d b such that j(b) = 0.
-4, 115
Let u(h) be the first derivative of 2/39*h**3 + 32/13*h + 8/13*h**2 + 22. Factor u(a).
2*(a + 4)**2/13
Let w(m) be the first derivative of -m**5/130 - 4*m**4/39 - 4*m**3/13 - 83*m + 66. Let z(o) be the first derivative of w(o). Factor z(x).
-2*x*(x + 2)*(x + 6)/13
Let p be (-112)/280 - (-34)/10. Find a such that -6*a**5 - 292*a**3 + 9*a**4 + 292*a**p = 0.
0, 3/2
Solve 128/3 + 113/3*n**3 + 112*n + 6*n**4 + 304/3*n**2 + 1/3*n**5 = 0 for n.
-8, -4, -1
Suppose -4*o - 3*s + 4*s = -336, -s = 0. Suppose -8*a - 4*a = -o. Factor -4*r - 4*r**2 + 11 + 4 - a.
-4*(r - 1)*(r + 2)
Let h be 9 + (-2272)/120 - (-10)/1. Let u(q) be the third derivative of 0 - h*q**5 + 0*q - 8/9*q**3 - 1/180*q**6 - 1/3*q**4 - 15*q**2. Factor u(x).
-2*(x + 2)**3/3
Let q(o) be the third derivative of -o**6/420 - 277*o**5/210 + o**4/84 + 277*o**3/21 - 28*o**2 - 2. Factor q(n).
-2*(n - 1)*(n + 1)*(n + 277)/7
Let b = -73 + 130. Suppose 0 = w + 54 - b. Factor 51*r**3 + 4 - 16*r - 4*r**2 + 0 - 35*r**w.
4*(r - 1)*(r + 1)*(4*r - 1)
Let o(r) be the third derivative of -r**8/840 - r**7/1575 + 13*r**6/150 - 34*r**5/75 + 38*r**4/45 + 910*r**2 - 2*r + 1. Factor o(h).
-2*h*(h - 2)**3*(3*h + 19)/15
Let w = -540125 - -1080871/2. Factor -w*i**2 - 529/2*i**3 - 48*i - 2.
-(i + 1)*(23*i + 2)**2/2
Let p be 47 - (15 + (-28 - -54)). Factor 3/2*v**4 + p*v**3 - 3/2*v**2 - 6*v + 0.
3*v*(v - 1)*(v + 1)*(v + 4)/2
Factor 111*h**2 - 154 + 301 - 2*h**3 - 141 - h**3 + 83*h + 3*h**4 - 40*h**4.
-(h - 2)*(h + 1)**2*(37*h + 3)
Let t(g) be the first derivative of -g**6/2700 - 17*g**5/900 + g**4/3 - 10*g**3 - 3*g**2/2 - 157. Let c(o) be the third derivative of t(o). Factor c(p).
-2*(p - 3)*(p + 20)/15
Let 9198/5*m**3 - 323433/5 + 291/5*m**4 - 49005*m + 87318/5*m**2 + 3/5*m**5 = 0. Calculate m.
-33, -1, 3
Let b(l) = -l**2 + 16*l + 31. Suppose 13*o = 15*o - 34. Let w be b(o). Factor 3*z**2 - 3*z**5 - w*z**3 - 10*z**4 + 5*z**5 + 7*z**2 - 8*z + 20*z**3.
2*z*(z - 4)*(z - 1)**2*(z + 1)
Let i(h) be the first derivative of 1/30*h**4 - 1/15*h**3 - 8*h - 2/5*h**2 - 18. Let z(c) be the first derivative of i(c). Suppose z(r) = 0. Calculate r.
-1, 2
Determine z so that 528/13 - 42/13*z**2 + 68/13*z - 2/13*z**3 = 0.
-22, -3, 4
Let t be 1/4 - (-337778)/(-184). Let y = t - -1836. Find l such that 12*l + y*l**2 + 72 = 0.
-12
Suppose 14 = -45*r + 194. Let m(d) be the first derivative of -3/14*d**2 + 0*d - 6/7*d**3 + 28 - 27/28*d**r. Factor m(u).
-3*u*(3*u + 1)**2/7
Factor 961 + 443 + 22*b**2 + 2*b**3 - 186*b - 35*b**2 - 7*b**2.
2*(b - 13)*(b - 6)*(b + 9)
Let f(r) be the second derivative of -r**8/3360 - 2*r**7/315 - 7*r**6/360 - 61*r**4/12 + 77*r. Let u(b) be the third derivative of f(b). Factor u(g).
-2*g*(g + 1)*(g + 7)
Suppose 128*f = 126*f + 10. Let h(r) be the third derivative of 0*r**4 - 1/12*r**f + 0*r**6 + 0*r**3 + 0*r + 5*r**2 + 0 + 1/42*r**7. Factor h(c).
