+ d*j**3 + 2/7*j.
2*j*(j - 1)**2/7
Factor 34/7*f + 2/7*f**2 + 0.
2*f*(f + 17)/7
Let r be -11 - (-161 - 4)/15. Let b(t) be the third derivative of 1/24*t**4 + 1/336*t**8 + 2*t**2 + 0 + 0*t**7 - 1/60*t**6 + 0*t**3 + 0*t**5 + r*t. Factor b(h).
h*(h - 1)**2*(h + 1)**2
Let r(w) be the first derivative of 3*w**4/20 - w**3 - 12*w**2/5 + 36*w/5 + 94. Factor r(g).
3*(g - 6)*(g - 1)*(g + 2)/5
Let k(x) be the third derivative of 0*x - 4/21*x**3 + 0 + 2/245*x**7 - 1/1176*x**8 - 1/105*x**5 - 104*x**2 + 3/28*x**4 - 2/105*x**6. Let k(i) = 0. Calculate i.
-1, 1, 4
Find m, given that 591*m + 273*m**2 + 912*m**2 + 9384*m**4 + 597*m**3 - 9381*m**4 = 0.
-197, -1, 0
Let s(u) be the first derivative of -3*u**4/4 - 189*u**3 - 279*u**2 + 1128*u + 2012. Factor s(w).
-3*(w - 1)*(w + 2)*(w + 188)
Suppose 3*y = -4*y + 35. Let k = y + -3. Determine z so that 4*z**k + 11*z**3 + 9*z**3 - 24*z**3 = 0.
0, 1
Let i be ((-16)/(-14))/(34/119). Let d be (1/(-4))/(i/(36/(-9))). What is z in 7/4*z - d - 3/2*z**2 = 0?
1/6, 1
Suppose -12*k - 17*k + 232 = 0. Suppose 9*n - 3 = k*n. Solve -2/3*r + 2/15*r**n - 2/5*r**2 + 2/15*r**4 - 4/15 = 0.
-1, 2
Let a(d) be the second derivative of 69*d**6/10 + 123*d**5/4 + 201*d**4/4 + 63*d**3/2 - 3*d**2 + 73*d - 7. What is v in a(v) = 0?
-1, 2/69
Suppose 0 = 4*m - 39 - 1. Let h be 15/m - (1 - (-3)/6). Factor 5/4*t**3 + h + 5/4*t + 5/2*t**2.
5*t*(t + 1)**2/4
Let w(y) = 2*y**2 + 38*y - 38. Let n be w(-20). Find b such that -10*b**2 + 720 + 26*b**n - b**2 - 10*b**2 - 120*b = 0.
12
Suppose 24 = -17*r + 92. What is s in 102 - 35*s**r + 65*s - 53 + 90*s**3 - 110*s**2 - 64 + 5*s**5 = 0?
1, 3
Let l(d) be the second derivative of -5*d**8/336 - 137*d**7/168 - 3*d**6/4 + 167*d**3/6 - 5*d + 8. Let x(v) be the second derivative of l(v). Solve x(k) = 0.
-27, -2/5, 0
Let k be (1 - 18/21)/((-95)/(-7030)). Factor -2/7*r**3 - 36/7 - 40/7*r**2 - k*r.
-2*(r + 1)**2*(r + 18)/7
Let x(m) be the second derivative of m**5/160 + 103*m**4/96 - 881*m**3/48 + 777*m**2/16 + 5520*m. Factor x(w).
(w - 7)*(w - 1)*(w + 111)/8
Let v(l) be the third derivative of 1/40*l**6 + 1/210*l**7 + 0*l + 2/3*l**3 - 25*l**2 - 1/8*l**4 - 1/12*l**5 + 2. Factor v(q).
(q - 1)**2*(q + 1)*(q + 4)
Let k(x) be the first derivative of 0*x**2 + 0*x - 1/18*x**6 - 1/15*x**5 + 1/12*x**4 - 63 + 1/9*x**3. Factor k(u).
-u**2*(u - 1)*(u + 1)**2/3
Suppose i + 754 = -l - l, 3*i + 5*l = -2257. Let d = i + 749. Factor -8/7*s**2 + 0 + 0*s + 4/7*s**d - 12/7*s**3 + 0*s**4.
4*s**2*(s - 2)*(s + 1)**2/7
Let l(q) be the second derivative of -q**4/24 - 59*q**3/12 - 57*q**2/2 + 1058*q. Solve l(b) = 0.
-57, -2
Suppose 48*t**2 + 2*t**4 - 4*t**4 - 4*t**3 + 68*t**3 - 8*t**4 - 6*t**5 + 4*t**3 = 0. What is t?
-4, -2/3, 0, 3
Let w be 716/418 + ((-14)/49)/((-1287)/819). Factor -w*p**2 + 40/19*p + 8/19*p**3 - 14/19 + 2/19*p**4.
