 - 5/4*n**3 + 1 + 3/40*n**5. Factor u(z).
3*(z - 3)*(z + 1)**2/2
Let d(g) be the second derivative of -1/90*g**5 - 5*g + 6 + 0*g**3 - 4/27*g**4 + 0*g**2. Solve d(m) = 0.
-8, 0
Let r(y) = 8*y**3 - 39*y**2 - 122*y - 65. Let v(a) = a**3 + 3*a**2 - a - 1. Let s(t) = -r(t) + 5*v(t). Factor s(p).
-3*(p - 20)*(p + 1)**2
Let y(n) = -n**3 - n**2 - n - 17. Let p(r) = -r**3 - 2131*r**2 - 378070*r + 380242. Let c(o) = p(o) + 2*y(o). Solve c(x) = 0 for x.
-356, 1
Let i be 231/42*96/(-440)*(-90)/42. Find b such that -2/7*b**3 - i*b**2 - 40/7*b + 0 = 0.
-5, -4, 0
Let w = 67873 - 339364/5. Factor 0 + w*q**4 + 0*q - 4/5*q**2 + 3/5*q**3.
q**2*(q - 1)*(q + 4)/5
Suppose -5*v = -9*g - 39, 0 = -4*v + 33*g - 31*g + 26. Suppose -1/5*c**2 - 45 + v*c = 0. Calculate c.
15
Factor -123*d**2 - 689*d**2 + 755*d - 607*d**2 + 2076 + 3*d**3 + 277*d + 378*d**2.
3*(d - 346)*(d - 2)*(d + 1)
Let v(h) be the second derivative of 0*h**2 - 1/27*h**3 - 1/15*h**5 + 2/27*h**4 + 0 + 4/135*h**6 + 123*h - 1/189*h**7. Factor v(f).
-2*f*(f - 1)**4/9
Let r = 46265 - 46263. Factor 0*y + 4/7*y**5 + 0 + 0*y**r + 16/7*y**4 - 20/7*y**3.
4*y**3*(y - 1)*(y + 5)/7
Let g(l) be the first derivative of -2/27*l**3 - 46 - 20/9*l - 11/9*l**2. What is u in g(u) = 0?
-10, -1
Factor -2*m**2 + 1/2*m**5 + 0*m + 0 - 5/2*m**4 + 4*m**3.
m**2*(m - 2)**2*(m - 1)/2
Let w(t) be the first derivative of -145 - 1/50*t**5 + 1/5*t**3 - 1/10*t**4 - 1/2*t + 1/5*t**2. Let w(o) = 0. What is o?
-5, -1, 1
What is b in -528/7*b**2 - 88/7*b**3 - 52 - 4/7*b**4 - 808/7*b = 0?
-13, -7, -1
Let y = 54616 - 54613. Factor 3/2*k**y + 27/2*k**2 - 75/2 + 45/2*k.
3*(k - 1)*(k + 5)**2/2
Let u = -22 - -25. Suppose 2*d = 2*s + 6*d, -5*s + 3*d + 13 = 0. Factor 34*p**3 - 12*p + 40*p**s + 32*p + 0*p**4 - 9*p**u + 5*p**4.
5*p*(p + 1)*(p + 2)**2
Factor 277549*u**2 - 277544*u**2 - 175*u + 4 - 4.
5*u*(u - 35)
Let j be 0 - (2/5)/((1792/(-1645))/16). Let m = -37 + 39. Let 49/8*l**4 - j*l**m + 2 - 21/4*l**3 + 3*l = 0. What is l?
-4/7, 1
Let y(u) = 2*u**3 - u - 1. Let i(k) = 24*k**3 + 146*k**2 + 1299*k + 3139. Let j(c) = -2*i(c) + 22*y(c). Factor j(x).
-4*(x + 5)**2*(x + 63)
Let y(w) be the second derivative of -w**6/2 - 57*w**5/20 + w**4 + 1077*w. Solve y(x) = 0 for x.
-4, 0, 1/5
Let s be -54 + 125 + 2622/(-38). Suppose 12/11*h - 80/11 + 2/11*h**s = 0. What is h?
-10, 4
Let b be 33 - -84*29/(-87). Let 2/3*n**b + 4/3*n**3 - 2*n + 2/3 - 2*n**4 + 4/3*n**2 = 0. What is n?
-1, 1
Suppose -565*k**2 - 17*k**4 + 1081*k**2 - 8*k - 154*k**3 - 588*k**2 - 31*k**4 - 12*k**4 = 0. What is k?
-2, -2/5, -1/6, 0
Let n(b) be the first derivative of -52*b**3/3 - 68*b**2 - 84*b + 2150. Determine o so that n(o) = 0.
