Let j be (18/(-315))/((-6)/126). Factor 3/5*h + 0 - j*h**2 + 3/5*h**3.
3*h*(h - 1)**2/5
Let l(c) = 13*c**3 - 78*c**2 + 288*c - 160. Let h(d) = -4*d**3 + 26*d**2 - 96*d + 56. Let q(s) = 7*h(s) + 2*l(s). Let q(z) = 0. What is z?
1, 6
Let a be (-3)/12 + (-8)/(-32). Let c(d) be the second derivative of 0 - 1/6*d**4 + 4*d + a*d**2 - 1/3*d**3. Solve c(q) = 0 for q.
-1, 0
Let k(t) = 4*t**2 + 3*t + 8. Let b be k(-4). Suppose 20 + 5 - 35*q**3 - 5 - 45*q**2 + b*q = 0. Calculate q.
-2, -2/7, 1
Let -26/3*s**3 - 14/9*s**5 + 0 + 38/9*s**2 + 58/9*s**4 - 4/9*s = 0. What is s?
0, 1/7, 1, 2
Let y(u) be the second derivative of -u**4/54 + 19*u**3/27 + 92*u**2/9 + 167*u + 1. Factor y(m).
-2*(m - 23)*(m + 4)/9
Let t be 3/((-378)/(-37)) - (-6)/(-27). Let o = 199/42 - t. What is c in -8/3*c + o*c**2 - 2 = 0?
-3/7, 1
Find m such that -21*m**2 - 27/4 - 27/8*m**3 - 279/8*m = 0.
-3, -2/9
Let g(q) be the second derivative of -q**6/60 - 5*q**5/4 - 191*q**4/8 + 325*q**3/3 - 169*q**2 + 104*q - 5. Let g(d) = 0. What is d?
-26, 1
Suppose 4*l - 3*h = 0, -4*h + 8*h = -16. Let n be 153/(-36) - (l - 2). Let -9/4*i**3 - n*i**5 + 3*i - 3*i**2 + 3*i**4 + 0 = 0. What is i?
-1, 0, 1, 2
Factor -309/5*h + 102/5 + 9/5*h**2.
3*(h - 34)*(3*h - 1)/5
Let z = 14176 + -99228/7. What is l in -4/7*l**4 + 0*l + z*l**2 + 0 + 0*l**3 = 0?
-1, 0, 1
Let q(w) be the first derivative of w**6/540 - w**5/45 + w**4/12 + 19*w**3/3 + 4. Let p(m) be the third derivative of q(m). Find u such that p(u) = 0.
1, 3
Let l = 70 - 65. Let r(a) be the second derivative of 0 + 1/3*a**3 - 1/20*a**5 + l*a - 1/12*a**4 + 0*a**2. Factor r(m).
-m*(m - 1)*(m + 2)
Let d(b) be the second derivative of -b**9/22680 - b**8/4200 - b**7/2100 - b**6/2700 + b**4 - 35*b. Let s(h) be the third derivative of d(h). Factor s(u).
-2*u*(u + 1)**2*(5*u + 2)/15
Let d = -94690/3 - -31564. What is c in -2/3 - d*c**2 - 4/3*c = 0?
-1
Let t(w) = 2*w**3 + 20*w**2 - 97*w - 3. Let p be (0 - 3) + 6 + -5. Let u(y) = -y**3 - 20*y**2 + 98*y + 2. Let q(o) = p*t(o) - 3*u(o). What is r in q(r) = 0?
0, 10
Let i be 3/1*(-1 + 1 - -2). Factor -i*z - 3*z - 10 + 15*z - z**2 + z.
-(z - 5)*(z - 2)
Let o(y) be the first derivative of 1/150*y**5 + 4 - 1/20*y**4 + 0*y - 2*y**2 + 0*y**3. Let p(s) be the second derivative of o(s). Solve p(r) = 0 for r.
0, 3
Let 21*b**3 + 22*b**2 + 8*b + 6*b**5 + 15*b**4 - 5*b**5 - 7*b**4 = 0. What is b?
-4, -2, -1, 0
Let f be 153*(-5)/(-105) - 7. Factor -9/7 + f*q**2 - 4/7*q**3 - 1/7*q**4 + 12/7*q.
-(q - 1)**2*(q + 3)**2/7
Let h(v) be the first derivative of -1/450*v**5 + 0*v**4 + 5 + 0*v - 9/2*v**2 - 1/225*v**6 + 0*v**3. Let i(d) be the second derivative of h(d). Factor i(s).
