0*a + x + 3/8*a**4 + 0*a**2 - 3/4*a**3 = 0.
0, 2
Let a(m) be the first derivative of -m**6/180 - m**5/12 + 7*m**4/6 - 92*m**3/3 + 150. Let t(h) be the third derivative of a(h). Factor t(u).
-2*(u - 2)*(u + 7)
Let r(p) be the first derivative of 23*p + 22 + 2/3*p**3 - p**2 - 1/6*p**4. Let s(w) be the first derivative of r(w). Find j, given that s(j) = 0.
1
Let b be 176/(-1672) + 25836/(-38). Let g be 2/(-21) + b/(-1785). Factor g*n**2 + 4/7 + 6/7*n.
2*(n + 1)*(n + 2)/7
Let n(d) be the first derivative of -d**6/45 - d**5/10 - d**4/9 - 72*d + 89. Let o(s) be the first derivative of n(s). Factor o(f).
-2*f**2*(f + 1)*(f + 2)/3
Suppose -4*r + h + 5 = 0, 0 = 3*r + 4*h - 448 + 430. Let y(p) be the first derivative of -1/8*p**4 + 1/4*p**r - 7 - 1/6*p**3 + 1/2*p. Solve y(o) = 0 for o.
-1, 1
Let d(v) be the first derivative of 4*v**5/45 - 130*v**4/9 + 18352*v**3/27 - 15376*v**2/3 - 4482. Factor d(f).
4*f*(f - 62)**2*(f - 6)/9
Suppose -22*h - 619 = -245. Let z(o) = o**2 + 2*o - 252. Let m be z(h). Find n, given that 6*n - m*n**2 + 12 - 3/2*n**3 = 0.
-2, 2
Let v(t) be the first derivative of -12*t**5/5 - 429*t**4/4 - 1260*t**3 + 486*t**2 - 463. Factor v(s).
-3*s*(s + 18)**2*(4*s - 1)
Factor 5/3*i**2 - 23470/3*i + 27542045/3.
5*(i - 2347)**2/3
Let x = -53 + 56. Let v(c) = c**3 - 1. Let i be v(x). Factor -i*p**5 + 2*p + 6*p**4 - 2*p + 30*p**5 - 2*p**2.
2*p**2*(p + 1)**2*(2*p - 1)
Let r(k) = 2*k**2 - 11*k - 6. Let z be r(9). Let x = -55 + z. Factor 67*q**x - 71*q**2 + 0*q**4 - 24*q + 18 + 8*q**3 + 2*q**4.
2*(q - 1)**2*(q + 3)**2
Let f(k) = -2*k + 2*k - k**4 + k**3. Suppose 3*j - 20 + 26 = 0. Let z(y) = 15*y**5 - 4*y**4 - 2*y**3. Let r(p) = j*f(p) - z(p). Factor r(o).
-3*o**4*(5*o - 2)
Let x(s) be the first derivative of s**4/2 + 8*s**3 + 29*s**2 + 36*s - 559. Factor x(q).
2*(q + 1)*(q + 2)*(q + 9)
Let o(y) be the first derivative of -4*y**5/15 - 53*y**4/3 - 448*y**3/3 - 1304*y**2/3 - 1472*y/3 - 2777. What is z in o(z) = 0?
-46, -4, -2, -1
Let d = 15 + 2. Let i = 20 - d. Factor -b**3 + 0*b - 8*b + 5*b**i + 4*b.
4*b*(b - 1)*(b + 1)
Let a(s) = 11*s**4 + 6*s**3 + 33*s**2 + 50*s - 10. Let x(j) = -9*j**4 - 7*j**3 - 34*j**2 - 48*j + 8. Let l(w) = -4*a(w) - 5*x(w). Factor l(r).
r*(r + 2)*(r + 4)*(r + 5)
Suppose -16*s + 225 = -25*s. Let r be s/15*(-2)/5. Let r*d**2 + 0 - 2/3*d - 1/6*d**3 = 0. Calculate d.
0, 2
Factor -88086*t + 87978*t - 44 - 396 - 4*t**2.
-4*(t + 5)*(t + 22)
Let n(v) be the second derivative of -v**5/4 + 235*v**4/12 + 310*v**3 + 810*v**2 - 4919*v. Find i such that n(i) = 0.
-6, -1, 54
Let x(j) = 2*j**2 + 78*j + 759. Let c be x(-18). Let u(t) be the first derivative of 1/4*t**2 + 12 + t - 1/6*t**c. Let u(h) = 0. Calculate h.
-1, 2
Factor 0 + 2/11*y**2 + 60*y.
2*y*(y + 330)/11
Let s(j) be the second derivative of -j**5/40 - j**4/2 - 1772*j. Factor s(g).
