
Let g = -14585497/17 - -857971. Solve g*b + 2/17*b**2 + 12/17 = 0.
-3, -2
Suppose 8354*r + 1614 = 8352*r. Let i = -803 - r. Factor 0*h + 3/4*h**i + 0*h**2 + 0 + 3*h**3.
3*h**3*(h + 4)/4
Let m(j) = j**3 - 20*j**2 - 23*j - 6. Let a be m(21). Let v = a - -53. Factor 20*p**2 - 22*p + 13*p + v*p**3 + 4 - 46*p + 26.
5*(p - 1)**2*(p + 6)
Let u(a) be the first derivative of -62 - 1/4*a**4 + 1/6*a**6 + 1/5*a**5 + 0*a**2 - 1/3*a**3 + 0*a. Let u(p) = 0. Calculate p.
-1, 0, 1
Let k = 87 + -85. What is c in 23*c + 13*c + 88 + 842*c**k + 840*c**2 - 1686*c**2 = 0?
-2, 11
Factor 0 + 78/5*v - 41/5*v**2 + 1/5*v**3.
v*(v - 39)*(v - 2)/5
Let j(y) = -y**4 - 2*y**3 + y**2 - 2*y. Let n(x) = 115*x**4 - 46940*x**3 - 97535*x**2 + 60*x + 12580. Let b(l) = 40*j(l) + n(l). Solve b(d) = 0 for d.
-2, -2/5, 1/3, 629
Let c(b) be the first derivative of -509/7*b**4 - 1/21*b**6 - 68 - 134/35*b**5 + 6932/21*b**3 + 350*b - 515*b**2. Suppose c(n) = 0. Calculate n.
-35, 1
Let w be (-24)/(-12)*5/2. Let s(t) = 7*t**3 + 3*t**2 - 10*t. Let g(f) = 26173 + f - 26173 - f**2. Let v(i) = w*s(i) + 40*g(i). Factor v(x).
5*x*(x - 1)*(7*x + 2)
Let z(r) be the third derivative of -23*r**4/24 - 45*r**3/2 - 20*r**2. Let t be z(-6). Let -2*l**t + 2/3*l**2 + 2*l - 4/3 + 2/3*l**4 = 0. Calculate l.
-1, 1, 2
Let j be ((2 + 8)/((-164)/(-123)) - 7)*7. Factor 4*d**2 + j*d**3 + 0 - 2*d - 5/2*d**4.
-d*(d - 2)*(d + 1)*(5*d - 2)/2
Solve -608*h + 118*h + 4104 - 675*h + 4*h**2 - 1131*h + 236*h = 0.
2, 513
Let m = -496 - -824. Let v = m + -328. Factor v*k + 0 - 1/5*k**4 + 1/5*k**2 + 0*k**3.
-k**2*(k - 1)*(k + 1)/5
Determine r so that 83*r**2 + 10*r**3 - 8*r**2 - 180*r + 1152 - 5*r**4 - 1152 = 0.
-4, 0, 3
Suppose -13 = -4*l - 5*q, -3*l - 28*q + 22*q + 12 = 0. Factor 0 - 2/3*g - 2/3*g**3 - 4/3*g**l.
-2*g*(g + 1)**2/3
Let -26 + 99/4*m - 24*m**4 + 835/2*m**2 + 4*m**5 - 1585/4*m**3 = 0. What is m?
-8, -1/4, 1/4, 1, 13
Find c, given that -39/2*c**2 - 93*c - 60 = 0.
-4, -10/13
Let p be 37/6 - 4/24. Suppose 0 = -o - 4 + p. Determine t, given that 0*t**2 - 13*t**2 - 3*t**3 + 4*t**o = 0.
-3, 0
Suppose 2*u - 3*j - 332 = 0, 16*u + 3*j = 19*u - 498. Let h = 9160 + -2753. Factor 50 - n**4 - 90*n**2 + u + h*n**3 - 6424*n**3 - 108*n.
-(n - 1)*(n + 6)**3
Let i = 744029/6 + -248009/2. Find z, given that -11*z - 6*z**2 - 16/3 - i*z**3 = 0.
-16, -1
Factor 0 + 62/3*v**3 + 16/3*v**2 + 0*v - 8/3*v**4.
-2*v**2*(v - 8)*(4*v + 1)/3
Suppose 0 = -85*n + 86*n + 4*j - 37, -115 = n - 15*j. Suppose 0 = 5*h - 19 + 4. Let -6/7*o**4 + 0 + 3/7*o**n + 0*o**h + 0*o + 0*o**2 = 0. What is o?
0, 2
Let c(z) be the third derivative of z**7/35 + 371*z**6/60 - 877*z**5/30 + 629*z**4/12 - 42*z**3 - 579*z**2. Suppose c(p) = 0. Calculate p.