2*(p - 1)**3*(p + 7)/19
Let c(a) be the third derivative of 1/120*a**6 - 8 + 1/15*a**5 - 8*a**2 + a**3 - 11/24*a**4 + 0*a. Factor c(h).
(h - 1)**2*(h + 6)
Let x = 35 - 32. Suppose y - 5*c = 6*y - 40, 4*y - 3*c = -x. Factor -6*f - 9*f**4 + 78*f**2 - 70*f**2 + 2*f**5 + f**4 + y*f**3 + f**3.
2*f*(f - 3)*(f - 1)**2*(f + 1)
Factor 114075/2 + 3/2*u**2 - 585*u.
3*(u - 195)**2/2
Let r(h) be the third derivative of -h**8/56 - 2*h**7/15 - 2*h**6/15 + 8*h**5/5 + 20*h**4/3 + 32*h**3/3 - 1033*h**2. Suppose r(g) = 0. Calculate g.
-2, -2/3, 2
Let x(k) = k**3 + 186*k**2 + 4023*k - 320. Let m be x(-161). Factor 0*j - 2/21*j**3 + 0 + 8/3*j**m.
-2*j**2*(j - 28)/21
Factor 316/7*j + 2/7*j**2 + 12482/7.
2*(j + 79)**2/7
Let w(f) be the second derivative of 0 + 32*f**2 - 8/3*f**3 - 105*f - 4/3*f**4 + 1/5*f**5. Factor w(a).
4*(a - 4)*(a - 2)*(a + 2)
Let m(w) be the first derivative of 3*w**4/4 + 27*w**3 + 243*w**2 + 5742. Factor m(u).
3*u*(u + 9)*(u + 18)
Let n be (2 - 0) + (6 - 2) + -4. Determine y so that -4*y**3 - 405 - 495*y - 16*y**n - 55*y**2 - 24*y**2 - y**3 = 0.
-9, -1
Let u be (-7378)/6 - (143/(-39) + 4). Let o = u - -1230. What is a in o - 9/8*a**3 - 1/8*a**5 - 1/4*a - 5/8*a**4 - 7/8*a**2 = 0?
-2, -1, 0
Suppose -t = -398 + 390. Factor s**4 - 4*s - 10*s**2 - 7*s**3 - 6 + 3*s**4 + s**5 + 14 + t*s**3.
(s - 1)**2*(s + 2)**3
Let n(m) = 5*m**2 - 563*m - 44. Let t(c) = c**2 - 112*c - 8. Let k(q) = -8*n(q) + 44*t(q). Suppose k(r) = 0. Calculate r.
0, 106
Factor -1/2*s**2 + 408 - 269/2*s.
-(s - 3)*(s + 272)/2
Let j be 21/56 + (-5)/((-80)/58). Factor 885*i**2 + 1537879 + 40581*i + 11634*i - 510984 + i**3 + j*i**3.
5*(i + 59)**3
Let n(x) be the third derivative of x**8/84 + 2*x**7/35 - x**6/6 - x**5/5 + 2*x**4/3 + 2*x**2 - 343*x. Determine q, given that n(q) = 0.
-4, -1, 0, 1
Factor -16/9*r**3 + 0*r + 10/9*r**4 - 2/9*r**5 + 8/9*r**2 + 0.
-2*r**2*(r - 2)**2*(r - 1)/9
Factor -207/2*o**2 + 42849/4*o + 1/4*o**3 + 0.
o*(o - 207)**2/4
Let s(i) = 1372*i - 115596. Let m(o) = -o**2 - 2747*o + 231191. Let d(c) = -4*m(c) - 9*s(c). Factor d(u).
4*(u - 170)**2
Let j be ((-11)/((-2288)/36))/((-1)/(-8828)). Let v = 1529 - j. Factor -v*l + 6/13 + 10/13*l**2 - 2/13*l**3.
-2*(l - 3)*(l - 1)**2/13
Let i(d) = -2*d**2 + d - 3. Let f(p) = -7*p**2 + 1486*p + 549069. Let n(j) = f(j) - 4*i(j). Let n(b) = 0. Calculate b.
-741
Let t(k) = -k + 6. Let s be t(1). Let z(u) be the second derivative of 5/42*u**7 + 5/6*u**6 + 0*u**2 + 9/4*u**s + 5/3*u**3 + 35/12*u**4 + 0 - 9*u. Factor z(n).
5*n*(n + 1)**3*(n + 2)
Let a(v) be the first derivative of v**4/5 - v**3/3 - 7*v**2/10 + 2*v/5 + 2035. Factor a(t).
(t - 2)*(t + 1)*(4*t - 1)/5
Let c(j) be the first derivative of 3*j**5 + 1413*j**4/4 + 11139*j**3 + 6627*j**2/2 + 4462. Solve c(o) = 0 for o.