-g**2*(g + 12)/2
Let y(m) = -91*m**3 - 2*m**2 - 4*m - 2. Let c be y(-1). Suppose g + 87 = c. Factor 2/7*b**2 + 0 - 2/7*b**5 + 2/7*b**3 + 0*b - 2/7*b**g.
-2*b**2*(b - 1)*(b + 1)**2/7
Let i = 33952/50991 + 14/16997. Solve i*o**2 - 1/6*o**3 - 2/3 + 1/6*o = 0.
-1, 1, 4
Let j(b) be the first derivative of 3*b**4/8 - 89*b**3/4 + 273*b**2/2 - 120*b + 9925. Solve j(d) = 0 for d.
1/2, 4, 40
Let a(d) = d**2 - 17*d + 23. Let h be a(9). Let b = h + 353/7. Factor -b*j + 2/7*j**2 + 8/7.
2*(j - 4)*(j - 1)/7
Let k(v) = v**2 + 162*v - 313. Let w(y) = -12*y**2 - 1782*y + 3442. Let z(r) = -68*k(r) - 6*w(r). Factor z(d).
4*(d - 79)*(d - 2)
Suppose -p + 0 + 4 = 0. Suppose 2*a + 6 = p*a, -2*j + a = -1. Factor 53*c**4 - 53*c**4 + 32*c**j - 4*c**5 + 24*c**3 + 12*c.
-4*c*(c - 3)*(c + 1)**3
Let y(t) = 832*t**2 + 9*t + 10. Let m be y(-1). Let z = m + -833. Find x, given that -164/9*x**4 - 32/3*x**3 + 0*x - 16/9*x**2 - 28/3*x**5 + z = 0.
-1, -2/3, -2/7, 0
Let p(h) = 61*h**2 + 169*h - 18. Let b(o) be the second derivative of -265*o**4/4 - 733*o**3/2 + 117*o**2 + 142*o. Let f(t) = -2*b(t) - 27*p(t). Factor f(x).
-3*(x + 3)*(19*x - 2)
Find o, given that -16*o + 17 + 1/4*o**3 + 13/4*o**2 = 0.
-17, 2
Let b = 1939132 + -21310280/11. Suppose -b*t**2 - 551368/11*t - 328/11*t**3 - 5651522/11 - 2/11*t**4 = 0. What is t?
-41
Let k be 8/30 + (3 - (-104)/(-40)). Let u(i) be the second derivative of -1/7*i**2 + 0 - 8*i + k*i**3 - 7/6*i**4. Find w such that u(w) = 0.
1/7
Suppose -1 = -5*z + 14. Factor -64*q**3 + 24*q**z + 9*q - 4*q**2 + 3*q**4 + 31*q**3 + q**2.
3*q*(q - 3)*(q - 1)*(q + 1)
Let s(y) = 4*y**2 - 3*y + 15. Let l(o) = -o**2 + o - 6. Let a = 375 + -373. Let i(b) = a*s(b) + 7*l(b). Factor i(z).
(z - 3)*(z + 4)
Let k(p) be the second derivative of -9*p**7/56 - 33*p**6/40 - 3*p**5/8 + 15*p**4/8 + 19*p**3/8 + 9*p**2/8 + 3060*p. Find a, given that k(a) = 0.
-3, -1, -1/3, 1
Let b = 533 + -512. Let i be 7/(b/(-6))*(-1)/6. Factor -i + 1/3*w**2 + 0*w.
(w - 1)*(w + 1)/3
Let b(x) be the first derivative of 3*x**4/5 - 98*x**3/15 + 16*x**2 - 24*x/5 + 8188. Factor b(m).
2*(m - 6)*(m - 2)*(6*m - 1)/5
Let w(u) be the second derivative of 0 + 0*u**2 + 1/8*u**4 + 0*u**3 - 35*u + 0*u**5 - 1/20*u**6. Solve w(s) = 0 for s.
-1, 0, 1
Let a(d) be the first derivative of 0*d + 5/2*d**2 + 1/12*d**3 - 57. Find i, given that a(i) = 0.
-20, 0
Let z(c) be the first derivative of 7*c**4/8 + 53*c**3/6 + 81*c**2/4 - 45*c/2 - 2918. Solve z(f) = 0 for f.
-5, -3, 3/7
Let s(p) = 2*p**4 + 41*p**3 + 63*p**2 + 59*p - 7. Let i(j) = -3*j**4 - 42*j**3 - 64*j**2 - 46*j + 7. Let z(c) = -3*i(c) - 2*s(c). Factor z(m).
