r + 28. Factor -44*m + 38*m - m**l - 4 - 1.
-(m + 1)*(m + 5)
Let o(u) be the third derivative of 87808/3*u**3 + 1/120*u**6 + 77*u**2 - 1 + 392*u**4 + 0*u + 14/5*u**5. Factor o(n).
(n + 56)**3
Let t = 1002 + -1019. Let z be (2 - t/(-6)) + (-685)/(-822). Factor -2/7*k**2 + z + 10/7*k.
-2*k*(k - 5)/7
Suppose 5*s + 6*h - 46 = 0, 4*s - 3*h + 33 = 23. Let u(j) be the third derivative of 0*j - 1/90*j**5 + 1/9*j**4 + 0 + 10*j**s + 0*j**3. Factor u(w).
-2*w*(w - 4)/3
Let o(l) be the third derivative of l**6/180 + 4*l**5/9 + 197*l**4/36 - 238*l**3/9 + 3383*l**2. Factor o(m).
2*(m - 1)*(m + 7)*(m + 34)/3
Suppose -29*k = 1462 - 1520. Let j = -13235/17 + 779. Factor -j*q + 6/17 + 2/17*q**k.
2*(q - 3)*(q - 1)/17
Let a(l) = 7*l**4 + 196*l**3 + 3080*l**2 - 8. Let i(n) = 13*n**4 + 391*n**3 + 6158*n**2 - 14. Let u(j) = 7*a(j) - 4*i(j). Determine f, given that u(f) = 0.
-32, 0
Let l(v) be the second derivative of -v**7/231 + 3*v**6/55 + 3*v**5/22 - 53*v**4/66 + 10*v**3/11 + 700*v. Find x such that l(x) = 0.
-3, 0, 1, 10
Let m be (124/14 + -8)*7/3. Let q(r) be the first derivative of 0*r**m - 1/25*r**5 + 0*r + 0*r**4 + 4/15*r**3 + 21. Find x such that q(x) = 0.
-2, 0, 2
Solve -1319 - 409 + 976*p**2 + 606*p**2 - 1150*p**2 - 3*p**3 + 12*p = 0 for p.
-2, 2, 144
Let p(a) = -4*a**3 + 75*a**2 + 82*a - 9. Let w(x) = 4*x**3 - 74*x**2 - 80*x + 6. Let c(g) = 2*p(g) + 3*w(g). Factor c(y).
4*y*(y - 19)*(y + 1)
Suppose -713 + 311 = -201*f. Let z be (-2)/6 + (-19)/(-3). Factor -2 - 7*o**3 + z*o**3 + o - 29*o**f + 31*o**2.
-(o - 2)*(o - 1)*(o + 1)
Let h(a) = a**4 + a**3 - 2*a**2. Let d(k) = 30*k**4 + 3985*k**3 + 780060*k**2 - 1572120*k + 788045. Let x(q) = d(q) - 25*h(q). Determine u, given that x(u) = 0.
-397, 1
Let w(v) be the first derivative of -5*v**6/24 - 7*v**5/12 - 5*v**4/12 + 70*v**2 - 177. Let a(i) be the second derivative of w(i). Factor a(m).
-5*m*(m + 1)*(5*m + 2)
Suppose -5*i + 4*o + 31 = 0, 4*i + o + 4*o + 8 = 0. Suppose i*w - 22 = -8*w. Suppose -11 + 6 - 6*s + 2*s**2 + w*s**4 + 1 + 6*s**3 = 0. Calculate s.
-2, -1, 1
Let t(q) = 15*q**2 + 33*q + 18. Let g(d) be the first derivative of -7*d**3/3 - 17*d**2/2 - 8*d - 52. Let u(i) = -9*g(i) - 4*t(i). Factor u(z).
3*z*(z + 7)
Let x be ((-2)/(-3))/(30/90). Solve 73 + 45*d - 11*d + 6*d + 5*d**x + 2 = 0 for d.
-5, -3
Suppose -5*q = -d + 1586, 4*d = 21*q - 23*q - 630. Let h = q + 637/2. Factor -h*f**2 + 9/2 + 3*f.
-3*(f - 3)*(f + 1)/2
Suppose -524*s + 39*s - 433*s = 4148 - 17918. Factor -5/2*m**3 + 37/4*m**2 + 9 + 1/4*m**4 - s*m.
(m - 3)**2*(m - 2)**2/4
Let v be -1 - (-5 + 0/2). Determine h so that 75*h**v + h**2 + 155*h**3 + 4*h**2 + 10*h**2 + 20*h**5 - 10*h - 75*h**3 = 0.
-2, -1, 0, 1/4
Factor 5/3*n**2 + 202/3 - 169*n.