-126, 1/3, 1
Let g(w) be the third derivative of -1/100*w**5 + 1/600*w**6 + 0*w + 11*w**2 + 13/6*w**3 + 1/40*w**4 + 0. Let j(l) be the first derivative of g(l). Factor j(x).
3*(x - 1)**2/5
Suppose 15 = 2*q + w, 0 = q + 3*w - 28 - 7. Determine k so that 0*k**3 + 0 + 2/7*k**q + 0*k - 2/7*k**4 = 0.
-1, 0, 1
Factor -144/7 - 4/7*u**2 - 50/7*u.
-2*(u + 8)*(2*u + 9)/7
Let j(m) = -20*m + 3. Let q be j(0). Find d such that 7*d**2 - 8*d**3 - 6*d**q - 13*d**3 - 14*d**3 + 40*d**3 = 0.
0, 7
Let d(c) be the second derivative of -c**6/180 + 7*c**5/90 - 11*c**4/36 + 5*c**3/9 + 25*c**2 + 11*c. Let a(s) be the first derivative of d(s). Factor a(m).
-2*(m - 5)*(m - 1)**2/3
Let y(t) be the first derivative of t**3/15 - 11*t**2 + 216*t/5 - 4001. Suppose y(c) = 0. What is c?
2, 108
Let x = -894030 + 894031. Factor 5/3*l**2 + 1/3*l**3 + 7/3*l + x.
(l + 1)**2*(l + 3)/3
Let r(l) = -4*l**3 - 396*l**2 - 7*l + 70. Let h(k) = 3*k**3 + 393*k**2 + 6*k - 60. Let g(u) = -7*h(u) - 6*r(u). Factor g(d).
3*d**2*(d - 125)
Let v(c) = -5*c**2 - 16*c - 43. Let i(n) = -n**2 + 4*n - 3. Let z(s) = -12*i(s) + 3*v(s). Let z(a) = 0. Calculate a.
-31, -1
Suppose -40 = -7*r + 30. Suppose r*p + 3*p - 65 = 0. Find x such that -1/11*x**4 + 1/11*x - 2/11*x**3 + 2/11*x**2 - 1/11 + 1/11*x**p = 0.
-1, 1
Let n(w) be the first derivative of 4*w**3/3 + 7088*w**2 + 12559936*w - 5927. Factor n(v).
4*(v + 1772)**2
Let p be (-421)/421 + (-7)/(-5). Factor -p*i**3 - 2*i**2 + 0 + 28/5*i.
-2*i*(i - 2)*(i + 7)/5
Factor 145*n + 210 + 9*n - 97*n + 0*n**2 + 3*n**2.
3*(n + 5)*(n + 14)
Let s(c) = -4*c**2 + 4*c + 2. Let t(n) = 3*n**2 - 5*n - 3. Suppose 0 = -p - p + 5*f - 8, f = -4*p - 38. Let h = p + 15. Let a(b) = h*t(b) + 5*s(b). Factor a(l).
-2*(l + 1)*(l + 4)
Let h be (-52)/(-78)*(-5 + 2). Let m be h*(-1)/(-13) + 12/78. Determine w so that -8/11*w - 26/11*w**3 - 2/11*w**5 + 12/11*w**4 + m + 24/11*w**2 = 0.
0, 1, 2
Let x(n) be the third derivative of -13*n**7/42 - 15*n**6/8 - 19*n**5/4 - 155*n**4/24 - 5*n**3 + 6*n**2 - 36*n. Factor x(h).
-5*(h + 1)**3*(13*h + 6)
Suppose 339*g**2 + 174240*g - 3733*g**3 + 1110*g**2 + 3736*g**3 - 175692 = 0. Calculate g.
-242, 1
Let u = -5656 + 5662. Let p(i) be the second derivative of -3/8*i**5 - i**3 + i**4 + 0 + 1/20*i**u + 5*i + 0*i**2. Factor p(w).
3*w*(w - 2)**2*(w - 1)/2
Let h = 261 + -255. Let -2*n**4 + 16*n**5 - h*n**2 + 16*n**2 + 22*n**4 - 11*n**5 + 25*n**3 = 0. Calculate n.
-2, -1, 0
Let n(v) be the first derivative of -1/8*v**4 + 0*v + v**2 + 1/3*v**3 - 40 - 1/20*v**5. Factor n(w).
-w*(w - 2)*(w + 2)**2/4
Let l(z) be the first derivative of -6*z**4/11 - 4190*z**3/11 - 822156*z**2/11 + 411864*z/11 - 1418. Factor l(p).
-6*(p + 262)**2*(4*p - 1)/11
Let m(l) be the third derivative of 4*l**7/21 + 7*l**6/12 + l**5/4 - 5*l**4/6 - 5*l**3/6 + 10*l**2 + 7*l. Suppose m(c) = 0. What is c?