-21/13, -1
Let o(f) = -5*f**4 + 62*f**3 - 14*f**2 - 63*f + 18. Let h(b) = -b**4 + b + 2. Let r(v) = -h(v) - o(v). Solve r(m) = 0.
-1, 1/3, 1, 10
Let k(b) = -b**3 + 66*b**2 - 128*b + 9. Let v(g) = 16*g**2 - 32*g + 2. Let h(l) = 2*k(l) - 9*v(l). Factor h(y).
-2*y*(y - 2)*(y + 8)
Let s = 120389 - 120380. Solve -1/3*b**2 - s*b - 26/3 = 0 for b.
-26, -1
What is o in 21*o**3 - 155/3*o**2 + 1/6*o**5 + 107/2*o - 7/2*o**4 - 39/2 = 0?
1, 3, 13
Let g(p) = -269*p - 53. Let u be g(-8). Factor 2102*m**4 + 6*m**2 - 3*m**2 - 6*m**3 - u*m**4.
3*m**2*(m - 1)**2
Let 7*j - 7*j + 12*j + j**2 - j = 0. Calculate j.
-11, 0
Let g(d) be the third derivative of d**7/7980 - d**6/1140 + d**5/570 + 11*d**3 + 124*d**2. Let y(v) be the first derivative of g(v). Let y(i) = 0. Calculate i.
0, 1, 2
Suppose -4*g + 35 = 100*t - 97*t, 4*g - 26 = -2*t. Factor 0 - 1/2*j - j**g - 1/2*j**3.
-j*(j + 1)**2/2
Let v be ((-66)/(-154))/((-3)/(-2 + 17) - (-3492)/1260). Let v*o**3 - 1/6*o - 1/3 - 1/6*o**4 + 1/2*o**2 = 0. Calculate o.
-1, 1, 2
Let s(l) = -l**2 - 1710*l + 626202. Let m be s(310). Factor -1/3*z**m - 34/3*z - 11.
-(z + 1)*(z + 33)/3
Let u(n) be the third derivative of -n**6/40 + 43*n**5/10 - 85*n**4/8 - 10*n**2 + 36*n. Factor u(j).
-3*j*(j - 85)*(j - 1)
Let l(x) be the third derivative of -x**6/300 + 11*x**5/150 - 2*x**4/5 - 545*x**2. Factor l(u).
-2*u*(u - 8)*(u - 3)/5
Let q be (12/(-4))/((-8)/304*6). Let s(y) be the second derivative of 0 - 4/27*y**3 - 2/27*y**4 - 1/9*y**2 - q*y. Determine f, given that s(f) = 0.
-1/2
Suppose -43*f + 52*f = 27. Factor 4*i**2 - 8 + 3*i + f*i - 3*i + i.
4*(i - 1)*(i + 2)
Let h(j) be the first derivative of j**4/16 + 39*j**3/4 - 481*j**2/8 + 363*j/4 + 546. What is o in h(o) = 0?
-121, 1, 3
Let q(v) be the third derivative of v**8/1176 + 8*v**7/735 + 2*v**6/35 + 16*v**5/105 + 4*v**4/21 - 3783*v**2. Factor q(u).
2*u*(u + 2)**4/7
Let h be (-6 - -9)/(-36) + 2 + 15/(-12). Let g(a) be the first derivative of 3 - a**2 + h*a**3 - 2/5*a**5 + 0*a + 1/2*a**4. Factor g(f).
-2*f*(f - 1)**2*(f + 1)
Suppose 907 - 41458 = -7*z. Solve 697*x**2 + 2528*x**3 + 491*x + 121*x + 5849 - 192*x**4 - z + 1499*x**2 = 0.
-1/3, -1/4, 14
Let d(a) be the third derivative of 1/90*a**5 + 78*a**2 + 0 + 0*a - 7/36*a**4 + 10/9*a**3. Factor d(x).
2*(x - 5)*(x - 2)/3
Solve 31106*o - 31666*o - 18*o**2 - 112 - 37*o**2 + 12 = 0 for o.
-10, -2/11
Let a(d) be the first derivative of -7*d**3 - 1/45*d**5 - 1/540*d**6 + 0*d - 1/12*d**4 + 0*d**2 - 21. Let h(b) be the third derivative of a(b). Factor h(g).
-2*(g + 1)*(g + 3)/3
Suppose -2*j = -3*a - 28 + 29, 2*a - 2 = j. Let n(m) be the third derivative of -13/90*m**5 + 0 - 1/30*m**6 - 1/9*m**a + 0*m - 11*m**2 - 2/9*m**4. Factor n(u).
-2*(u + 1)**2*(6*u + 1)/3
Let g be 16/102*4335/3060. Factor 4/9*y**3 + 0*y**2 - 2/9 + g*y**4 - 4/9*y.
