 16*g**2 - 4*g + 6*g**3. Let w(x) = -2*x**3 - 5*x**2 + 7*x. Let r(u) = 6*j(u) + 20*w(u). Find f, given that r(f) = 0.
-2, 0, 1
Let n(q) be the first derivative of -10 - 6*q**2 + 1/2*q**3 + 24*q. Suppose n(h) = 0. Calculate h.
4
Suppose -2*f - 79 = -5*r, 0 = 3*r + 10*f - 6*f - 37. Factor -3*d**4 - 2*d**4 - 10 - 3154*d**3 + 5*d + r*d**2 + 3149*d**3.
-5*(d - 1)**2*(d + 1)*(d + 2)
Let n be ((-351)/30 + -3)*(-252)/6. Let m = -615 + n. Determine i, given that 22/5*i**2 + m*i**3 - 8/5 - 18/5*i**4 - 8/5*i = 0.
-2/3, 1
Let a(n) = 136*n + 2. Let o be a(5). Factor o*i**2 - 682*i**2 - i**3 + i**5.
i**3*(i - 1)*(i + 1)
Let q(t) be the third derivative of -1/6*t**3 - 22*t**2 + 0*t**6 + 1/30*t**5 - 1/210*t**7 + 0 + 0*t**4 + 0*t. Factor q(o).
-(o - 1)**2*(o + 1)**2
Let b(n) = -23*n**2 - 21*n + 18. Let d(m) = -22*m**2 - 21*m + 21. Let g(p) = -5*b(p) + 4*d(p). Find c such that g(c) = 0.
-1, 2/9
Determine n, given that 800 + 220*n**2 - 161*n**3 + 351*n**3 - 185*n**3 + 820*n = 0.
-40, -2
Let f(m) be the first derivative of m**6/1080 - m**5/90 + m**4/18 + 3*m**3 - 22. Let s(d) be the third derivative of f(d). Suppose s(h) = 0. Calculate h.
2
Let g(x) be the third derivative of x**6/30 + 9*x**5/70 + x**4/7 - x**3/21 + 246*x**2 + 2*x. Suppose g(d) = 0. What is d?
-1, 1/14
Let g(z) = -20*z - 1100. Let r be g(-55). Factor -2/7*s**3 - 2/7*s**2 + r + 4/7*s.
-2*s*(s - 1)*(s + 2)/7
Let t(p) be the second derivative of -7*p**7/10 + 707*p**6/50 - 1452*p**5/25 - 221*p**4 - 992*p**3/5 - 384*p**2/5 - 144*p. Suppose t(x) = 0. What is x?
-1, -2/7, 8
Let i(k) = 19*k**4 + 4*k**3 - 9*k**2 + k + 5. Let f(x) = -9*x**4 - 2*x**3 + 5*x**2 - 2. Let c = -42 + 37. Let q(a) = c*f(a) - 2*i(a). Factor q(z).
z*(z - 1)*(z + 1)*(7*z + 2)
Let z(s) be the second derivative of -12769*s**4/3 + 452*s**3 - 18*s**2 + 502*s. Solve z(p) = 0.
3/113
Let r(n) be the third derivative of -n**6/200 - n**5/20 - n**4/10 - 222*n**2. Factor r(q).
-3*q*(q + 1)*(q + 4)/5
Let w(r) be the first derivative of 5*r**4/4 + 170*r**3/3 - 5*r**2/2 - 170*r - 59. Factor w(s).
5*(s - 1)*(s + 1)*(s + 34)
Let z(b) = -2. Let n(l) = 25*l - 21 - 7 - 9*l + 0 - 2*l**2. Let w(q) = -n(q) + 2*z(q). Factor w(c).
2*(c - 6)*(c - 2)
Let s(x) = -26*x**3 + 352*x**2 + 17*x + 17. Let w(a) = -3*a**3 + 44*a**2 + 2*a + 2. Let b(k) = -6*s(k) + 51*w(k). Factor b(h).
3*h**2*(h + 44)
Solve -10 + 6*v - v**2 - 1 - 1 + 7 = 0.
1, 5
Let r(u) be the first derivative of 0*u**4 + 0*u**2 - 1/3*u**3 + 1/10*u**5 + 6 - 5*u. Let b(k) be the first derivative of r(k). Factor b(a).
2*a*(a - 1)*(a + 1)
Let l(z) be the second derivative of 0 - 2*z**3 + 1/10*z**6 - 36*z - 7/4*z**4 + 0*z**2 - 3/10*z**5. Let l(w) = 0. Calculate w.
-1, 0, 4
Let d(i) be the first derivative of -i**6/6 - 9*i**5/5 - 8*i**4 - 56*i**3/3 - 24*i**2 - 16*i + 27. Find n, given that d(n) = 0.
