 2
Let i(b) be the second derivative of 2*b**6/15 - 27*b**5/5 + 218*b**4/3 - 320*b**3 + 576*b**2 + 56*b + 8. What is a in i(a) = 0?
1, 2, 12
Let w(q) be the third derivative of 1/20*q**6 - 76 + 0*q**3 + 2*q**2 - 1/105*q**7 + 0*q**5 - 1/3*q**4 + 0*q. Solve w(c) = 0 for c.
-1, 0, 2
Let s be (2 + (-64)/20)/((-96)/320). Let p(u) be the first derivative of s*u**2 - 16*u - 10 - 1/3*u**3. Suppose p(h) = 0. Calculate h.
4
Solve 525625/6 + 1/6*a**2 + 725/3*a = 0 for a.
-725
Let l = -4/15913 - -15925/47739. Factor -1/3*d - l*d**2 + 2.
-(d - 2)*(d + 3)/3
Factor p**3 + 4*p**2 - 834*p + 62*p**2 + 8*p**3 + 70*p**2 - 648 + 77*p**2.
3*(p - 4)*(p + 27)*(3*p + 2)
Factor 17483632/5*b**3 - 54/5 - 763848/5*b**2 + 11124/5*b.
2*(206*b - 3)**3/5
Let t(l) be the first derivative of 5/4*l**4 - 165*l + 235/2*l**2 - 25*l**3 + 10. Let t(o) = 0. What is o?
1, 3, 11
Factor -92 + 99*y**4 - 9*y**3 + 168*y + 89*y**5 - 376*y**2 - 276*y**3 + 32*y**5 + 137*y**2 + 236.
(y + 1)**3*(11*y - 12)**2
Let t(p) = -27*p**2 - 71*p + 76. Let b(f) = -58 + 14*f + 97 - 54 + 5*f**2. Let g(x) = -22*b(x) - 4*t(x). Find c such that g(c) = 0.
-13, 1
Let y(k) = -3*k**3 - 5*k**2 - 2*k + 14. Let m be y(-3). What is a in m*a**2 + 22*a**2 + 78*a**2 + 5*a**4 + 120*a + 54*a**3 - 8*a**4 - 3*a**5 = 0?
-2, 0, 5
Let l(a) be the first derivative of a**5/6 + 119*a**4/8 - 197*a**3/6 - 505*a**2/12 + 73*a - 3052. Determine p so that l(p) = 0.
-73, -1, 3/5, 2
Let x(s) be the first derivative of -12*s**2 + 16*s + 3*s**3 - 3 - 1/4*s**4. Factor x(m).
-(m - 4)**2*(m - 1)
Let k(m) be the first derivative of -2*m**6/3 - 164*m**5/5 - 77*m**4 + 164*m**3/3 + 156*m**2 + 1779. Determine v so that k(v) = 0.
-39, -2, -1, 0, 1
Let m = -3987794893/1071 - -3723431. Let j = 2/153 - m. What is b in -2/7*b**4 + 0*b - j*b**2 + 0 - 4/7*b**3 = 0?
-1, 0
Let k(n) = 31*n**5 + 13*n**4 - 17*n**3 + 3*n**2. Let x(m) = -42*m**5 - 12*m**4 + 18*m**3 - 4*m**2. Let i(l) = -4*k(l) - 3*x(l). Factor i(j).
2*j**3*(j - 7)*(j - 1)
Let s(u) = 2*u**2 + 2*u - 2. Let k(p) = p**2 + p - 1. Let t(g) = 7*k(g) - 4*s(g). Let x(w) = 3*w + w + w. Let n(m) = 5*t(m) + x(m). Factor n(i).
-5*(i - 1)*(i + 1)
Let w(y) be the second derivative of y**6/10 - 57*y**5/20 + 24*y**4 - 22*y**3 - 240*y**2 + 4364*y. Suppose w(i) = 0. Calculate i.
-1, 2, 8, 10
Let h(t) = -3828*t**2 + 11476*t + 48. Let l(p) = -3828*p**2 + 11476*p + 56. Let f(w) = 4*h(w) - 3*l(w). Factor f(c).
-4*(c - 3)*(957*c + 2)
Let r(g) be the second derivative of -g**7/98 + 3*g**6/35 - 33*g**5/140 + g**4/14 + 6*g**3/7 - 12*g**2/7 + 2163*g. Suppose r(h) = 0. What is h?
-1, 1, 2
Let j(l) be the first derivative of l + 5/8*l**4 + 15/8*l**2 + 5/3*l**3 + 46 - 1/24*l**6 + 0*l**5. Suppose j(q) = 0. Calculate q.
