 1)
Let q(p) be the first derivative of -p**6/6 - 12*p**5/5 + 3*p**4/4 + 34*p**3/3 - 12*p**2 - 1044. Solve q(n) = 0.
-12, -2, 0, 1
Let o(h) be the first derivative of 2*h**5/5 - 38*h**4 - 310*h**3/3 - 78*h**2 + 2368. Factor o(g).
2*g*(g - 78)*(g + 1)**2
Let y(v) = -v**3 + 11*v**2 + 19*v - 42. Let z be y(12). Suppose 47*h = -z*h + 84*h. Factor h*w - 2/3*w**5 + 0*w**2 + 0 - 4/3*w**4 - 2/3*w**3.
-2*w**3*(w + 1)**2/3
Let s = -520 - -521. Let r(h) = h**4 + 15*h**3 + 48*h**2 + 64*h + 29. Let a(m) = m**4 + m**3 + 3. Let c(t) = s*a(t) + r(t). Factor c(k).
2*(k + 2)**4
Suppose m - 13 = -0*m + 5*z, m + 5*z + 7 = 0. Let d be (-267)/5*-3*40/24. Suppose -d - 278 + 22*s**2 + m*s**2 + 530 - 10*s = 0. Calculate s.
-3/5, 1
Let f(u) = -2*u**3 + 2*u**2 - u. Let s(i) = -85*i**3 + 185*i**2 - 50*i - 60. Let j(r) = -10*f(r) + s(r). Factor j(x).
-5*(x - 2)*(x - 1)*(13*x + 6)
Let o(v) be the first derivative of v**6/24 - 7*v**5/20 + 11*v**4/16 - 5*v**3/12 - 1085. Factor o(r).
r**2*(r - 5)*(r - 1)**2/4
What is i in -3/2*i**2 + 57*i - 288 = 0?
6, 32
Let j(z) be the third derivative of z**7/840 - 41*z**6/5 + 1938479*z**5/120 - 80647*z**4 + 3869089*z**3/24 - 2*z**2 - 12*z + 23. Factor j(y).
(y - 1967)**2*(y - 1)**2/4
Suppose 2*q + 3*q - f = 14, -q + 3*f = -14. Suppose q*h - 50 = -3*h. Factor -4*y**2 - 3*y**2 - 19*y + h*y**2 - 4 + 23*y.
(y + 2)*(3*y - 2)
Let g(p) be the first derivative of p**3/3 - 171*p**2/2 + 668*p + 6776. Factor g(q).
(q - 167)*(q - 4)
Let a(i) be the third derivative of i**5/20 + 97*i**4/8 + 396*i**3 + 5461*i**2. Let a(f) = 0. What is f?
-88, -9
Let x be (62 + -63)*(-1)/((-1)/(-3)). Let n be ((-8)/3)/((-10)/15). Let 3*c - c**4 + 12*c**3 - 12*c**2 - 2*c**n + 3*c - x*c**2 = 0. What is c?
0, 1, 2
Suppose -11*k - 43 + 127 - 51 = 0. Let p(w) be the first derivative of -w + w**2 - 17 + 5/12*w**k. Factor p(d).
(d + 2)*(5*d - 2)/4
Let o(b) be the second derivative of 12 - 1/60*b**5 - 3*b + 0*b**2 + 0*b**4 - 7/3*b**3 + 1/180*b**6. Let r(x) be the second derivative of o(x). Factor r(a).
2*a*(a - 1)
Let c(b) be the first derivative of 0*b**2 + 0*b + 2*b**3 + 1/480*b**5 - 49 + 1/1440*b**6 + 0*b**4. Let t(f) be the third derivative of c(f). Factor t(v).
v*(v + 1)/4
Let h = 589753/160845 + 4/53615. Suppose h*g + 0 + 1/3*g**2 = 0. What is g?
-11, 0
Find j, given that j**3 - 1647 + 123*j**2 + 684 + 2*j**3 + 643 - 528*j + 860 = 0.
-45, 2
Let i(u) be the third derivative of -u**8/840 + u**6/60 - u**5/30 + 43*u**3/2 + 184*u**2. Let j(b) be the first derivative of i(b). Find n such that j(n) = 0.
-2, 0, 1
Suppose u - 5*r - 24 = 0, 3*r - 66 = -4*u + 7. Suppose 8*n = 19 - u. Solve n*y**2 + 0*y + 0 + 2*y**3 + 4/3*y**4 - 2/3*y**5 = 0 for y.
-1, 0, 3
Let 35/2*u**2 - 145/2*u + 75 = 0. What is u?
2, 15/7
Let j(z) be the second derivative of -3*z**5 + 107*z**4/3 + 1772*z**3/3 - 240*z**2 + 30*z - 5. Find g such that j(g) = 0.
-5, 2/15, 12
Let j(s) = -26*s**5 + 21*s**4 + 45*s**3 - 22*s**2 + 2*s. Let h(z) = -z**5 + z**4 - 2*z**2 + 2*z. Let i(r) = 11*h(r) - j(r). Determine x, given that i(x) = 0.
-1, 0, 2/3, 2
Let q be ((-3330)/(-29304))/((-20)/(-16)). What is l in -q*l**2 + 1/11 + 0*l = 0?
-1, 1
Let r = -43552/45 + 4848/5. Factor -26/9*f - r*f**2 - 4/3 - 2/9*f**3.
-2*(f + 1)**2*(f + 6)/9
Suppose v - 8 = -5*w, -16*w = -18*w + 2. Suppose -4*k**v + 556*k + 64 + 9*k**2 + 11*k**2 - 468*k = 0. What is k?