-2, -1
Let s = -180701 - -72822630/403. Let c = -5/31 + s. Factor -6/13*p**3 + c*p**5 + 0 + 8/13*p + 8/13*p**2 - 4/13*p**4.
2*p*(p - 2)**2*(p + 1)**2/13
Let q(x) be the first derivative of -2/7*x - 4 + 3/7*x**2 - 3/14*x**4 + 2/21*x**3. Factor q(m).
-2*(m - 1)*(m + 1)*(3*m - 1)/7
Let m(n) be the third derivative of 0*n**3 + 1/420*n**6 - 33*n**2 - 1/105*n**5 - 1/28*n**4 + 0*n + 0. Factor m(s).
2*s*(s - 3)*(s + 1)/7
Let m(r) = 3*r**3 + 2*r**2 - r - 7. Let h(g) = g**3 + g**2 - 2. Let k(v) = 14*h(v) - 4*m(v). Solve k(y) = 0.
-2, -1, 0
Let b be 606/342 + 14/(-133). Suppose -b*j**2 - 20/3*j - 20/3 = 0. Calculate j.
-2
Let k = 39 - 37. Solve 6 - u**3 - 10 + 9*u**2 - 8*u**2 + k*u**3 - 4*u = 0.
-2, -1, 2
Let g = 15 + -13. Factor -2*b + 7*b - 19*b**g + 4*b**2.
-5*b*(3*b - 1)
Let h be (-36 - -46) + 3*-1. Let g(i) be the third derivative of 0*i**3 + 8*i**2 + 0 + 0*i - 1/84*i**4 + 1/210*i**5 + 1/420*i**6 - 1/735*i**h. Factor g(x).
-2*x*(x - 1)**2*(x + 1)/7
Suppose -2*r = 2*r - 5*o + 4, -4 = -5*r + 4*o. Factor -3*v**r + 5*v**3 + v**3 - 188 + 191 - 6*v.
-3*(v - 1)**3*(v + 1)
Let a(k) = k**2 - 1. Let n(g) = -g**3 - 8*g**2 - 3. Let c(u) = 3*a(u) - n(u). Factor c(z).
z**2*(z + 11)
Let b(x) be the second derivative of -13*x**6/30 - 3*x**5/4 - x**4/6 + 7*x. Determine p so that b(p) = 0.
-1, -2/13, 0
Let a be 720/348 - -3*4/(-174). Factor -2/7*c**a + 26/7 + 24/7*c.
-2*(c - 13)*(c + 1)/7
Let w be (-1 + 0 + 1)/(78 - 79). Factor w + 3/7*j**3 + 15/7*j**2 + 12/7*j.
3*j*(j + 1)*(j + 4)/7
Suppose -3*f + 26 - 23 = 0. Let k(w) be the first derivative of -1/3*w + 2/3*w**2 + 1/3*w**4 - 1/15*w**5 - f - 2/3*w**3. Factor k(b).
-(b - 1)**4/3
Factor 21 + 4*w**3 + 116*w + 90 - 55 + 64*w**2.
4*(w + 1)**2*(w + 14)
Suppose 0 = -13*r + 106 - 54. Let u(g) be the third derivative of -1/150*g**5 - 1/60*g**r + 0*g + 0*g**3 + 0 - 8*g**2. Factor u(b).
-2*b*(b + 1)/5
Let u = -894 - -898. Suppose 0*v + 20 = 5*v. Factor -i**4 + 4*i**4 + i**u - i**v.
3*i**4
Find h, given that 23*h**3 + 25*h**3 - 21 + 31*h - 47*h**3 - 11*h**2 = 0.
1, 3, 7
Let o = -19363/4 + 4812. Let j = o - -233/8. Factor -3/4*r**3 + 3/2*r - j*r**4 + 9/8*r**2 - 3/2.
-3*(r - 1)**2*(r + 2)**2/8
Let d = 203/20 + -31/4. Find k, given that 6/5*k**4 + 0*k + 0 + 8/5*k**2 - 1/5*k**5 - d*k**3 = 0.
0, 2
Let n(q) be the second derivative of 0*q**2 - 1/90*q**5 - 16*q - 1/9*q**3 + 0 + 2/27*q**4. Factor n(c).
-2*c*(c - 3)*(c - 1)/9
Let z be (13 + -28 + 15)*2/12. Let n(u) = -u**3 + 4*u**2 - 3*u + 3. Let t be n(3). Factor 0*j + 0*j**2 + z*j**t + 3/2*j**5 + 0 - 3*j**4.
3*j**4*(j - 2)/2
Let p(t) = -9*t**2 - 13*t - 17. Suppose 9 = 2*s - 3*l, -s - l + 7 = -0*l. Let i(j) = -2*j**2 - 3*j - 4. Let r(x) = s*p(x) - 26*i(x). Factor r(w).