-1, 4
Let k(g) = 4*g**3 + 4*g**2 - 148*g + 407. Let q(t) = t**3 - t**2 - t - 6. Let d(a) = 4*k(a) - 12*q(a). Determine c so that d(c) = 0.
-17, 5
Suppose -1/6*q**2 - 17/2*q + 110/3 = 0. What is q?
-55, 4
Let k be (-5 - 0/1)*(-772)/965. Let t(g) be the first derivative of 5/4*g**k + 135/2*g**2 - 135*g + 14 - 15*g**3. What is j in t(j) = 0?
3
Suppose 640/19 + 352/19*p - 246/19*p**2 - 2/19*p**4 + 40/19*p**3 = 0. Calculate p.
-1, 5, 8
Let y(p) be the first derivative of -p**4/4 - 5*p**3/3 - 9*p**2/2 - 7*p + 5. Let c be y(-6). Factor -480*h + 2 - 127*h**2 - h**3 - 162 - 24*h**3 - c*h**2.
-5*(h + 4)**2*(5*h + 2)
Let v(i) = -22*i + 6. Let f be v(0). Let 5*d**4 - d**3 + 44*d**2 - 42*d**2 - f*d**3 = 0. What is d?
0, 2/5, 1
Let i(p) be the first derivative of -p**6/360 + p**5/120 - 122*p**3/3 + 131. Let n(v) be the third derivative of i(v). Factor n(b).
-b*(b - 1)
Let -268*v**2 + 32986*v + 406*v**3 - 46*v**4 - 32938*v + 14*v**5 - 154*v**4 = 0. What is v?
0, 2/7, 1, 12
Let q(u) be the second derivative of -u**8/6720 - u**7/1260 + u**6/240 + 5*u**4/12 - 7*u**3/6 + 4*u. Let o(b) be the third derivative of q(b). Factor o(i).
-i*(i - 1)*(i + 3)
Let v be 1/(69/(-24) - (-27)/9). Factor -16*a + 8 - 17*a + 37*a - v*a**2 - 4*a**3.
-4*(a - 1)*(a + 1)*(a + 2)
Let o(z) be the third derivative of -z**9/60480 + z**8/1260 + z**7/5040 - z**6/45 - 29*z**5/20 + 45*z**2. Let p(n) be the third derivative of o(n). Factor p(s).
-(s - 16)*(s - 1)*(s + 1)
Suppose -1120765 + 1121305 = 90*r. Let 3/2*b**3 - 21/2*b**2 + 9/2*b**5 - r*b + 21/2*b**4 + 0 = 0. What is b?
-4/3, -1, 0, 1
Let t = 739 + -737. Factor -50*d**t - 59*d**3 + 6*d - d + 239*d**3 - 270*d**4 + 135*d**5.
5*d*(d - 1)*(3*d - 1)**3
Let d(k) = 20*k - 78. Let x be d(4). Factor -68*q**2 - 3*q + 36*q**x + 33*q**2 + q.
q*(q - 2)
Suppose 15*i - 27 = 12*i - 3*x, -3*x = 4*i - 31. Let w(q) be the second derivative of 1/54*q**i + 0 - 6*q + 5/9*q**2 + 2/9*q**3. Factor w(j).
2*(j + 1)*(j + 5)/9
Let w(i) = 2*i**3 + 72*i**2 - 388*i + 904. Let p be w(-41). What is n in 8/9*n**4 + 0 + 2/9*n**3 - 8/9*n**p - 2/9*n**5 + 0*n = 0?
-1, 0, 1, 4
Let x(y) be the third derivative of 2*y**2 - 1 + 0*y + 1/1020*y**6 + 0*y**4 + 2/85*y**5 - 256/51*y**3. Factor x(g).
2*(g - 4)*(g + 8)**2/17
Let b = 138 + -111. Factor -2*w + 0*w - b*w**2 + 63*w**2 - 2 - 24*w**2.
2*(2*w - 1)*(3*w + 1)
Let c(f) be the third derivative of 2*f**7/105 + f**6/15 - 79*f**5/15 + 110*f**4/3 + 2*f**2 + 18*f + 28. Factor c(v).
4*v*(v - 5)*(v - 4)*(v + 11)
Let u = 35845/17 - 107263/51. Factor -32/3*m**2 + 8/3*m**4 + 0 - 4/3*m**5 + 0*m + u*m**3.
-4*m**2*(m - 2)**2*(m + 2)/3
Let g(h) = 5*h**2 - 62*h + 57. Let d(x) = -x**2 + 2*x - 1. Suppose 22*o = 42*o - 120. Let p(m) = o*d(m) + g(m). Factor p(l).
