Let q(w) be the first derivative of i(w). Solve q(f) = 0 for f.
-1, 1
Suppose -6*m = -m - 20. Factor 5*o - 53*o**3 + o**m + 0 - 3*o**2 + 52*o**3 - 2.
(o - 1)**3*(o + 2)
Let w(v) be the third derivative of v**6/24 - v**5/3 + 5*v**4/6 - 9*v**2. Solve w(z) = 0 for z.
0, 2
Let y(u) be the first derivative of u**7/6300 - u**5/900 + 35*u**3/3 + 40. Let f(p) be the third derivative of y(p). Suppose f(k) = 0. Calculate k.
-1, 0, 1
Let o(q) be the third derivative of q**7/2100 - 11*q**6/600 + q**5/10 - 11*q**4/8 + 11*q**2. Let p(z) be the second derivative of o(z). Factor p(r).
6*(r - 10)*(r - 1)/5
Let j(h) be the first derivative of 1/4*h**2 - 1/5*h**5 + 4 + 1/3*h**3 + 0*h - 1/8*h**4. Let j(p) = 0. Calculate p.
-1, -1/2, 0, 1
Let j(s) be the second derivative of -1/12*s**4 - 1/30*s**6 + 0*s**3 + 0*s**2 - 13*s + 0 - 1/10*s**5. Factor j(x).
-x**2*(x + 1)**2
Factor 166/7*b**2 + 4*b**3 - 60*b + 225/7 + 1/7*b**4.
(b - 1)**2*(b + 15)**2/7
Suppose 4*j**4 + 0 + 0*j + 12/5*j**2 + 4/5*j**5 + 28/5*j**3 = 0. What is j?
-3, -1, 0
Let x(a) = a**2 + 2*a + 4. Let u(g) = 11 + 8*g + 1 - 3*g + 3*g**2. Let y(l) = 6*u(l) - 17*x(l). Let y(c) = 0. What is c?
2
Let q = -177/11 + 907/55. Let 0 - 2/5*n**4 + 0*n - q*n**2 - 4/5*n**3 = 0. What is n?
-1, 0
Let d = 106 + -106. Let v(c) be the third derivative of 0*c**3 - 2/15*c**5 - 1/6*c**4 + 5*c**2 + d - 1/30*c**6 + 0*c. Find s, given that v(s) = 0.
-1, 0
Let n = -1547 - -1547. Let z(m) be the second derivative of -1/45*m**6 - 1/15*m**5 + 0*m**2 + 11*m + n*m**3 + 0 - 1/18*m**4. Find l such that z(l) = 0.
-1, 0
Let l(r) = -r**3 + 5*r**2 + 7*r - 4. Suppose 0 = -5*p + 25 + 5. Let w be l(p). Suppose 20*h + 3*h**w - 12*h + 4*h**4 - 4 - 8*h**3 - 3*h**2 = 0. What is h?
-1, 1
Let 3/5*j**3 - 3/5*j - 3 + 3*j**2 = 0. What is j?
-5, -1, 1
Suppose 0 = -p + 5, -2*p - 2 - 4 = 4*r. Let z(a) = -2*a**3 + 6*a - 2. Let t(b) = -3*b**3 - b**2 + 7*b - 3. Let f(c) = r*z(c) + 3*t(c). Solve f(l) = 0 for l.
-1
Let y(r) = -r - 3. Let v be y(-3). Suppose -6*q + 2*q + 16 = v. Find i such that 14*i**3 + 28*i - 5*i - 2 - q*i**4 - 18*i**2 - 13*i = 0.
1/2, 1
Let h(m) be the second derivative of -3*m**5/100 - 7*m**4/20 - 11*m**3/10 - 3*m**2/2 - 86*m. Find i such that h(i) = 0.
-5, -1
Let k(v) be the third derivative of v**7/490 + v**6/140 - 3*v**5/140 + 356*v**2. Solve k(y) = 0.
-3, 0, 1
Let q(b) be the third derivative of b**9/90720 + b**8/15120 - b**5/6 - 5*b**2. Let m(v) be the third derivative of q(v). Let m(z) = 0. What is z?
-2, 0
Let q(z) be the third derivative of -z**5/180 - z**4/72 + 136*z**2. Suppose q(l) = 0. What is l?
-1, 0
Solve -36/7*v - 2/7*v**4 + 0 + 22/7*v**2 + 16/7*v**3 = 0.
-2, 0, 1, 9
Let j(z) = -z**3 - 8*z**2 + 9. Let u be j(-8). Let g be 6/u - (-5)/(-10). Find w, given that -1/3*w + 1/6*w**2 + g = 0.
1
Solve 0 - 14/3*v**2 + 7/3*v**3 + v + 4/3*v**4 = 0 for v.
