u = 0.
-1, 1, 2
Factor 15*g + 0*g**2 - 109*g + 33*g - 48 + g**3 - 12*g**2.
(g - 16)*(g + 1)*(g + 3)
Let c(o) be the first derivative of 2/35*o**5 + 6/7*o + 1 + 8/7*o**3 - 10/7*o**2 - 3/7*o**4. Determine w, given that c(w) = 0.
1, 3
Let x(k) be the third derivative of -k**8/42 - 2*k**7/35 + k**6/10 + 2*k**5/15 + 3*k**2 + 3. Find u, given that x(u) = 0.
-2, -1/2, 0, 1
Let m(q) be the second derivative of 0*q**2 + 2*q - 1/80*q**6 - 3/112*q**7 + 3/80*q**5 + 0 + 0*q**4 + 0*q**3. Find v such that m(v) = 0.
-1, 0, 2/3
Let r(o) = -10*o - 25. Let y be r(8). Let k be (-126)/y*(-10)/(-6). Determine p, given that -p**k + 3*p - p**3 - 6*p**3 + 2*p**3 - 3*p**4 - 2*p = 0.
-1, 0, 1/3
Let p(t) = -6*t**2 + 660*t - 18177. Let j(b) = -3*b**2 + 330*b - 9087. Let g(f) = 9*j(f) - 4*p(f). Factor g(n).
-3*(n - 55)**2
Solve 10 + 19*l**2 + 161*l**2 - 25*l**4 + 140*l - 65*l**3 - 73 - 17 = 0 for l.
-4, -1, 2/5, 2
Let n(y) be the first derivative of -6*y**3 - 3 - y**3 + 3*y**3 + 5*y**3 - 27*y**2 + 243*y. Suppose n(d) = 0. What is d?
9
Suppose 486/7*d - 2*d**2 + 20 = 0. Calculate d.
-2/7, 35
Let p be 14/1 - (7 - -4). Let q(j) be the second derivative of j + 0 + 21/20*j**5 - 3/4*j**4 + p*j**2 - 3/2*j**3 - 3/10*j**6. Factor q(u).
-3*(u - 1)**3*(3*u + 2)
Suppose 55 = -2*j + 13*j. Let g(z) be the first derivative of 1/10*z**4 + 1/15*z**6 + 0*z**2 - 6 + 0*z + 4/25*z**j + 0*z**3. Factor g(x).
2*x**3*(x + 1)**2/5
Let m(u) be the second derivative of u**7/60 - 2*u**6/9 + 17*u**5/20 + 3*u**4/2 + 17*u**3/6 - 12*u. Let y(s) be the second derivative of m(s). Factor y(n).
2*(n - 3)**2*(7*n + 2)
Factor -3/7*w**2 + 81/7 + 78/7*w.
-3*(w - 27)*(w + 1)/7
Suppose -1/3*m**5 + 20/3 - 23/3*m**3 + 8*m - 3*m**4 - 11/3*m**2 = 0. Calculate m.
-5, -2, -1, 1
Let z(s) = -6*s**3 + 29*s**2 + 21*s + 7. Let a(l) = -l**3 - l**2 + l + 1. Let b(x) = -4*a(x) + z(x). Let f be b(17). Factor -2*n - 4/3 + 4/3*n**f + 2*n**2.
2*(n - 1)*(n + 2)*(2*n + 1)/3
Suppose 30*k - 117 = 123. Let m(o) be the second derivative of -5/57*o**3 + 0 + 1/190*o**5 - 2/19*o**2 - k*o + 1/285*o**6 - 1/38*o**4. Factor m(z).
2*(z - 2)*(z + 1)**3/19
Let f(i) be the first derivative of -i**3/3 - i + 9. Let n(k) = -2*k**2 + 23. Let l(y) = -3*f(y) - n(y). Factor l(o).
5*(o - 2)*(o + 2)
Suppose -5*k - 5*m = -4 - 11, k - 9 = -3*m. Solve 2 - 4*z**3 + 46*z**5 + 14*z**4 - 38*z**5 - 16*z**2 - 4*z + k = 0.
-1, 1/4, 1
Let t(a) be the second derivative of 2*a**7/63 - 4*a**6/45 - 7*a**5/15 - 4*a**4/9 + 18*a. Find m, given that t(m) = 0.
-1, 0, 4
Let s = 2592 - 2592. Let f = 6955/17 + -409. Factor -2/17*v**2 - f*v + s.
-2*v*(v + 1)/17
Let s be -2 - 102/(-17) - 8/3. Determine i, given that 16/3*i**2 + s*i**3 + 20/3*i + 8/3 = 0.