5*c**2*(c - 1)*(c + 1)
Let r = -45/337 + 1191/1348. Factor 0*o + 3*o**4 - r*o**5 + 0*o**2 + 0 - 3*o**3.
-3*o**3*(o - 2)**2/4
Let d(c) be the second derivative of -10*c - 5/4*c**5 - 20*c**2 - 1/2*c**6 + 35/6*c**4 + 50/3*c**3 - 1. Find m, given that d(m) = 0.
-2, 1/3, 2
Let g be (-1267)/35 + (66 - 24). Find n, given that g*n**4 + 51/5*n**2 - 9/5*n - 67/5*n**3 + 0 - 4/5*n**5 = 0.
0, 1/4, 1, 3
Let j(q) be the third derivative of -q**7/350 - 119*q**6/50 - 28083*q**5/50 + 28441*q**4/10 - 57121*q**3/10 + 7*q**2 + 4*q + 85. Determine m so that j(m) = 0.
-239, 1
Suppose 2*z = z + 1, -w - 4*z = -37. Suppose 756 = w*p - 12*p. Factor -28 - 4/7*m**3 - 60/7*m**2 - p*m.
-4*(m + 1)*(m + 7)**2/7
Let r(t) be the third derivative of -t**7/60 + 29*t**6/240 + 73*t**5/120 + 31*t**4/48 - t**3/2 - 40*t**2 - 74. Solve r(m) = 0.
-1, 1/7, 6
Let y(z) be the third derivative of z**7/168 - 7*z**6/72 + z**5/2 - 41*z**3/6 + 87*z**2. Let n(i) be the first derivative of y(i). Determine k so that n(k) = 0.
0, 3, 4
Let j(r) = -r**3 - 55*r**2 - 10*r + 28. Let d be j(-55). Let m = -1155/2 + d. Factor -m*k**4 + 0 + 1/2*k**2 + 0*k**3 + 1/4*k - 1/4*k**5.
-k*(k - 1)*(k + 1)**3/4
Let f = 1359 - 939. Let o = f + -417. Determine q so that 87/4*q**o + 69/2*q - 189/4*q**2 - 6 - 3*q**4 = 0.
1/4, 1, 2, 4
Let c = -359110 + 359112. Find w such that 0 + 144/5*w + 2/5*w**c = 0.
-72, 0
Let t(p) be the third derivative of 1/12*p**4 + 1/210*p**5 + 14*p**2 + 10/21*p**3 + 0*p + 0. Factor t(j).
2*(j + 2)*(j + 5)/7
Suppose f + 26*f = -23*f + 20*f. Let 0*h - 3/5*h**5 + 9/5*h**3 + 0 + 6/5*h**2 + f*h**4 = 0. Calculate h.
-1, 0, 2
Factor -15*m**2 - 7/2*m**3 + 125/4 - 1/4*m**4 - 25/2*m.
-(m - 1)*(m + 5)**3/4
Let l = 12 + 18. Let x be 9/(-3) + l/6. Find h, given that -h - 1 + 101*h**x + 1 - 100*h**2 = 0.
0, 1
Determine z, given that -23883 + 4*z**5 + 23883 - 20*z**4 = 0.
0, 5
Let 0 + 728/9*y**3 - 110/9*y**2 + 4/9*y + 392/9*y**4 = 0. Calculate y.
-2, 0, 1/14
Determine a so that -4/9*a**3 + 0 - 8*a + 76/9*a**2 = 0.
0, 1, 18
Let t(k) be the first derivative of -5*k**3/3 + 11*k**2/2 - 2*k + 1245. Factor t(u).
-(u - 2)*(5*u - 1)
Let a be (-24)/(-84)*(-14)/(-4)*2. Let r(i) be the second derivative of -4*i**a - 1/4*i**5 - 10*i + 3/4*i**4 + i**3 + 0. Suppose r(q) = 0. What is q?
-1, 4/5, 2
Let l(t) be the first derivative of -5*t**3/3 - 265*t**2 - 525*t + 1938. Factor l(b).
-5*(b + 1)*(b + 105)
Let n(g) be the second derivative of g**5/240 + g**4/96 - g**3/12 + 67*g**2 + 118*g. Let x(z) be the first derivative of n(z). Find s, given that x(s) = 0.
-2, 1
Let p(r) be the third derivative of r**6/1260 - r**5/21 + 3*r**4/28 + 58*r**3/63 - 2*r**2 - 173. Factor p(s).
2*(s - 29)*(s - 2)*(s + 1)/21
Let 17 - 4 + 4 + 5 + 2 - 20*q + 4*q**2 = 0. What is q?