-3, 0, 1/4, 1
Let i(o) be the second derivative of -7*o**7/3 + 217*o**6/15 + 19*o**5/5 - 214*o**4/3 - 232*o**3/3 - 32*o**2 + 72*o. Find u such that i(u) = 0.
-1, -2/7, 2, 4
Let d be (-23)/6*21/28 + 3. Let h(y) be the second derivative of 4*y + d*y**3 + 3/80*y**5 - 1/8*y**4 + 0 + 0*y**2. Let h(s) = 0. Calculate s.
0, 1
Factor -44/3 + 14*c + 2/3*c**2.
2*(c - 1)*(c + 22)/3
Let p(r) be the second derivative of r**7/1470 + 17*r**3/6 - 9*r. Let k(h) be the second derivative of p(h). Let k(z) = 0. Calculate z.
0
Let l = 3 + -9. Let y be 88/20 + l/15. Let 0*w - 12 - 4*w - y*w**3 + 12 + 8*w**2 = 0. Calculate w.
0, 1
Let r be -6 + -305*7/(-350). Let j(z) be the second derivative of -1/10*z**5 - 3*z + 2/3*z**2 + r*z**6 + 2/9*z**3 + 0 - 11/36*z**4. Factor j(f).
(f - 1)**2*(3*f + 2)**2/3
Let h be ((-32)/42)/((-847)/105 + 8). Factor -2/7*c**5 - 1280/7*c**3 + h*c**4 - 40960/7*c + 10240/7*c**2 + 65536/7.
-2*(c - 8)**5/7
Let r(z) = -3*z**4 + 3*z**3 + 6*z**2 + 6*z - 6. Let d(c) = c**4 + c**3 - c + 1. Suppose -14 = -4*l + 10. Let q(b) = l*d(b) + r(b). Factor q(y).
3*y**2*(y + 1)*(y + 2)
Let t(j) be the first derivative of j**6/900 - j**5/150 + j**4/60 + 13*j**3/3 - 1. Let g(u) be the third derivative of t(u). Factor g(l).
2*(l - 1)**2/5
Suppose -92*m + 82*m + 20 = 0. Factor 1/6*z**4 + 1/6*z**m + 1/2*z - 1/2*z**3 - 1/3.
(z - 2)*(z - 1)**2*(z + 1)/6
Let w(u) = 11*u**3 - 50*u**2 + 45*u - 6. Let a(n) = 45*n**3 - 200*n**2 + 180*n - 25. Let p(z) = -6*a(z) + 25*w(z). Factor p(g).
5*g*(g - 9)*(g - 1)
Let f(d) be the third derivative of 0*d**3 + 0*d + 0 - 26*d**2 + 1/3*d**4 + 1/15*d**5. Determine q so that f(q) = 0.
-2, 0
Let o = -508 + 510. Factor -2/9 + 4/9*l**o - 2/9*l.
2*(l - 1)*(2*l + 1)/9
Let q(g) be the second derivative of -g**5/5 + 16*g**4/3 - 56*g**3/3 - 89*g. Factor q(m).
-4*m*(m - 14)*(m - 2)
Suppose -116 = -2*x + 3*m, -3*x = -3*m - 181 + 13. Let u = 54 - x. Solve -2/7*h + 0 + 1/7*h**u = 0.
0, 2
Let b(o) be the second derivative of o**7/21 - 2*o**6/15 - 3*o**5/5 + 2*o**4/3 + 13*o**3/3 + 6*o**2 - 4*o - 5. Factor b(i).
2*(i - 3)*(i - 2)*(i + 1)**3
Determine m so that -m**5 + 368*m**2 + 222*m**2 + 1075*m + 147*m**3 + 750 + 195*m**3 - 186*m**3 + 20*m**4 + 2*m**5 = 0.
-5, -3, -2
Suppose 4*h + 24 = 2*f, 2*f = -4*h - 2 - 14. Factor m - 13*m**2 + 4*m**f + 10*m**2.
m*(m + 1)
Let b(q) = q. Let y(l) = l**2 + 8*l + 1. Let x be y(-9). Suppose 4*g + 6 = x. Let r(d) = 2*d**3 - 2*d - 4. Let t(k) = g*r(k) - 4*b(k). Factor t(o).
2*(o - 2)*(o + 1)**2
Suppose 0 = -4*h - 2 - 10. Let j be h/(-12)*4 - -1. Factor o**2 + 8 - 10*o + j - 1 + 4*o.
(o - 3)**2
Factor 0*u - 14/11*u**3 + 0 + 6/11*u**4 + 4/11*u**2.
2*u**2*(u - 2)*(3*u - 1)/11
Let f be -3*(-4)/15*3430/1029. Determine s so that 154/3*s**2 - 20*s + 21*s**4 + f - 55*s**3 = 0.