-2, -1
Let o(m) = m**2 + m - 15. Let w be o(-5). Suppose j - 4*s = -11 - 6, -3*j = 2*s - 19. Determine v so that 0*v + 0 + 3/2*v**j + 0*v**2 - 3*v**4 + 3/2*v**w = 0.
0, 1
Factor 38 + 3*u**2 - 116 + 38 - 116 - 81*u - 18.
3*(u - 29)*(u + 2)
Let d(h) be the first derivative of h**8/1344 - h**7/168 - 2*h**3/3 - 17. Let p(j) be the third derivative of d(j). Factor p(v).
5*v**3*(v - 4)/4
Let t(h) be the second derivative of 35*h - 1/72*h**4 + 0*h**2 + 0 - 1/36*h**3. Factor t(v).
-v*(v + 1)/6
Let j = -233/21 - -35/3. Factor -2/7*r**2 + 0 + 0*r - 2/7*r**4 + j*r**3.
-2*r**2*(r - 1)**2/7
Suppose -10*o - 48 = -25*o - 18. Factor 0 + 10/9*g**3 + 2/3*g**o - 4/9*g.
2*g*(g + 1)*(5*g - 2)/9
Let i(h) be the third derivative of 3*h**8/32 + 73*h**7/70 + 473*h**6/120 + 82*h**5/15 + 61*h**4/16 + 3*h**3/2 - 536*h**2. Find v such that i(v) = 0.
-3, -1/3, -2/7
Let t = 733 + -10993/15. Let v(h) be the second derivative of -h**2 + 0 - 3/10*h**5 - 3*h + t*h**6 + h**3 - 1/6*h**4. Factor v(a).
2*(a - 1)**2*(a + 1)*(2*a - 1)
Factor -6*i**2 - 15*i - 7*i**2 + 33*i**2 - 5*i**3.
-5*i*(i - 3)*(i - 1)
Suppose -108 - 23 = -3*x + q, 2*x - 4*q = 94. Suppose -3*j - j**5 + 2*j + x*j**3 - 41*j**3 = 0. Calculate j.
-1, 0, 1
Let j(z) be the second derivative of -z**4/72 - 29*z**3/36 + 31*z**2/6 + 118*z + 3. Factor j(f).
-(f - 2)*(f + 31)/6
Suppose -7*a + 15*a = 7*a. Let c(s) be the second derivative of -1/18*s**4 + 0*s**2 + 0*s**3 + 1/60*s**5 + a + 1/90*s**6 - s. Factor c(l).
l**2*(l - 1)*(l + 2)/3
Let b(k) be the first derivative of 3/2*k**3 - 1/2*k**5 + 1/12*k**6 + 3/8*k**4 + 38 + 0*k + 0*k**2. Find x, given that b(x) = 0.
-1, 0, 3
Factor 60*z - 185*z**2 + 20 + 57*z**3 - 6*z**3 - 2*z**3 + 26*z**3.
5*(z - 2)*(3*z - 2)*(5*z + 1)
Suppose -2*q - 3 = q + 3*n, -n - 1 = -3*q. Let b be 3 + 4 + -4 + q. Let -3*i**5 - i**3 + 2*i**5 - i**3 + b*i**5 = 0. What is i?
-1, 0, 1
Let x(v) be the second derivative of -5*v**4/12 - 80*v**3/3 - 640*v**2 + 46*v. Factor x(g).
-5*(g + 16)**2
Determine m, given that -8/7*m**3 + 0 + 2/7*m**2 - 2/7*m**4 + 8/7*m = 0.
-4, -1, 0, 1
Solve 0*n**2 - 26551 + 2*n**2 + 26589 - 40*n = 0.
1, 19
Let h(o) be the first derivative of o**4/8 - 9*o**3/2 + 51*o**2/4 - 25*o/2 - 139. Factor h(n).
(n - 25)*(n - 1)**2/2
Suppose 5 = -7*t - 2, -2*t + 37 = 3*z. Let k(l) be the second derivative of 0 + 4/3*l**3 - 1/3*l**4 - z*l - 2*l**2. Determine r, given that k(r) = 0.
1
Let g(x) be the second derivative of -x**5/210 + 3*x**4/14 - x - 30. Factor g(d).
-2*d**2*(d - 27)/21
Let u(r) be the second derivative of -1/28*r**4 + 3/35*r**5 - 8*r + 3/14*r**2 + 0 - 2/7*r**3. Find p such that u(p) = 0.
-1, 1/4, 1
Let g(p) be the third derivative of -2*p**7/147 - p**6/420 + 4*p**5/105 + p**4/28 - 24*p**2. Suppose g(i) = 0. What is i?
-3/5, -1/2, 0, 1
Let k = 2 - -2. Let a be 11/k + (-6)/8. Factor -16*u + 2*u**2 + 0*u**a - 25 + 28 + 29.
