e p = -3*v + 102, 4*v + p + p = 134. Let n be (-75)/v*(-8)/20. Let -n*c + 4/7 + 2/7*c**2 = 0. What is c?
1, 2
Suppose 18*m = -5*m + 667. Factor -120 - 26*x**2 - 25*x + 2*x**2 + m*x**2.
5*(x - 8)*(x + 3)
Factor 110/7*s**2 - 2/7*s**3 + 348/7*s + 0.
-2*s*(s - 58)*(s + 3)/7
Suppose -5*p = 2*f - 36, 3*p + 0 - 6 = 4*f. Factor 13*v + 77*v**2 - 35*v**2 - 37*v**2 - p.
(v + 3)*(5*v - 2)
Let w(m) be the third derivative of m**6/240 - 2*m**5/15 - 55*m**4/48 - 19*m**3/6 - 32*m**2 - 10. Determine r, given that w(r) = 0.
-2, -1, 19
Suppose -u = -6*u + 25. Let y be (3/u)/((-9)/(-135)). Factor -y*g - 4*g**2 + 3*g**2 + 4*g.
-g*(g + 5)
Let a(w) be the third derivative of -2*w**8/21 + 19*w**7/315 + 271*w**6/180 + 287*w**5/90 + 77*w**4/36 - 2*w**3/3 - 2*w**2 + 176*w. Let a(h) = 0. What is h?
-1, -2/3, 1/16, 3
Suppose 3 - 18 = -5*h. Let p(i) = 4*i + 198. Let j be p(-49). Factor -6/7*w + 3/7*w**j + 3/7*w**h + 0.
3*w*(w - 1)*(w + 2)/7
Let 65*t**3 + 4148*t**4 - 46*t**2 - 19*t + 7*t - 4070*t**4 - 21*t**3 = 0. Calculate t.
-1, -3/13, 0, 2/3
Suppose 14*n - 17*n = 3. Let u(z) = -z**3 - 3*z**2 - 4*z - 2. Let l be u(n). Determine r so that -4/5*r**3 + 2/5*r**5 + 0*r**2 + 0 + l*r**4 + 2/5*r = 0.
-1, 0, 1
Let t(s) be the second derivative of -273*s**5/20 - 271*s**4/12 + 274*s**3/3 - 2*s**2 - 4489*s + 2. Let t(h) = 0. What is h?
-2, 2/273, 1
Let y = 113/3084 + 418859/15420. Let 78/5*p**2 + 24/5 + 98/5*p**4 - y*p + 336/5*p**3 = 0. What is p?
-3, -1, 2/7
Let c(y) be the third derivative of -y**7/1155 + 5*y**6/132 + 53*y**5/330 + 9*y**4/44 - 936*y**2. Factor c(f).
-2*f*(f - 27)*(f + 1)**2/11
Let w(m) = m**3 - 4*m**2 - 440*m - 57. Let p be w(-19). Suppose p*y + 3/4*y**2 - 3/4 = 0. What is y?
-1, 1
Let h(m) be the first derivative of m**8/672 - m**7/70 + m**6/20 - m**5/15 + 3*m**2/2 - 7*m - 57. Let z(u) be the second derivative of h(u). Factor z(r).
r**2*(r - 2)**3/2
Suppose -9*s = -457 - 38. Let a be 18/15*s/22. Factor 0 - 2/3*u**a + 2/3*u**2 + 0*u.
-2*u**2*(u - 1)/3
Let x(c) = -5*c**2 + 9*c. Let j(p) = 5*p**2 - 8*p. Let q(h) = -5*h - 22. Let k be q(-14). Let u = k - 55. Let f(d) = u*x(d) - 6*j(d). Find w such that f(w) = 0.
0, 3
Suppose -612 - 858 = -15*j. Find a, given that j*a**2 + 35*a - 95*a**2 + 22*a = 0.
-19, 0
Suppose 2*g - 6*l = -8*l + 96, 2*g - 2*l - 80 = 0. Let y be (-212)/742 + g/105. Find o such that -2/15 + 0*o + y*o**2 = 0.
-1, 1
What is d in -1045/2*d**3 - 11495/2*d**2 - 25/2*d**4 - 41615/2*d - 13230 = 0?
-27, -7, -4/5
Factor -2/5*v**2 + 84/5*v - 304/5.
-2*(v - 38)*(v - 4)/5
Suppose 65*j**4 + 3*j + 21*j - 67*j**2 + 26*j + 2*j**2 + 15*j**5 - 65*j**3 = 0. Calculate j.
-5, -1, 0, 2/3, 1
Let c(w) be the first derivative of w**3/18 + 5*w**2/12 - 7*w/3 + 2921. Factor c(a).