-47, -1/5, 0
Suppose -27*i + 61 = 10 - 57. Let z(x) be the first derivative of -2/35*x**5 + 0*x**2 + 0*x - 6/7*x**i - 6 - 24/7*x**3. Factor z(t).
-2*t**2*(t + 6)**2/7
Let h be 348/30*((-817)/(-76) - 2). Let 92*o**2 + 49/2*o**4 + 24*o + 0 + h*o**3 = 0. What is o?
-3, -4/7, 0
Let c be 17/(-918)*18*(-9)/1. Let s(x) be the third derivative of 43*x**2 + 0 - 1/30*x**5 + 0*x + x**c + 1/6*x**4. Factor s(t).
-2*(t - 3)*(t + 1)
Let t(o) = 5*o**2 - 349*o + 28. Let n(f) = 6*f**2 - 348*f + 35. Let a(b) = -4*n(b) + 5*t(b). Factor a(q).
q*(q - 353)
Let s(f) be the second derivative of 54*f**7/7 + 132*f**6/5 - 1868*f**5/5 - 856*f**4/3 - 64*f**3 - 6230*f. Solve s(a) = 0 for a.
-6, -2/9, 0, 4
Let o(y) = y**3 - 6*y**2 - 73*y - 11. Let w be o(-6). Let i be 78*w/(-70) + (-25)/5. Factor 0*m**2 + 0*m**4 + 0 + 0*m - i*m**5 + 4/7*m**3.
-4*m**3*(m - 1)*(m + 1)/7
Let l = -197809/4 + 49456. Let 0 - 3/4*w**4 - 3*w**3 - 3/2*w - l*w**2 = 0. What is w?
-2, -1, 0
Let h = -381655 + 381657. Solve -23/2 - 1/2*n**h + 12*n = 0 for n.
1, 23
Factor 2/5*t**2 - 692/5 + 138*t.
2*(t - 1)*(t + 346)/5
Let k be (176/4)/(-2 - (-1 + 0)). Let x = -85/2 - k. Solve -x*q**2 - 9/2 - 3/2*q**3 + 15/2*q = 0.
-3, 1
Let i(w) = -1223*w + 116. Let a be i(-1). Let t be ((-36)/(-50))/(a/(-195) - -7). Solve -1/5*j**3 - 27/5*j - t - 9/5*j**2 = 0 for j.
-3
Factor -4020 + 147*r**2 - 4*r**3 - 5591*r + 416*r + 3*r**3 - 12855.
-(r - 75)**2*(r + 3)
Let x(p) = 4*p**2 - 11883*p + 8820906. Let s(t) = -8*t**2 + 23767*t - 17641814. Let h(g) = -3*s(g) - 7*x(g). Find q such that h(q) = 0.
1485
Let z = 3 - -19. Let c = 24 - z. Factor -11*a**c + a**2 + 5*a - 430 + 430.
-5*a*(2*a - 1)
Let i(d) be the third derivative of d**5/30 - 430*d**4/3 + 11158*d**2. Determine m so that i(m) = 0.
0, 1720
Let m(l) = l**2 - 15*l + 44. Let w be m(11). Suppose 5*t + 5 = -5*c, -16*t + 12*t - 4 = w. Suppose c*a**3 + 0 - 1/3*a**2 + 0*a + 1/3*a**4 = 0. What is a?
-1, 0, 1
Factor -12/5*s + 4/5*s**2 + 8/5.
4*(s - 2)*(s - 1)/5
Let f(o) be the third derivative of 9*o**6/40 - 193*o**5/5 + 16469*o**4/8 + 1849*o**3 - 9442*o**2. Determine r, given that f(r) = 0.
-2/9, 43
Suppose 0 = -792*b + 807*b. Suppose b = -6*i - 2*i + 10*i. What is c in 0*c**2 + 2/5*c**3 + i + 0*c = 0?
0
Let g be (40 - 20)*1/1. Suppose 6 = 13*a - g. Factor -2/11*z**3 + 4/11*z**a - 16/11 + 8/11*z.
-2*(z - 2)**2*(z + 2)/11
Let d = 4 + 20. Let b(o) = -11*o - d*o + 2*o - 4*o**2 - 37. Let m(c) = 2*c**2 + 16*c + 18. Let j(p) = 6*b(p) + 13*m(p). Factor j(g).
2*(g + 2)*(g + 3)
Let o(b) be the second derivative of -49/8*b**3 - 9 + 69/40*b**5 + b**6 + 3*b - 9/2*b**2 + 3/56*b**7 - 7/4*b**4. Let o(k) = 0. Calculate k.
-12, -1, -1/3, 1
Let z(q) be the third derivative of -2*q