-(l - 1)*(l + 51)
Let x = -3083 - -3085. Let q(c) be the third derivative of 0*c + 3/4*c**3 - 1/4*c**4 + 1/40*c**5 + 6*c**x + 0. Let q(g) = 0. What is g?
1, 3
Let f(h) be the third derivative of -2/9*h**3 + 0*h**4 + 1/360*h**6 + 40*h**2 + 1/60*h**5 + 0*h + 0. Factor f(v).
(v - 1)*(v + 2)**2/3
Let a(b) be the first derivative of b**3/12 - 129*b**2/4 - 2779. Factor a(i).
i*(i - 258)/4
Let d(t) be the third derivative of -13/240*t**5 - 1/240*t**6 + 1/168*t**7 + 0*t - 1/16*t**4 - 45*t**2 + 0*t**3 + 0. What is r in d(r) = 0?
-1, -3/5, 0, 2
Factor -586/3*f**3 + 195*f**2 + 0 + 0*f + 1/3*f**4.
f**2*(f - 585)*(f - 1)/3
Let t = -168165/7 - -168240/7. Solve 30/7*w - t - 3/7*w**2 = 0 for w.
5
Let o be -580*8/(-384) + -12. Let c(s) be the third derivative of -1/32*s**4 - 2*s**2 + 0 + 1/480*s**6 + 0*s + o*s**3 + 0*s**5. Factor c(z).
(z - 1)**2*(z + 2)/4
Suppose 140*q = 141*q - 12. Let l(x) be the second derivative of 0*x**2 + 0 + x**4 - q*x - 2/3*x**3. Find f such that l(f) = 0.
0, 1/3
Let m(s) be the first derivative of 192*s + 3/4*s**4 + 17*s**3 + 120*s**2 + 10. Factor m(b).
3*(b + 1)*(b + 8)**2
Let w = 1138 + -1138. Let s(p) be the second derivative of 0*p**2 + 1/6*p**6 + 1/4*p**5 + 0*p**3 - 9*p + w*p**4 + 0. Let s(l) = 0. Calculate l.
-1, 0
Let w(c) be the third derivative of -4/5*c**3 - 1/150*c**6 + 1/525*c**7 + 0*c + 3 + 7*c**2 + 1/3*c**4 - 7/150*c**5. Determine u so that w(u) = 0.
-3, 1, 2
Let m(j) = -79*j**2 - 98*j - 412. Let v(t) = -99*t**2 - 98*t - 413. Let z(h) = -5*m(h) + 4*v(h). Solve z(u) = 0.
-4, 102
Let n(v) be the first derivative of v**3/3 + 16*v**2 - 105*v + 2180. Find r such that n(r) = 0.
-35, 3
Let x be ((-840)/49 - -18)*28/6. Suppose 0 = -x*m + 37 - 29. Determine k, given that -2/17*k**m - 10/17*k - 12/17 = 0.
-3, -2
Let q be (-6)/(-36) - (-29)/6. Suppose -o = -3*f + 7, q*o - 4*f - 37 = -7*f. Factor 0*z**4 + 4*z**4 - 1 + o - 8*z**2.
4*(z - 1)**2*(z + 1)**2
Let p(t) be the second derivative of 0*t**3 + 3/8*t**4 + 0*t**2 - 67*t - 2 + 3/40*t**5. Determine y, given that p(y) = 0.
-3, 0
Let f(s) be the third derivative of -s**5/570 - 262*s**4/57 - 274576*s**3/57 + 1332*s**2. Find h, given that f(h) = 0.
-524
Let v(p) be the third derivative of -p**6/660 + 38*p**5/165 + 155*p**4/132 + 26*p**3/11 + p**2 - 31. Factor v(k).
-2*(k - 78)*(k + 1)**2/11
Let r(q) be the first derivative of -3*q**4/20 - 58*q**3/15 - 63*q**2/2 - 324*q/5 + 1532. Factor r(x).
-(x + 9)**2*(3*x + 4)/5
Let n(p) be the second derivative of p**8/2240 + p**7/280 + p**6/120 + 7*p**3/3 - p**2 + 16*p + 2. Let b(i) be the second derivative of n(i). Factor b(z).
3*z**2*(z + 2)**2/4
Suppose 0 = 165*p - 130*p. Let n(t) be the third derivative of 0*t**3 + p*t**5 + 0 + 1/600*t**6 + 0*t**4 + 0*t - 25*t**2. Factor n(y).
y**3/5
Let x(p) = 717*p**3 + 48*p**2 + 759*p + 708. Let q(w) = 2271*w**3 + 14