2, 3
Let l(i) be the first derivative of -147*i**5/20 + 7119*i**4/16 + 342*i**3 + 147*i**2/2 + 171. Factor l(g).
-3*g*(g - 49)*(7*g + 2)**2/4
Let x(a) = 14*a**2 + 16*a + 2. Let y be x(-3). Solve -169*s**2 + 226*s**3 - 35 - 55 + 99*s**2 - y*s**4 - 282*s + 8*s**5 = 0.
-1/2, 3, 5
Suppose 0 = 66*k - 65*k - 7. Suppose -k = -s + 4. Let 6*j**2 - 9*j**4 - 10*j**3 - s*j**3 + 24*j**4 = 0. What is j?
0, 2/5, 1
Determine x, given that 27/4 - 15/4*x**4 + 45/2*x - 51*x**2 + 51/2*x**3 = 0.
-1/5, 1, 3
Let h(o) be the third derivative of -o**6/180 + o**5/45 + 37*o**4/12 + 12*o**3 - 2072*o**2. Factor h(k).
-2*(k - 12)*(k + 1)*(k + 9)/3
Suppose -11*m + 135 - 113 = 0. Suppose -2*a - 4*a = -3*a. Determine q so that 0*q**m - 10/7*q**4 - 2/7*q**3 + 0 + a*q = 0.
-1/5, 0
Suppose t + 5 = -2*q + 1, t + 4 = -3*q. Suppose q = -4*w + 8. Factor 6 + 2*h**2 + h**2 + 0*h**w - 9*h.
3*(h - 2)*(h - 1)
Suppose -2 - 51183*k**4 + 51187*k**4 - 176*k**2 + 172*k**3 + 2 = 0. What is k?
-44, 0, 1
Suppose 11*l = 2*l. Suppose l*i = 2*i + i. Factor 6 + i*b**2 - 4*b**2 + 3 - 5.
-4*(b - 1)*(b + 1)
Suppose -323*b + 329*b + 780 = 0. Let v be 1/(3/10)*(-832)/b. Factor -256/3 - v*o - 4/3*o**2.
-4*(o + 8)**2/3
What is b in 2/7*b**4 + 12/7 + 2/7*b**3 - 2*b**2 - 2/7*b = 0?
-3, -1, 1, 2
Let h be (-53)/(18073/4030) - (-16 - -2) - 4/2. Let -288/11 + 26*r**2 + h*r**4 - 48/11*r**3 + 48/11*r = 0. Calculate r.
-1, 1, 12
Factor -34*q**2 - 28 + 1/4*q**5 + 1/4*q**4 - 8*q**3 - 52*q.
(q - 7)*(q + 2)**4/4
Let n = 4858229/11 - 441657. Find f, given that 2/11*f**3 - n*f**4 + 0 - 90/11*f + 42/11*f**2 = 0.
-5, 0, 3
Let v be 502/(-45)*57 - 0. Let s = v + 636. Factor s*d**2 + 0 - 2/15*d.
2*d*(d - 1)/15
Let n(p) be the third derivative of -p**6/300 + 11*p**5/75 + 571*p**4/60 - 592*p**3/15 + 3202*p**2. Find o, given that n(o) = 0.
-16, 1, 37
Let a(l) be the third derivative of -l**6/300 + 3*l**5/50 + 11*l**4/30 - 8*l**3 + 437*l**2. Factor a(s).
-2*(s - 10)*(s - 3)*(s + 4)/5
Let o be ((-1)/(-3))/((-19)/(-18)). Let c = -1821241/19 - -95855. Factor 0 + 2/19*s**2 - 10/19*s**4 - c*s**5 - o*s**3 + 2/19*s.
-2*s*(s + 1)**3*(2*s - 1)/19
Let a = 329758 + -659489/2. Factor 3/8*b**2 + a - 9/2*b.
3*(b - 6)**2/8
Let b(t) be the third derivative of -70/3*t**3 - 3*t**2 + 17/3*t**4 + 12*t + 0 + 1/15*t**5. Solve b(y) = 0.
-35, 1
Let p(m) be the third derivative of -m**6/24 + 10*m**5/3 + 1645*m**4/24 + 4*m**2 + 3*m - 79. Solve p(h) = 0.
-7, 0, 47
Let u be (-1169)/28 + (-6)/(-8). Let y = u + 57. Factor 128 + y*l - 4*l**2 - 128.
-4*l*(l - 4)
Let l(k) = -5*k - 8. Let n be (-85)/20 - -2*3/24. Let j be l(n). Let -13*r**4 + j*r**4 + 4*r**2 - 3*r**2 = 0. What is r?
-1, 0, 