(n - 101)*(5*n - 2)/3
Let f = 302132/264537 + 28/37791. Find l such that 0 - f*l**3 - 26/7*l**2 + 6/7*l**4 - 12/7*l = 0.
-1, -2/3, 0, 3
Let w be (-7)/(-3)*150/(-105)*(-129)/215. Factor 1/3*f**3 - 47/3*f - 22/3*f**w - 8.
(f - 24)*(f + 1)**2/3
Let -d**3 + 3*d**3 - 10*d**2 + 6*d + 1459*d**4 - 1457*d**4 = 0. What is d?
-3, 0, 1
Suppose 0 = 3*p - 3*n - 3, 4*n - 12 - 2 = -5*p. Factor -175*t**p + 56*t + 14 + 0 - 11*t - 6 + 2.
-5*(5*t - 2)*(7*t + 1)
Let q(r) be the first derivative of 2*r**3/21 + 111*r**2 + 450. Find a, given that q(a) = 0.
-777, 0
Suppose -188*t + 165549 = 165549. Let i be 8/(-15)*25/(-2). Determine r so that t + 49/3*r**5 + 4/3*r - r**3 - 70/3*r**4 + i*r**2 = 0.
-2/7, 0, 1
Let v(c) = 6*c**3 + 36*c**2 + 164*c. Let y(g) = 2*g**3 - 3*g**2 + 2*g. Let n(k) = -v(k) + 2*y(k). Factor n(q).
-2*q*(q + 5)*(q + 16)
Let g(l) be the third derivative of -l**7/105 - l**6/18 + 2*l**5/5 + 29*l**4/18 + 5*l**3/3 - 298*l**2 - 2*l. What is m in g(m) = 0?
-5, -1, -1/3, 3
Let d(a) = -a**4 - a**3 + 40*a**2 + 88*a - 96. Let g(t) = -t**4 - t**3 + 39*t**2 + 84*t - 96. Let s(w) = 5*d(w) - 6*g(w). Solve s(v) = 0 for v.
-4, 1, 6
Let q(m) = -2*m**2 - 5*m - 27. Let i(r) = -5 + r**2 - 2 - 15 - 3*r**2 - 6 - 8*r. Let t(w) = -5*i(w) + 4*q(w). Solve t(b) = 0 for b.
-8, -2
Solve -89/3*r**3 + 0 - 2/3*r**4 + 0*r + 235/3*r**2 = 0.
-47, 0, 5/2
Let x = -973 - -985. Suppose -3*y - 3*q + x = 0, 5*q = 3*y + q + 16. Factor y + 3/4*p**2 - 3/4*p**4 + 3/4*p**5 - 3/4*p**3 + 0*p.
3*p**2*(p - 1)**2*(p + 1)/4
Let h = 79 - 45. Let w = 36 - h. Factor -188*d**3 + 16*d - w*d**4 + 160*d**3 - 10*d**4.
-4*d*(d + 1)*(d + 2)*(3*d - 2)
What is q in -93*q**5 - 450 + 455*q - 18290*q**3 + 72*q**2 + 18*q**4 + 18196*q**3 + 92*q**5 = 0?
-2, 1, 5, 9
Let t(v) be the first derivative of 4*v**7/315 - v**6/12 - 2*v**5/45 + 3*v**2/2 - 4*v - 48. Let w(d) be the second derivative of t(d). Factor w(a).
2*a**2*(a - 4)*(4*a + 1)/3
Let o = 207/740 + 3/148. Let q(l) be the first derivative of 24 - o*l**4 + 12/5*l**2 + 3/25*l**5 + 0*l - 4/5*l**3. Factor q(x).
3*x*(x - 2)**2*(x + 2)/5
Let k = -514 + 516. Factor h**2 - 43*h - 14 + h**2 - 5*h**k + 2*h**2 - 28.
-(h + 1)*(h + 42)
Factor -125*p**2 + 578*p**2 - 419*p + 3*p**4 + 28*p**3 + 192*p**2 - 7*p - 250*p**3.
3*p*(p - 71)*(p - 2)*(p - 1)
Solve 220323/2 + 3/2*o**2 + 813*o = 0 for o.
-271
Let j = 6616 + -6600. Let i(d) be the first derivative of -2/3*d**3 - j + 11/2*d**2 - 5*d. Factor i(y).
-(y - 5)*(2*y - 1)
Let i(w) be the second derivative of w**5/80 - 7*w**4/6 - 19*w**3/8 + 3*w - 185. Factor i(q).
q*(q - 57)*(q + 1)/4
Let n(y) = -4*y + 67. Let m be n(15). Let v be (126/24 - 5) + m/4. Factor 36*o + 198 - 4*o**v - 198.
-4*o*(o - 9)
Suppose 464/7*x - 4/7*x**3 + 68/7*x**2 - 528/7 = 0. What is x?