(a - 2)*(a + 7)/6
Suppose 5588 + 5842 = 5*x. Let o be 2/4 - x/(-12). Factor -16 - 303*r**2 - 373*r**2 + 17*r + o*r.
-4*(13*r - 2)**2
Let u = -31 - -33. Suppose -3*t + 7 + 0 = -2*f, -3*f + u*t = -2. Solve 10*a**3 + f*a - 26*a**3 + 8*a**2 - 8 + 12*a**3 = 0.
-1, 1, 2
Let w(r) be the first derivative of 12/25*r**5 + 4/5*r + 9/5*r**2 + 68 + 32/15*r**3 + 7/5*r**4 + 1/15*r**6. Factor w(l).
2*(l + 1)**4*(l + 2)/5
Let y(q) be the first derivative of q**4/24 + 25*q**3 + 16875*q**2/4 - 5317. Factor y(n).
n*(n + 225)**2/6
Let s(m) be the first derivative of -50 + 0*m + 10*m**2 + 125/4*m**4 + 100/3*m**3. Solve s(d) = 0 for d.
-2/5, 0
Factor -31/5*i**2 + 2 - 153/5*i.
-(i + 5)*(31*i - 2)/5
Let x(q) be the first derivative of 11*q**5 - 2*q**4 - 3*q - 1591. Let c = 6 - -4. Let b(z) = 166*z**4 - 24*z**3 - 10. Let d(t) = c*x(t) - 3*b(t). Factor d(p).
4*p**3*(13*p - 2)
Let p be (18/(-126)*-21)/(6/4). Let v(x) be the first derivative of 0*x**p + 3/5*x**5 + 0*x**4 + 3*x + 4 - 2*x**3. Factor v(y).
3*(y - 1)**2*(y + 1)**2
Let h be ((-32)/(-16))/(132/198). Determine o so that 5/2*o**2 + o - 1/4*o**4 - 6 - 1/4*o**h = 0.
-3, -2, 2
Let o(j) be the second derivative of -j**4/84 - 149*j**3/42 - 21*j**2 + 466*j - 1. Factor o(b).
-(b + 2)*(b + 147)/7
Let a(j) be the third derivative of -4/735*j**7 - 1/588*j**8 + 0*j + 1/105*j**6 - 111*j**2 + 1/6*j**4 + 0 + 4/21*j**3 + 8/105*j**5. What is i in a(i) = 0?
-1, 2
Let i = -4340/19 + 30608/133. Factor 4/7*j**3 - 8/7*j**2 + 0 - i*j.
4*j*(j - 3)*(j + 1)/7
Let n(t) be the second derivative of 149*t + 0 - 1/5*t**5 - 16/3*t**3 + 0*t**2 + 2/15*t**6 - 10/3*t**4. Factor n(m).
4*m*(m - 4)*(m + 1)*(m + 2)
Let 1/4*j**2 - 353/2*j + 124609/4 = 0. What is j?
353
Let q(v) be the first derivative of -19/7*v**2 + 42 - 361/7*v - 1/21*v**3. Factor q(f).
-(f + 19)**2/7
Let y(r) be the third derivative of -r**5/90 + 67*r**4/36 + 286*r**3/3 - 615*r**2. Factor y(f).
-2*(f - 78)*(f + 11)/3
Factor -11/4*i**2 + 14*i - 1/4*i**3 - 15.
-(i - 2)**2*(i + 15)/4
Let p(b) be the third derivative of b**7/70 - 3*b**6/5 - 27*b**5/20 + 25*b**4/4 - b**2 - 12. Factor p(t).
3*t*(t - 25)*(t - 1)*(t + 2)
Let q = -28996 - -29004. Factor -q*k - 60/7 + 4/7*k**2.
4*(k - 15)*(k + 1)/7
Let i be (-13314)/420 - -41 - 18/(-15). Factor -i + 3/4*a**2 + 15/4*a.
3*(a - 2)*(a + 7)/4
Let l be 7812/1890 + (-1 - 13/(-15)). Let y(m) = -m**2 + 5*m. Let k be y(5). Let 7*w**2 - 4 + 16*w - w**4 - 20*w**3 - 2*w**2 + k*w**2 + l*w**5 = 0. Calculate w.
-2, -1, 1/4, 1, 2
Let d(b) be the second derivative of 2*b**7/21 + 4*b**6/5 - 3*b**5 - 44*b**4/3 + 56*b**3 + 884*b. Solve d(m) = 0.
-7, -3, 0, 2
Determine s, given that 160*s + 42*s**2 + s**3 - 300 - 39*s**2 - 26*s**2 = 0.