2*(y - 1)*(y + 1)**3/9
Let m(u) be the second derivative of u**4/84 + 7*u**3/6 - 106*u**2/7 - 16*u - 107. Determine v so that m(v) = 0.
-53, 4
Let z(q) be the third derivative of q**6/1380 - 11*q**5/230 + 121*q**4/92 - 1331*q**3/69 + 2818*q**2. Let z(u) = 0. Calculate u.
11
Let h(m) = 5*m**2 + 49*m + 98. Let c(x) = 21*x**2 + 195*x + 396. Let z(d) = 2*c(d) - 9*h(d). Factor z(t).
-3*(t + 2)*(t + 15)
Let w(c) be the first derivative of c**3/5 + 181*c**2/10 - 122*c/5 - 51. Find r, given that w(r) = 0.
-61, 2/3
Let i(l) = 2*l**2 - 5*l - 3. Let r be i(4). Suppose 6*c - r*c = -4*c. Factor 4/17*g**2 + c + 0*g - 6/17*g**3 + 2/17*g**4.
2*g**2*(g - 2)*(g - 1)/17
Let u(j) = -8*j**2 - 80*j - 195. Let d(h) = -12*h**2 - 120*h - 292. Let l be (-16 - -16)/(0 + 1) + 5. Let p = -28 + 20. Let y(o) = l*d(o) + p*u(o). Factor y(x).
4*(x + 5)**2
Let h(s) be the first derivative of -1/4*s**6 - 11/5*s**5 - 62 - 7*s**4 + 16*s + 4*s**2 - 8*s**3. Determine t so that h(t) = 0.
-2, 2/3
Suppose 2*v + 4*n + 4 = 0, 2*v - 16 = 4*n + 4. Factor 38*t - 4*t**4 + 4*t**2 + 8*t**3 - 54*t + 8*t**3 + 0*t**v.
-4*t*(t - 4)*(t - 1)*(t + 1)
Factor 712*f**3 + 38831*f**2 - 2295*f**2 + 11116*f**2 + 27*f**4 + 16422*f**2 - 25*f**4 + 125316*f.
2*f*(f + 2)*(f + 177)**2
Let b(p) = p - 12. Let u(a) = 2*a - 23. Let g(h) = -11*b(h) + 6*u(h). Let n be g(19). Factor -8*r + 31*r + 18*r**2 + 35 - 11 + 3*r**3 + n*r.
3*(r + 2)**3
Find d such that -5*d**2 + 55*d**3 + 267*d - 105*d + 5*d**4 - 217*d = 0.
-11, -1, 0, 1
Let j(v) be the second derivative of -v**5/20 + 13*v**4/2 - 76*v**3/3 - 5382*v. Factor j(c).
-c*(c - 76)*(c - 2)
Let m = 551 - 546. Suppose 2*n - 4*n = m*n. Solve n + 0*q - 1/4*q**5 - 1/4*q**3 + 1/2*q**4 + 0*q**2 = 0 for q.
0, 1
Let r(g) be the first derivative of -g**6/9 - 16*g**5/5 - 199*g**4/6 - 416*g**3/3 - 448*g**2/3 + 942. Determine m so that r(m) = 0.
-8, -7, -1, 0
Let u(y) be the first derivative of -y**4/6 - 8*y**3/3 + 405. Find k such that u(k) = 0.
-12, 0
Let b(z) be the first derivative of -z**3/6 + 53*z**2/4 + 27*z + 430. Factor b(o).
-(o - 54)*(o + 1)/2
Suppose 0 = -2*i + 14*i - 24. Let 13*y**2 + 8*y**2 + 22*y + i*y**3 - 12 - 33*y**2 = 0. What is y?
1, 2, 3
Let w(k) be the second derivative of 6*k**2 + 3/2*k**4 - 13/3*k**3 - 1/5*k**5 + 0 - 100*k. Factor w(i).
-2*(i - 2)*(i - 1)*(2*i - 3)
Factor 22*l + 1499*l**3 - 680*l**4 - 8*l**3 - 530*l**4 - 17*l**3 - 8*l + 298*l**2.
-2*l*(5*l - 7)*(11*l + 1)**2
Let s = 5323/7998 + 3/2666. Solve -4/3*v**4 - 5/3*v + s*v**2 + 2/3 + 1/3*v**5 + 4/3*v**3 = 0.
-1, 1, 2
Let z(s) be the first derivative of 4*s**5/5 + 246*s**4 + 59524*s**3/3 - 61008*s**2 + 61504*s + 435. Find c, given that z(c) = 0.
-124, 1
Suppose -9 = 4*q - 9, -60 = -6*w + 2*q. Let j(p) be the first derivative of -2/3*p - 1/9*p**3 + w + 1/2*p**2. Suppose j(m) = 0. Calculate m.