(m + 1)**2*(m + 7)*(5*m - 1)
Let y(j) = 80*j**3 + 376*j**2 - 2396*j + 2028. Let s(n) = -179*n**3 - 751*n**2 + 4790*n - 4058. Let q(b) = 4*s(b) + 9*y(b). Determine w so that q(w) = 0.
-101, 1, 5
Let a = -23950 - -23950. Factor -2/3*n**2 + 32/3 + a*n.
-2*(n - 4)*(n + 4)/3
Factor 119/6*h - 1/6*h**2 + 20.
-(h - 120)*(h + 1)/6
Suppose 8*c - 268 + 244 = 0. Let r(o) be the third derivative of 0*o + 3/32*o**4 + 1/160*o**6 + 14*o**2 + 0 + 0*o**c + 1/20*o**5. What is i in r(i) = 0?
-3, -1, 0
Let m(u) = 165*u**2 - 219*u + 32. Let w(g) = -g**2 - 8*g - 2. Let o(c) = 3*m(c) - 6*w(c). Factor o(d).
3*(d - 1)*(167*d - 36)
Factor -148/9 + 70/9*c + 2/9*c**3 + 76/9*c**2.
2*(c - 1)*(c + 2)*(c + 37)/9
Let s(g) be the second derivative of g**9/5040 + g**8/1120 - 11*g**4/12 - g**3/6 - 81*g. Let r(c) be the third derivative of s(c). Determine h so that r(h) = 0.
-2, 0
Solve -19/3*k - 1/3*k**3 - 11/3*k**2 - 3 = 0.
-9, -1
Let p(o) = 62*o - 237. Let k(h) = -4*h + 1. Let s(v) = -4*k(v) - p(v). Let n be s(5). What is a in -1/2*a**2 + 0 + 0*a**n + 1/6*a**4 - 1/3*a = 0?
-1, 0, 2
Determine m, given that 139/3*m**4 + 0 + 1258/3*m**3 + 289*m**2 + 0*m + 4/3*m**5 = 0.
-17, -3/4, 0
Let s(z) be the second derivative of -z**4/3 - 2212*z**3/3 - 611618*z**2 + 124*z + 1. Factor s(j).
-4*(j + 553)**2
Suppose -12*z + 36 = 6*z. Find k such that 3*k**2 + 5*k**z + 6*k**2 + k**3 - 31*k + 16 = 0.
-16, 1
Let p(k) be the second derivative of -k**7/210 - 4*k**6/75 - 3*k**5/20 + 2*k**4/15 + 8*k**3/15 + k + 243. What is v in p(v) = 0?
-4, -1, 0, 1
Let t(a) be the first derivative of a**3/3 - 7*a**2/2 + 13*a - 9. Let f be t(5). Factor -2*j**f + 0*j**3 + 0*j**3.
-2*j**3
Let i be ((-7)/(-441))/(-7*(-7)/294). Let n(c) = -c**3 + 21*c**2 + 20*c + 44. Let h be n(22). Factor -i*x**2 + 0 + h*x + 2/21*x**4 - 2/21*x**3 + 2/21*x**5.
2*x**2*(x - 1)*(x + 1)**2/21
Let p(g) be the first derivative of -g**5/12 + 5*g**4/8 + 7*g**2 + 5*g + 86. Let v(u) be the second derivative of p(u). Factor v(b).
-5*b*(b - 3)
Let x(y) = -3*y**2 + 4*y + 1. Let a = -3 - -7. Let n(f) = 21*f + 2917*f**2 - 5840*f**2 + 4 + 2907*f**2. Let l(r) = a*n(r) - 22*x(r). Solve l(i) = 0.
-1, 3
Let k(a) be the second derivative of 1/4*a**5 + 14*a - 35/6*a**3 - 1 + 10*a**2 + 5/6*a**4. Factor k(f).
5*(f - 1)**2*(f + 4)
Suppose -9*a = -74 + 47. Suppose 15*k = 16*k + a*y - 3, -2*k - 2*y = -2. Determine w so that k*w - 2/17 + 2/17*w**2 = 0.
-1, 1
Solve -2576/9 - 10316/9*c**3 - 15464/9*c**2 - 2/9*c**5 - 10306/9*c - 2584/9*c**4 = 0.
-1288, -1
Factor 417/4 - 3/4*k**2 - 207/2*k.
-3*(k - 1)*(k + 139)/4
Let q be (3 + -2)/(1/5). Suppose 30 = 5*r + m, 0 = 5*m - 1014 + 964. Suppose -5/2 - 5/2*n**r + 0*n + q*n**2 + 0*n**3 = 0. Calculate n.
-1, 1
Let b(m) be the first derivative of m**7/10080 - m**6/216 - 7*m**5/480 - 56*m**3 + 160. Let d(v) be the third derivative of b(v). Factor 