3, 10
Let z = 39 - 28. Suppose -z*v + 13*v - 6 = 0. Factor -5*o**2 - 25*o**4 - 9*o**2 - 19*o**3 - o**v + 10*o**2.
-o**2*(5*o + 2)**2
Suppose -56 + 66 = 5*b. Suppose -2*o = -6 + b. Determine j so that -55*j**o - 8*j - 55*j**2 - 4*j**3 + 114*j**2 + 8*j**3 = 0.
-2, 0, 1
Let w be ((-15)/(-2))/((-63)/(-672)). Suppose 24*y + 16*y - w = 0. Factor 128/9 + 2/9*q**3 + 32/3*q + 8/3*q**y.
2*(q + 4)**3/9
Let v(r) = -3*r**3. Let j(c) = -14*c**3 + c**2 - 16*c - 16. Let k(d) = -j(d) + 5*v(d). Determine w, given that k(w) = 0.
-4, -1, 4
Let x(w) be the first derivative of -w**6/200 - w**5/10 - 33*w**4/40 - 18*w**3/5 + w**2 - 15*w + 92. Let f(o) be the second derivative of x(o). Factor f(h).
-3*(h + 3)**2*(h + 4)/5
Let c(q) = -33504*q - 100510. Let m be c(-3). What is g in -3/5*g**m + 4/5 - 4/5*g = 0?
-2, 2/3
Let q(o) be the third derivative of -7*o**5/60 + 17*o**4/4 - 10*o**3/3 + 2*o**2 - 8. Let g(y) = -29*y**2 + 407*y - 78. Let t(n) = 6*g(n) - 26*q(n). Factor t(k).
2*(k - 26)*(4*k - 1)
Let u(k) be the first derivative of 3*k - 9/5*k**5 + 3/2*k**4 - 9/2*k**2 + 1/2*k**6 - 39 + 2*k**3. Factor u(o).
3*(o - 1)**4*(o + 1)
Let r(j) be the first derivative of j**6/120 + 7*j**5/60 + j**4/2 + 43*j**2/2 - 2*j - 87. Let l(b) be the second derivative of r(b). What is k in l(k) = 0?
-4, -3, 0
Let d(o) = 2*o**2 + o. Let l be d(-4). Suppose 6*g = 10*g - l. Factor 21*r + 2 + 14*r**2 + 6*r**2 + g*r + 6.
4*(r + 1)*(5*r + 2)
Suppose 4*u - 10 - 2 = 0. Let d be (((-60)/25)/(-6))/((-154)/(-11550)). Determine o so that d*o - 5/2*o**5 - 5*o**2 - 15*o**4 + 20 - 55/2*o**u = 0.
-2, -1, 1
Let q(b) be the third derivative of 7*b**4/6 + 71*b**3/6 + 22*b**2. Let y be q(21). Suppose -6*t - 3*t**2 + 2*t**2 + y - 669 + 13*t = 0. What is t?
2, 5
Let a(f) = -f**2 + 27*f - 138. Let c be a(20). Let y(p) be the first derivative of 4/3*p**c + 8/3*p + 2/9*p**3 - 10. Factor y(n).
2*(n + 2)**2/3
Suppose 2*r + 4*u - 28 = 0, -4*r - 41*u + 108 = -46*u. Let k(d) be the first derivative of 3/5*d**5 + 3*d - 2*d**3 + 0*d**2 + 0*d**4 - r. Solve k(f) = 0 for f.
-1, 1
Let a(w) be the first derivative of -w**4/4 + 16*w**3/3 - 14*w**2 - 1406. Factor a(i).
-i*(i - 14)*(i - 2)
Let n(k) be the first derivative of -14*k**3/3 + 4*k**2/3 + 1886. Factor n(g).
-2*g*(21*g - 4)/3
Let g(f) be the second derivative of -5*f**4/12 + 845*f**2/2 + 2*f + 185. Factor g(m).
-5*(m - 13)*(m + 13)
Suppose 4*f = -2*k + 18, -23*f + k = -20*f - 11. Solve 1/4 - 1/2*b**3 + 0*b**2 - 1/4*b**f + 1/2*b = 0.
-1, 1
Let o = 135846 + -135841. Determine a so that -1/4*a**o + 0*a**2 + 0 + 1/2*a**3 + 0*a**4 - 1/4*a = 0.
-1, 0, 1
Let a be 4/22 + ((-5712)/66)/(-8). Factor -66 - 19*o - 6 - 12*o**2 - 10*o**2 + 19*o**2 - a*o.
-3*(o + 4)*(o + 6)
Let l(x) be the second derivative of -x**4/4 + 67*x**3 + 408*x**2 - 484*x - 4. Solve l(g) = 0.
-2, 136
Let z be (-228)/9804 + (-1010)/(-6450). What is c in -