-6, 1, 22
Let m(j) be the third derivative of j**7/210 - 11*j**6/120 + j**5/15 + 5*j**4/2 - 2084*j**2. Factor m(c).
c*(c - 10)*(c - 3)*(c + 2)
Let c = 239922/11609 - 8/34827. Factor c*v + 14/9*v**2 + 52/9.
2*(v + 13)*(7*v + 2)/9
Let d(i) be the second derivative of -2*i**7/21 + 4*i**6/15 - i**5/5 + 142*i. Factor d(h).
-4*h**3*(h - 1)**2
Let a = -1308049 - -17004801/13. Factor -6*l + a - 2/13*l**2.
-2*(l - 2)*(l + 41)/13
Let v(z) = -215*z**2 + 445*z - 155. Let i(o) be the first derivative of 37/2*o**2 - 9 - 13*o - 6*o**3. Let b(f) = -25*i(f) + 2*v(f). Solve b(l) = 0.
3/4, 1
Suppose -26*b - 6*b + 1760 = 0. Solve 2*d**2 + 54 - 6*d**2 - 4*d - 2*d**2 - 4*d**3 - b - d**4 = 0.
-1
Let v(f) be the second derivative of -5*f**4/12 - 640*f**3/3 - 1270*f**2 - 6428*f. Factor v(k).
-5*(k + 2)*(k + 254)
Let n be 3/3*15/3. Suppose m - 3*o = -0*o + 17, 5*m + o - n = 0. Let 3*j**3 + 2*j**4 + j**m - 25*j**5 - 3*j**4 - 4*j**3 + 26*j**5 = 0. What is j?
-1, 0, 1
Suppose -2*f - 5*f = 0. Suppose 5*o - 6*o + 4 = f. Solve -o*n**3 + 4*n + 30*n**2 + 2*n**3 + 6*n**3 - 38*n**2 = 0 for n.
0, 1
Let g(z) = 30*z**2 + 330*z + 1515. Let y(x) = 35*x**2 + 330*x + 1513. Let r(l) = -6*g(l) + 5*y(l). Determine t so that r(t) = 0.
-61, -5
Let u(y) be the third derivative of y**9/181440 + y**8/12096 - y**7/2520 - 229*y**5/60 - 13*y**2 + 1. Let d(v) be the third derivative of u(v). Factor d(w).
w*(w - 1)*(w + 6)/3
Let m(z) be the second derivative of -z**5/80 - 3*z**4/16 - 9*z**2 + 5*z + 2. Let f(y) be the first derivative of m(y). Let f(i) = 0. What is i?
-6, 0
Let c(p) be the first derivative of 2/21*p**6 - 24/7*p**4 + 0*p + 0*p**5 - 96/7*p**2 - 116 + 256/21*p**3. Factor c(q).
4*q*(q - 2)**3*(q + 6)/7
Let 2629*h**2 + 2637*h**2 + h**5 + 92*h + 20*h**4 - 47*h**3 - 5328*h**2 + 88 = 0. Calculate h.
-22, -1, 2
Let h(j) = j**3 + j**2 - 3. Let w = -292 - -207. Let v be 306/w + (-2)/10*2. Let d(f) = -f**3 + f + 4. Let x(b) = v*h(b) - 3*d(b). Factor x(z).
-z*(z + 1)*(z + 3)
Let z = -179 + 183. What is x in 6*x**4 + 28*x**3 + 2*x**2 - 8*x**z + 26*x**3 - 22*x**3 - 16*x - 16*x = 0?
-1, 0, 1, 16
Suppose -4*g + 23 = -3*j, -2*g - 2*j + 7*j = -29. Determine x, given that 18280*x - 44*x**4 - 18280*x + 10*x**5 + 46*x**3 - 12*x**g = 0.
0, 2/5, 1, 3
Factor -13268148878/21 + 2/21*s**3 + 7061282/7*s - 3758/7*s**2.
2*(s - 1879)**3/21
Let n(h) be the first derivative of 4*h**3/3 - 134*h**2 + 520*h - 909. Factor n(u).
4*(u - 65)*(u - 2)
Let o be 9997/13*3/(-3). Let s = -6149/8 - o. Solve 3/2*a + 0 - s*a**2 = 0 for a.
0, 4
Let j be (24/(-28))/(-3 + 100/42 - 119/(-357)). Factor 6/5*d**2 - 9/5*d - 1/5*d**j + 4/5.
-(d - 4)*(d - 1)**2/5
Factor 132 - 85*p + 27*p**2 - 22*p**2 - 1343 - 1690 - 519.
5*(p - 36)*(p + 19)
Suppose 4 = 22*t - 20*t. Suppose 4*s**2 + t*s - 12*s - 6*s**2 + 14*s = 0. What is s?
0, 2
Let y