2/7, 2/3, 1
Let q(a) be the first derivative of a**4/5 - 4*a**3/5 - 48*a**2/5 - 112*a/5 - 82. Factor q(m).
4*(m - 7)*(m + 2)**2/5
Let r(m) = 2*m - 48. Let s be r(-12). Let b = s + 74. Factor 0*f + 2/5*f**b - 2/5.
2*(f - 1)*(f + 1)/5
Let j(y) = 3*y**2 + 23*y + 22. Suppose 2*n = -0*n - 16. Let i = -9 - n. Let h(v) = v - 1. Let p(g) = i*j(g) + 5*h(g). Determine r, given that p(r) = 0.
-3
Let v(w) = -w. Let o be v(-1). Let m = -10 - -15. Determine n, given that -n**2 - 5*n + o + m*n = 0.
-1, 1
Let z(h) be the second derivative of 3*h**5/20 + 3*h**4/4 - 9*h**3/2 - 81*h**2/2 + 181*h. Factor z(f).
3*(f - 3)*(f + 3)**2
Factor -729 + 1215/2*k + 29/2*k**3 - 297/2*k**2 - 1/2*k**4.
-(k - 9)**3*(k - 2)/2
Let o = 21/2231 - -15554/6693. Factor o*u**5 + 40/3*u**4 + 46/3*u**2 - 2 + 1/3*u + 24*u**3.
(u + 1)**3*(u + 3)*(7*u - 2)/3
Suppose 2*u - 3*g - 13 = 0, 2*u = 5*g - 425 + 444. Factor -1/5*z**3 + 0*z + 2/5*z**u + 0.
-z**2*(z - 2)/5
Let c(g) = -g**3 + 7*g**2 - 6*g. Let k be c(6). Suppose 2*t - v = 5, k*t - 2*t = v + 1. Factor 4*p - t - 3*p**2 - 5*p**3 - p + 6*p**3 + 0.
(p - 1)**3
Let h = 1342 + -1340. Factor 0*p**h - 3/4*p**3 + 3/2 + 9/4*p.
-3*(p - 2)*(p + 1)**2/4
Let a(q) be the first derivative of -2/3*q**3 - 19 - 14*q + 8*q**2. Let a(r) = 0. What is r?
1, 7
Let u(c) = -c**2 - 3*c + 3. Let x be u(-3). Suppose -w + 48 = 4*w + 3*a, -a = 4. Find k such that 4*k - x*k**2 - 4*k + 3*k**3 + w*k**2 + 6*k = 0.
-2, -1, 0
Let 3*l**2 + 18*l**3 + 5*l**2 + 11 + l**2 - 21*l - 17*l**3 = 0. What is l?
-11, 1
Factor 23*t + 23*t**3 - 71*t**2 - 7*t + 23*t**2 - 3*t**3.
4*t*(t - 2)*(5*t - 2)
Determine g, given that 20/7*g**3 - 172/7*g**2 + 333/7*g + 162/7 = 0.
-2/5, 9/2
Let a be (84/20 - 3)/2. Factor a*y + 1/5*y**2 + 2/5.
(y + 1)*(y + 2)/5
Let t = 798 - 795. Let s(x) be the first derivative of 1/34*x**4 - 2/17*x**t - 2/17*x + 9 + 3/17*x**2. Factor s(z).
2*(z - 1)**3/17
Let c(q) be the second derivative of -2*q**7/21 + 13*q**6/10 + q**5/2 - 12*q + 3. What is l in c(l) = 0?
-1/4, 0, 10
Let a(g) = -g**3 + 5*g**2 + 14*g + 1. Let q be a(5). Let d = q - 139/2. Factor -1/2*t**3 - d*t**2 - 3/2*t - 1/2.
-(t + 1)**3/2
Find p such that 36*p**2 - 3*p**4 + 5*p**3 + 79*p**3 + 5*p**2 + 20*p**3 + 18*p**3 = 0.
-1/3, 0, 41
Suppose 4/3*r**2 - 2/3*r**3 + 16/3*r + 0 = 0. What is r?
-2, 0, 4
Let t(k) be the second derivative of k**7/840 + k**6/960 - k**5/240 - k**4/192 + 3*k**2/2 - 14*k. Let f(z) be the first derivative of t(z). Solve f(u) = 0.
-1, -1/2, 0, 1
Let k(g) be the third derivative of -7*g**5/270 - 10*g**4/27 - 52*g**3/27 - 3*g**2 - 32*g. Factor k(t).
-2*(t + 2)*(7*t + 26)/9
Let h(n) be the first derivative of 4*n**5/5 - n**4 - 20*n**3/3 - 6*n