-2*(w - 1)*(w + 1)
Factor 3/5*t**4 - 6/5*t**2 + 0*t + 3/5 + 0*t**3.
3*(t - 1)**2*(t + 1)**2/5
Let s be 2*1*(-3 - -14). Factor 2*o**3 - 4*o**3 + 12*o**2 - s*o + 4*o.
-2*o*(o - 3)**2
Let d = -21365/4 - -5281. Let n = d - -61. Factor t - t**3 - 1/4*t**4 + n - 1/2*t**2.
-(t - 1)*(t + 1)**2*(t + 3)/4
Factor -3226*l - 3312*l + 5*l**4 + 6358*l + 200*l**2 - 65*l**3.
5*l*(l - 9)*(l - 2)**2
Factor 1/7*g**2 - 1/7*g - 6/7.
(g - 3)*(g + 2)/7
Suppose 2*f + 3 = 15. Suppose -2*o = -3*u - 22, -o = 3*u - f - 5. Factor 10*b - 2*b**2 - b**3 + 0*b**2 - o*b.
-b*(b + 1)**2
Factor 40*o - 18*o**3 + 264*o**2 + 123*o**3 + 54*o + 5*o**4 - 69*o**2 + o.
5*o*(o + 1)**2*(o + 19)
Let i = -7/507 + 373/2535. What is t in -2/3*t + i*t**2 + 2/15*t**3 + 2/5 = 0?
-3, 1
Suppose -3*j + 58 = -68. Let u be (-1)/(-7)*98/j. Suppose 2/3*r + 1/3*r**2 - u*r**3 + 0 = 0. Calculate r.
-1, 0, 2
Suppose -2*u - 21 + 25 = 0. Factor 89*m**3 + 18*m**2 + 8*m - 6*m**u - 85*m**3.
4*m*(m + 1)*(m + 2)
Let s(r) be the third derivative of r**5/90 + 7*r**4/4 - 130*r**3/9 + 364*r**2. Find i such that s(i) = 0.
-65, 2
Let i be (386/180)/((-165)/45). Let s = 1/66 - i. Factor -9/5*t - s*t**2 - 6/5.
-3*(t + 1)*(t + 2)/5
Suppose -20*x**3 - 8300*x - 20*x**3 - 15*x**2 + 8300*x + 75*x**4 - 20*x**5 = 0. What is x?
-1/4, 0, 1, 3
Suppose -9*h + 68 = 8*h. Let s(b) be the second derivative of 1/45*b**6 + 2/3*b**h + 0 - 6*b - 1/5*b**5 + b**2 - 10/9*b**3. Let s(r) = 0. Calculate r.
1, 3
Let h = 5927/5 + -1185. Let u(d) = -d + 4. Let f be u(4). Let 2/5*x**4 + 0*x + h*x**2 + f + 4/5*x**3 = 0. What is x?
-1, 0
Let p = 28 + -22. Find w, given that -4*w**4 + 32 + 11*w**2 - p*w**2 + 20*w**3 - 16*w - 29*w**2 = 0.
-1, 2
Let v(s) = 2*s**3 - s**2 - s. Let u(w) = -w**3 - 31*w**2 - 85*w - 72. Let t(k) = u(k) - v(k). Solve t(p) = 0 for p.
-6, -2
Let w be (3 - 7/2)*-8. Suppose -3*i + 29 = 4*b, -2 = -w*b + 5*i + 3. What is y in b*y**3 + 4*y**5 - 2*y**5 - 3*y**5 + 3*y**2 + y**4 = 0?
-1, 0, 3
Let h(k) be the first derivative of -k**4/6 + 4*k**3/9 + k**2 + 92. What is c in h(c) = 0?
-1, 0, 3
Let a(u) = -u**2 + 7*u + 11. Let i be a(8). Suppose -g + 0*g - g**2 + 5*g - i + 0*g**2 = 0. Calculate g.
1, 3
Suppose -3*w - 5*a = 0, 3*w + 0*w - a = 0. Let x(n) be the third derivative of 0*n**5 + 0*n + 0*n**4 + 3*n**2 - 1/300*n**6 + w*n**3 + 0. Factor x(g).
-2*g**3/5
Let q(c) be the first derivative of 0*c**4 + 3/35*c**5 + 0*c**2 - 1/7*c**3 - 9 + 0*c. Determine t so that q(t) = 0.
-1, 0, 1
Let j = -996/11 - -5013/55. Let -3/5*a**3 - 3/5*a**2 + 3/5*a**4 + j*a + 0 = 0. Calculate a.
-1, 0, 1
Let j(k) be the second derivative of k**7/8820 + k**6/420 + 3*k**5/140 - 7*k**4/12 + 2*k. Let s(p) be the third derivative of j(p). Factor s(a).
2*(a + 3)**2/7
Let y(p) be the second derivative of -5*p**7/42