)*(a + 1)/3
Let y(n) be the second derivative of n**6/135 - 5*n**5/9 - 17*n**4/18 - 256*n. Find v such that y(v) = 0.
-1, 0, 51
Let p(x) be the first derivative of -10*x**6 - 52*x**5/5 + 257*x**4 - 1036*x**3/3 + 60*x**2 + 701. Let p(d) = 0. What is d?
-5, 0, 2/15, 1, 3
Let u be 56/(-36)*375/(-175). Let l(w) be the first derivative of -2/3*w - 16 - 3*w**2 - u*w**3 + 25/6*w**4. Let l(s) = 0. What is s?
-1/5, 1
Let x(h) be the first derivative of 3*h**6/2 + 4*h**5 - 5*h**4/4 - 20*h**3/3 - 2*h**2 + 861. Find q, given that x(q) = 0.
-2, -1, -2/9, 0, 1
Suppose 0 = -1828*x + 1822*x + 6222. Let w = -1025 + x. Find h such that 9/2*h**5 - 27*h**2 - w*h**3 - 3 + 6*h**4 - 33/2*h = 0.
-1, -1/3, 2
Let j = -247821 - -247824. Factor 1/6 - 1/3*z**j + 5/6*z**2 - 2/3*z.
-(z - 1)**2*(2*z - 1)/6
Let b be (-37 - 1952/(-56))/(10/(-4)). Factor 0 + 2/7*i**3 + 4/7*i + b*i**2.
2*i*(i + 1)*(i + 2)/7
Let s(h) be the first derivative of 2*h**5/35 - 11*h**4/14 - 80*h**3/21 - 4*h**2 - 3469. Let s(r) = 0. Calculate r.
-2, -1, 0, 14
Suppose 2*p**3 - 128837285*p**2 + 128837301*p**2 - 32*p - 4*p**3 = 0. What is p?
0, 4
Suppose -58*n + 55*n + 1965 = 0. Let c be (20/(-6))/(n/(-393)). Find j such that 1/3*j**c - 1/6 - 1/3*j**3 + 1/6*j - 1/6*j**4 + 1/6*j**5 = 0.
-1, 1
Let d(o) be the first derivative of -16*o + 137 - 1/5*o**5 + 15/2*o**2 + 17/3*o**3 - 15/4*o**4. Factor d(s).
-(s - 1)**2*(s + 1)*(s + 16)
Let y(i) = 4*i**3 + 41*i**2 - 693*i - 700. Let c(s) = 4*s**3 + 42*s**2 - 694*s - 696. Let b(f) = -5*c(f) + 6*y(f). Solve b(o) = 0 for o.
-18, -1, 10
Determine j, given that 286/7*j**2 - 31974/7 + 9782/7*j + 2/7*j**3 = 0.
-73, 3
Let o = -58/3121 - -3268151/24968. Determine i so that -o*i**2 - 15/8*i**4 + 243/4 - 837/8*i + 261/8*i**3 = 0.
-1, 2/5, 9
Factor 98*c**3 - 126*c**3 + 75*c**2 + 23*c**3.
-5*c**2*(c - 15)
Let l(x) be the third derivative of x**5/30 - 20*x**4 + 4800*x**3 + 4*x**2 - 321*x + 1. Factor l(v).
2*(v - 120)**2
Suppose 2*v - 32 = -4*u - 0*u, v = 5*u - 33. Let t(x) = 4*x + 4. Let c be t(u). Factor 2*j**2 + c*j + 2*j**2 + 39 - 13 + 38.
4*(j + 4)**2
Let -146*n + 616 - 2754*n**2 + 1402*n**2 + 1350*n**2 = 0. What is n?
-77, 4
Let u(n) be the first derivative of 0*n**3 + 0*n**2 - 1/22*n**4 - 101 + 0*n. Find v such that u(v) = 0.
0
Factor 0 + 14/15*j**3 - 8/5*j + 8/15*j**2 + 2/15*j**4.
2*j*(j - 1)*(j + 2)*(j + 6)/15
Suppose r + 4*m - 16 = 0, -5*r + 21 + 35 = -4*m. Suppose -13 + 1 = -r*i. Let -1/2*h**2 - i + 3/2*h = 0. What is h?
1, 2
Let x(n) be the third derivative of n**7/280 + n**6/60 - n**5/8 - 3*n**4/4 - 104*n**3/3 - 17*n**2 - 4. Let g(d) be the first derivative of x(d). Factor g(i).
3*(i - 2)*(i + 1)*(i + 3)
Let w = -93082 + 93084. Suppose 0 + 0*q**w + 0*q - 4/19*q**3 - 2/19*q**4 + 2/19*q**5 = 0. Calculate q.