-1, -1/4, 1/2
Suppose -22*v - 141 = 57. Let x(k) = 24*k**2 + 274*k + 42. Let a(h) = 51*h**2 + 547*h + 83. Let o(t) = v*x(t) + 4*a(t). Factor o(w).
-2*(w + 23)*(6*w + 1)
Let y = -2 + 18. Let t(b) = 6*b - 22. Let g be t(y). Factor -3*a + a**2 - g + 74.
a*(a - 3)
Let b(z) be the third derivative of z**6/240 + 23*z**5/40 - 35*z**4/24 + 2*z**2 - 4*z + 9. Factor b(v).
v*(v - 1)*(v + 70)/2
Let y = 48588523/134176141 + -2938/16417. Let v = -1/743 + y. Factor -6/11 + 10/11*g - v*g**3 - 2/11*g**2.
-2*(g - 1)**2*(g + 3)/11
Let a(x) = 6*x**2 + 6*x + 4. Let p(y) = y**2 - 1. Let f(w) = 4*w - 38. Let d be f(17). Suppose 3*j = -0*j + d. Let k(c) = j*p(c) - 2*a(c). Factor k(h).
-2*(h + 3)**2
Factor 124*y**3 - 67*y**4 - 192*y**3 + 69*y**4 + 130*y**2 - 64*y.
2*y*(y - 32)*(y - 1)**2
Let q(r) be the third derivative of -r**7/70 + 47*r**6/40 - 251*r**5/20 + 205*r**4/8 - 4*r**2 + 79*r + 6. What is g in q(g) = 0?
0, 1, 5, 41
Factor 96*f - 105/2*f**2 + 18.
-3*(f - 2)*(35*f + 6)/2
Let m = 8361730/9 - 929080. Let -m*k**4 + 16/3 - 164/9*k**2 - 86/9*k**3 - 40/9*k = 0. What is k?
-6, -2, -1, 2/5
Let a(t) be the second derivative of -1/36*t**5 - 8/9*t**4 + 3/2*t**3 - 235*t + 0 + 10/9*t**2. Determine x so that a(x) = 0.
-20, -1/5, 1
Factor -3/5*s**2 - 1278/5 - 231/5*s.
-3*(s + 6)*(s + 71)/5
Let u = 350 + -350. Let d(z) be the first derivative of z**5 + 0*z**2 + 15*z**3 + u*z + 15/2*z**4 + 14. Factor d(a).
5*a**2*(a + 3)**2
Let i be 1 + ((-5202)/(-10))/9. Let h be -1*(-45)/27*3. Solve -116/5*b**2 + i*b**h + 152/15*b - 334/15*b**3 + 1064/15*b**4 - 16/15 = 0.
-1, 2/9, 2/7
Suppose -1973*q = -589*q. What is a in 0 - 9/7*a**2 + 12/7*a**4 + 3/7*a**3 + q*a = 0?
-1, 0, 3/4
Let u(p) = 11*p - 113. Let w be u(-22). Let i = -1063/3 - w. Let 16/3*x - 32/3 - i*x**2 = 0. Calculate x.
4
Let z(i) be the first derivative of i**4/4 + 22*i**3 + 189*i**2/2 - 2141. Determine v, given that z(v) = 0.
-63, -3, 0
Suppose 11*l - 50 = -14*l. Factor -15 - 126*r + 5*r**2 - l*r**2 + 138*r.
3*(r - 1)*(r + 5)
Factor -783363/4 - 3/4*q**2 - 1533/2*q.
-3*(q + 511)**2/4
Suppose -3*s = -0*s - 105. Let c = s - 33. Suppose -1 - 4*n + 82*n**c - 7 - 78*n**2 = 0. What is n?
-1, 2
Let i(g) be the third derivative of -g**6/2160 + g**5/72 - 25*g**4/144 + 85*g**3/6 - g**2 - 7. Let h(o) be the first derivative of i(o). Factor h(l).
-(l - 5)**2/6
Let k = 11110 - 11107. Let i(v) be the third derivative of 0*v**k + 0 + 1/300*v**5 + 0*v + 1/20*v**4 + 19*v**2. Factor i(b).
b*(b + 6)/5
Determine r, given that -3*r**2 - 63*r + 61*r - 306 + 88*r + 0*r**2 + 73*r = 0.
2, 51
Suppose 80/3*p**3 + 5104/3*p - 2/3*p**4 - 4114/3 - 356*p**2 = 0. Calculate p.
1, 11, 17
Solve 811538/3 + 2/3*x**2 - 2548/3*x = 0.
637
Let h be (-20989)/(-135942) - (-4)/326. Factor -2*u**2