-2*s**2*(4*s + 1)/15
Let y = 4357/12 + -1447/4. Let u(j) be the first derivative of 1/9*j**3 + 2/3*j**2 + y*j - 12. Suppose u(m) = 0. What is m?
-2
Let x be 1/(-1) - 10/75. Let r = x - -22/15. Factor -1 + r*k - 1/3*k**3 + k**2.
-(k - 3)*(k - 1)*(k + 1)/3
Let g be (-32)/(-14) - 6/21. Determine y so that 0*y**g + 0*y**2 - 8*y + 10 + 2*y**2 - 2 = 0.
2
Suppose -5*g - 6 + 26 = 0. Factor 8*s**2 - 4 + g*s - 9*s**2 + 0*s + 0*s**2.
-(s - 2)**2
Let n(j) be the third derivative of j**6/180 + 5*j**3/6 + 5*j**2. Let q(s) be the first derivative of n(s). Find m such that q(m) = 0.
0
Let u(c) be the second derivative of -3*c - 9/2*c**2 + c**3 + 1/4*c**4 + 0. Factor u(i).
3*(i - 1)*(i + 3)
Let h(s) = -3*s**3 - 21*s**2 - 36*s - 15. Let u(b) = -b. Let j(l) = h(l) - 3*u(l). Solve j(c) = 0 for c.
-5, -1
Let u be (-4 - (-8 + 3)) + 12/2. Let a(r) = 5*r - 32. Let y be a(u). Suppose -2/5*d**2 + 0 - 1/5*d - 1/5*d**y = 0. What is d?
-1, 0
Let f = 1034 - 1034. Factor 2/13*s**3 + 4/13*s**2 + f + 2/13*s.
2*s*(s + 1)**2/13
Let j(b) = -b**2 - 4*b - 2. Let x be j(-1). Let l be (0 - 4/(-14))*(2 - x). Find w such that 0 + 2/7*w**3 + l*w - 4/7*w**2 = 0.
0, 1
Let k = -10/419 + 3422/2933. Factor 12/7*t + 4/7*t**2 + k.
4*(t + 1)*(t + 2)/7
Let f(n) = -5*n - 13. Let o = 20 - 23. Let q be f(o). Find i, given that -2/3*i**q + 4/3 + 2*i - 2/3*i**4 - 2*i**3 = 0.
-2, -1, 1
Let r(n) be the second derivative of n**6/80 + 87*n**5/20 + 9009*n**4/16 + 29645*n**3 + 1369599*n**2/16 + 403*n. Factor r(x).
3*(x + 1)*(x + 77)**3/8
Factor -50/7*j - 10/7*j**2 + 250/7 + 2/7*j**3.
2*(j - 5)**2*(j + 5)/7
Let k = 21888 - 131327/6. Solve -1/6*g**3 + 1/6*g - k + 1/6*g**2 = 0 for g.
-1, 1
Let j = -1075 - -1077. Factor 2/7*i**3 - 2/7*i**4 + 0 + 2/7*i**j + 0*i - 2/7*i**5.
-2*i**2*(i - 1)*(i + 1)**2/7
Let z be -268 - -270 - 10/(-9). Suppose -z*f + 8/9*f**2 + 16/9 + 4/9*f**3 = 0. What is f?
-4, 1
Let q(a) = a**3 - a**2 + a + 3. Let g be q(0). Suppose -9*k + 14*k - r - 11 = 0, 3*k - 2*r - 1 = 0. Factor -6*c**2 - 6*c**g - 6*c**k + 5*c - c - 2*c**2.
-4*c*(c + 1)*(3*c - 1)
Let o(t) = -2*t - 13. Let p be o(-7). Suppose 2*q - p = 3. Solve -u + 6*u**q - 7*u + 4*u**3 + 8*u = 0.
-3/2, 0
Let c(y) = -3*y**3 + 2*y**2 + 2*y + 1. Let m be c(-1). Suppose -m = -6*f + 5*f. Determine h, given that -2/7*h**f + 4/7*h + 0*h**3 + 6/7*h**2 + 0 = 0.
-1, 0, 2
Suppose 3*d - 301 = 2*q + 24, -4*q + 5*d - 645 = 0. Let i = q + 157. Solve 15/7*t**3 + 6/7*t**i + 12/7*t**4 + 0*t + 3/7*t**5 + 0 = 0.
-2, -1, 0
Factor -16*b + 0 + 2/7*b**2.
2*b*(b - 56)/7
Let k(t) be the third derivative of 0*t + 1/180*t**6 - 2*t**2 - 8/9*t**3 + 1/3*t**4 + 0 - 1/15*t**5. What is b in k(b) = 0?
2
Let z(v) = -56*v**5 + 51*v**