2*(u - 4)**2
Let p(d) be the first derivative of -5/14*d**4 + 2/21*d**3 + 0*d**2 + 0*d + 8/35*d**5 - 16. Determine j so that p(j) = 0.
0, 1/4, 1
Let t = -8 - -12. Determine z, given that t*z**2 - 7 + 270*z - 254*z + 23 = 0.
-2
Let u(v) = -2*v**5 + 5*v**4 - 3*v**3 - 11*v**2 - v. Let r(o) = -2*o**5 + 5*o**4 - 4*o**3 - 13*o**2 - 2*o. Let t(p) = -3*r(p) + 4*u(p). Solve t(x) = 0.
-1, 0, 1/2, 1, 2
Let f(l) be the third derivative of 3*l**6/80 + l**5/8 + l**4/8 + 228*l**2. Find h, given that f(h) = 0.
-1, -2/3, 0
Let o be 6/(-27) + -5*(-12)/270. Factor 0*r**3 + 0*r + o - 1/3*r**4 + 1/3*r**2.
-r**2*(r - 1)*(r + 1)/3
Let d(r) be the first derivative of r**4/4 + 2*r**3/3 - 13*r**2/2 + 10*r + 438. Find s such that d(s) = 0.
-5, 1, 2
Let k be (-14)/(-5) + (2 - 98/35). Determine d so that -k*d + 56*d**2 - 54*d**2 - 2*d = 0.
0, 2
Let p(v) be the second derivative of -5*v**7/126 + 52*v**6/9 - 338*v**5 + 87880*v**4/9 - 1142440*v**3/9 - v - 22. Suppose p(z) = 0. Calculate z.
0, 26
Let b(k) = -3*k**2 - k + 2. Let u(a) = 2*a**2 - 2. Let m(d) = 3*b(d) + 4*u(d). Factor m(i).
-(i + 1)*(i + 2)
Factor -2/5*t**4 - 29766/5*t**2 + 98*t**3 - 30258/5*t + 0.
-2*t*(t - 123)**2*(t + 1)/5
Suppose 2*p**5 + 2/7*p**3 - 16/7*p + 46/7*p**2 - 38/7*p**4 - 8/7 = 0. What is p?
-1, -2/7, 1, 2
Let q(h) be the second derivative of -h**5/5 + 2*h**4 + 50*h**3/3 + 36*h**2 + 228*h. Find g such that q(g) = 0.
-2, -1, 9
Let r(m) be the third derivative of m**8/224 + m**7/140 + 96*m**2. Solve r(p) = 0.
-1, 0
Let h(o) = o**3 - 6*o**2 + 2*o. Let g be h(0). Let d(w) be the first derivative of 2/11*w - 2/33*w**3 + 2 + g*w**2. Factor d(s).
-2*(s - 1)*(s + 1)/11
Let s = 11660 - 81618/7. Suppose -3*j + 5*q = -2 + 22, 2*q = -5*j + 8. Determine u, given that 4/7*u - 2/7*u**2 + s*u**4 - 4/7*u**3 + j = 0.
-1, 0, 1, 2
Let q(o) be the first derivative of 1/7*o**4 + 0*o**2 + 0*o + 11 + 2/21*o**3 + 2/35*o**5. Find a, given that q(a) = 0.
-1, 0
Let m = 66 + -64. Factor 10*j**2 - 3*j**3 - m - 4*j**2 - 14*j**2 - 7*j + 0*j**3.
-(j + 1)**2*(3*j + 2)
Let f(v) be the first derivative of 0*v**2 + 49 + 0*v**4 + 0*v + 0*v**3 + 1/45*v**5. Let f(w) = 0. What is w?
0
Let g = 21 - 5. What is t in -28*t**4 + g*t**3 + 18*t**3 + 24*t**2 - 40*t - 12*t**2 + 6*t**5 + 16 = 0?
-1, 2/3, 1, 2
Let v(t) = -6*t**2 + 18*t - 9. Let s(o) = -11*o**2 + 35*o - 19. Let q(n) = 3*s(n) - 5*v(n). Suppose q(p) = 0. Calculate p.
1, 4
Let w(x) be the third derivative of -x**8/1848 + 3*x**6/220 - 2*x**5/165 - x**4/11 + 5*x**2 + 7. Let w(g) = 0. Calculate g.
-3, -1, 0, 2
Let w(b) = 24*b**2 + 91*b - 16. Let n(c) = -c. Let m(u) = -n(u) + w(u). Let m(h) = 0. Calculate h.
-4, 1/6
Let p(g) be the first derivative of 5/4*g**2 - 20 + 3/2*g - 1/8*g**4 + 1/6*g**3. Factor