-1, 0, 2
Let d(i) be the second derivative of 863041*i**4/3 + 3716*i**3/3 + 2*i**2 + 61*i - 8. Factor d(t).
4*(929*t + 1)**2
Let a(u) be the first derivative of -u**5/50 + 9*u**4/40 + 3*u**3/10 - 81*u**2/20 - 2675. Factor a(m).
-m*(m - 9)*(m - 3)*(m + 3)/10
Let m(v) = v**2 + 1636*v. Let x(l) = 5*l**2 + 8163*l. Let u(o) = 22*m(o) - 4*x(o). Solve u(w) = 0 for w.
-1670, 0
Let p(o) = -o**4 - o**2 - o + 1. Let y(i) = -i + 6 + 362*i**4 - 11*i**2 - 183*i**4 - 5*i**3 - 180*i**4. Let s(q) = -6*p(q) + y(q). Factor s(v).
5*v*(v - 1)**2*(v + 1)
Let s(m) be the second derivative of 0*m**2 + 8/5*m**3 + m - 1/50*m**5 + 27 - 1/3*m**4. Find w, given that s(w) = 0.
-12, 0, 2
Factor 321615*z**3 - 321617*z**3 - z + 6*z**2 - 2*z**4 - 4 + 3*z + 0*z.
-2*(z - 1)**2*(z + 1)*(z + 2)
Let q(u) be the third derivative of 23/40*u**6 + 2*u**5 + 0*u**3 + 275*u**2 + 3/2*u**4 - 1/14*u**7 + 0*u + 0. Factor q(s).
-3*s*(s - 6)*(s + 1)*(5*s + 2)
Let c(b) = -3*b**3 + 490*b**2 - 495*b - 2. Let a(q) = q**3 - q**2 + 4*q + 1. Let h(x) = -6*a(x) - 3*c(x). Determine y, given that h(y) = 0.
0, 1, 487
Let r(i) = 9*i**4 - 4*i**3 - 6*i**2 + 14*i + 5. Let d(j) = -22*j**4 + 8*j**3 + 14*j**2 - 29*j - 8. Let z(h) = -2*d(h) - 5*r(h). Solve z(g) = 0 for g.
-1, 3
Suppose -25179 = -104*r + 83*r. Suppose 0 = -r*f + 1195*f. Factor 0*j - 6/13*j**2 - 10/13*j**3 + f.
-2*j**2*(5*j + 3)/13
Suppose -4*j + 32 = -3*y, 0 = -2*j - 4*y - 0*y - 6. Suppose 2*i + 2*r - r = 3, -4*r + 12 = -j*i. Factor -6*h**3 - 5*h**2 + 2*h**2 + i*h**3 - 4*h**4 + h**4.
-3*h**2*(h + 1)**2
Let m(n) be the third derivative of n**7/2940 + n**6/252 - n**5/70 + 41*n**3/2 + 76*n**2. Let q(v) be the first derivative of m(v). Factor q(w).
2*w*(w - 1)*(w + 6)/7
Let z = 84004 + -84001. Determine a so that -98*a**2 - 131*a**z - 11/2*a - 55*a**4 - 7/2*a**5 + 13 = 0.
-13, -1, 2/7
Let f = -32936 + 32939. Let c(p) be the first derivative of 0*p - 2/39*p**f + 43 + 6/13*p**2. Determine a, given that c(a) = 0.
0, 6
Let s be ((-27)/(-15))/((-6)/(-270)). Suppose -10*b = 17*b - s. Factor 8/5 + 68/5*f**5 + 88*f**b + 64*f**2 + 56*f**4 + 20*f.
4*(f + 1)**4*(17*f + 2)/5
What is g in -4*g**3 + 278*g**2 - 695*g**2 + 296*g + 125*g**2 = 0?
-74, 0, 1
Determine x, given that -4740*x + 1926*x**2 - 402 + 825 + 1341 - 64*x**3 + 1306*x**2 = 0.
3/4, 49
Factor 0*g - 582182875/4*g**2 + 0 + 2091675/4*g**3 - 2505/4*g**4 + 1/4*g**5.
g**2*(g - 835)**3/4
Let g = -40411 - -686991/17. Factor g*c - 2/17*c**2 + 30/17.
-2*(c - 5)*(c + 3)/17
Let p(w) = -5*w**3 - 11*w**2 + 7*w + 3. Let z(u) = 5 + 6*u - 9*u**3 + 2*u + 0*u - 21*u**2 + 6*u. Let s(i) = 11*p(i) - 6*z(i). Factor s(y).
-(y - 3)*(y - 1)**2
Let k be -4 - (-2269 + -4)*1. Factor -6*j**2 + k*j**3 - 2273*j**3 + 2*j**2.
-4*j**2*(j + 1)
Let i(r) be the third derivative of r**8/1848 + 34*r**7/1155 + 24*r**6/55 - 17*r**5/165 - 289*r**4/132 + 1560*r**2. Find q such that i(q) = 0.
-17, -1, 0, 1
Let j(b) be the third derivative of -b**5/12 - 25*b**4/24 + 35*b**3/3 - 2*b**2 + 298*b. Factor j(y).
-5*(y - 2)*(y + 7)
Let x(j) be the third derivative of j**6/160 - j**5/80 - 25*j**4/16 - 6*j**3 + 12*j**2 + 58. Factor x(s).
3*(s - 8)*(s + 1)*(s + 6)/4
Let a be ((-2)/6)/((100/330)/(-10)). Factor 2101*j**3 + 3*j**2 - a*j**2 - 2100*j**3.
j**2*(j - 8)
Factor 0 - 3/2*g**3 + 51/2*g**2 + 0*g.
-3*g**2*(g - 17)/2
Let d(i) be the second derivative of i**5/5 - 209*i**4 + 643*i. Factor d(m).
4*m**2*(m - 627)
Let z(t) be the third derivative of t**8/336 + 13*t**7/105 + 49*t**6/30 + 21*t**5/2 + 297*t**4/8 + 72*t**3 + 38*t**2 + 26*t - 1. Suppose z(u) = 0. What is u?
-16, -3, -1
Let y(c) be the first derivative of -1/2*c**4 + 877952*c + 152*c**3 - 17328*c**2 - 248. Let y(j) = 0. Calculate j.
76
Suppose 5*b + o - 34 = 0, -68 = 3*b - 2*o - 65. Find t, given that 0 + 6*t**3 + 6/5*t**b + 32/5*t**4 + 0*t - 36/5*t**2 = 0.
-3, 0, 2/3
Suppose 14*k + 7*k = -25*k + 10*k. Let l(i) be the second derivative of 1/8*i**5 + 0 + k*i**2 - 5/4*i**4 + 15/4*i**3 - 22*i. Factor l(n).
5*n*(n - 3)**2/2
Let a = -723 + -78. Let d = -797 - a. Solve -1/3*y**d - 14/3*y**3 - 19/3*y + 1/3*y**5 - 26/3*y**2 - 5/3 = 0 for y.
-1, 5
Let r(m) be the third derivative of -m**5/20 - 329*m**4/4 - 837*m**2. Solve r(c) = 0.
-658, 0
Suppose v = -v + 6, 4*g + v - 27 = 0. Suppose -3*t + 42 = 36. Factor 9 - 2*i + g*i - 9 + 2*i**t.
2*i*(i + 2)
Let c(s) be the third derivative of -19/12*s**4 + 0 - 8/3*s**3 - 25*s**2 + 0*s + 19/20*s**5 - 41/240*s**6 + 1/120*s**7. Solve c(p) = 0.
-2/7, 2, 8
Factor 43605*b**2 + 1/2*b**4 - 5000211/2 - 256*b**3 - 2456244*b.
(b - 171)**3*(b + 1)/2
Let o = 26755 - 26753. Factor -12/5*v**o + 0 + 12/5*v + 3/5*v**4 - 3/5*v**3.
3*v*(v - 2)*(v - 1)*(v + 2)/5
Let r(m) be the second derivative of m**4/54 - 155*m**3/27 - 12893*m. Suppose r(h) = 0. What is h?
0, 155
Let r be 18/153 - ((-828)/(-391) - (-4 + 6)). Let 1/9*x**4 - 2*x**2 + 0 + r*x + 7/9*x**3 = 0. Calculate x.
-9, 0, 2
Let d(w) be the third derivative of -w**7/840 - w**6/48 + w**5/240 + 5*w**4/48 - 4581*w**2. Factor d(t).
-t*(t - 1)*(t + 1)*(t + 10)/4
Let u be (34 - 27 - 8)/(2/(-18)). Factor -3/4*p**2 + u - 13*p.
-(p + 18)*(3*p - 2)/4
Solve -203*k - 312*k + 0*k**2 - 12*k**2 + 5*k**2 + 8*k**2 = 0 for k.
0, 515
Let l = 906747 + -906745. Let 99*m - 81*m**4 - 459/4*m**3 + 30 + 81/4*m**5 + 93/2*m**l = 0. Calculate m.
-2/3, 1, 5
Let o(q) be the second derivative of 0 - 14*q - 81/2*q**2 + 147/4*q**3 - 23/6*q**4 + 1/8*q**5. Factor o(b).
(b - 9)**2*(5*b - 2)/2
Factor 52 + 37*p - 10*p**2 + 68 - 3*p**2 - 7*p**2 + 19*p**2.
-(p - 40)*(p + 3)
Let s(z) be the f