-2, -1, 8
Suppose 15 = -2*f - 3*f. Let w be (f/2)/(2/(-4)) - -1. Find n such that 12*n + n - 16*n - n**2 + w = 0.
-4, 1
Suppose 96*v - 24596 = -463*v. Let d(t) be the first derivative of 3/2*t**4 - 8/3*t**3 + 0*t**2 + v + 0*t. Solve d(b) = 0 for b.
0, 4/3
Let s(n) = -120*n + 14763. Let w be s(123). Factor 0 + 4/11*l**2 + 2/11*l**4 + 6/11*l**w + 0*l.
2*l**2*(l + 1)*(l + 2)/11
Let -188 + 224 + 2*p**2 + p**2 - 18*p - p**2 - 4*p = 0. Calculate p.
2, 9
Let g = -7394 - -7398. Let k(r) be the first derivative of -9*r**2 + 5*r**3 - 3/4*r**g + 0*r + 29. Factor k(w).
-3*w*(w - 3)*(w - 2)
Solve -3/10*w**3 - 1/5*w**4 + 0 + 66/5*w + 263/10*w**2 = 0 for w.
-12, -1/2, 0, 11
Factor -804 + 5*g**3 - 362 + 1439*g - 199*g - 425*g**2 + 346.
5*(g - 82)*(g - 2)*(g - 1)
Let w(c) = 18062*c + 72250. Let s be w(-4). Factor -9/2*o**3 + 9 + 45/2*o**s - 51/2*o - 3/2*o**4.
-3*(o - 1)**3*(o + 6)/2
Let m be (-53)/(-5) - (-14)/35. Suppose 12*v = m*v + 5. Determine n so that 58*n**5 - 61*n**v - n**3 + 9*n**4 - 5*n**3 = 0.
0, 1, 2
Let b(g) = -3*g**5 + 61*g**4 - 36*g**3 - 74*g**2 - 41*g - 12. Let x(f) = -f**5 + 13*f**4 - 2*f**2 + f. Let u(i) = b(i) - 5*x(i). Factor u(r).
2*(r - 6)*(r + 1)**4
Let n(m) = 69*m**3 + 286*m**2 - 919*m + 889. Let g(c) = 30*c**3 + 142*c**2 - 460*c + 444. Let a(i) = 9*g(i) - 4*n(i). Factor a(s).
-2*(s - 2)**2*(3*s - 55)
Let v(d) be the first derivative of -d**3/7 + 1917*d**2/7 - 1224963*d/7 - 7778. Determine p, given that v(p) = 0.
639
Let c(o) be the first derivative of -59 - 2/3*o**3 + 5/3*o**2 - 5/6*o**4 + 8/3*o - 2/15*o**5. Suppose c(w) = 0. Calculate w.
-4, -1, 1
Solve 9*b**2 + 5*b**2 - 2040*b + 7*b**2 + 260100 - 17*b**2 = 0.
255
Factor 0 + 3*f**2 - 46/7*f + 1/7*f**3.
f*(f - 2)*(f + 23)/7
Factor -48/5*k + 4/5*k**4 - 16/5*k**2 + 12/5*k**3 + 0.
4*k*(k - 2)*(k + 2)*(k + 3)/5
Let i = -4097321/7 + 585332. Factor 45/7 - i*w**2 - 6*w.
-3*(w - 1)*(w + 15)/7
Suppose -15 = -i + l - 10, 2*i + 2*l = 2. What is o in -2*o**4 + 31*o**2 - 5*o**i + 5*o**3 - 2*o**3 - 126*o + 35*o**2 = 0?
-7, 0, 3
Let s be -2 + -2 - (26 - 5220/165). Factor 12/11 + 6/11*b**2 + s*b.
6*(b + 1)*(b + 2)/11
Let o(t) be the second derivative of -1/15*t**6 + 1/5*t**5 - 36*t**2 - 15 + 11/6*t**4 + 10*t - 4*t**3. Determine f so that o(f) = 0.
-2, 3
Let m be ((-977968)/728)/(-38) + (-10)/(-130). Factor -m*d**2 + 4/7*d**3 + 3844/7*d + 0.
4*d*(d - 31)**2/7
Let m = 69 + -69. Let a be (m - -10)/(0 - 0 - -2). What is v in 285*v**4 - 25*v**3 - 45*v**2 + 10*v - 15*v**5 - 189*v**5 - 21*v**a = 0?
-2/5, 0, 1/3, 1
Let q(r) = -8*r**2 - 6*r - 418. Let p(t) = -6*t**2 - 5*t - 415. Let v(b) = 6*p(b) - 5*q(b). Find x such that v(x) = 0.
-10, 10
Let q be -23*240/6624 - (16/3)/(-1). Factor 0 - q*f - 1/2*f**2.
-f*(f + 9)/2
Determine r so that 8/11 - 28/11*r - 2/11*r**2 + 7/11*r**3 = 0.
-2, 2/7, 2
Let f(n) be the third derivative of -n**6/540 + 127*n**5/135 - 16129*n**4/108 - 79*n**2 - 13*n. Factor f(p).
-2*p*(p - 127)**2/9
Let i = -758 - -737. Let m(r) = 36*r**4 + 84*r**3 - 21*r**2. Let q(w) = 7*w**4 + 17*w**3 - 4*w**2. Suppose 7 = n + 3. Let j(u) = i*q(u) + n*m(u). Factor j(a).
-3*a**3*(a + 7)
Suppose -98*o + 10*o = 176. Let p be (-21)/(-42) - (-15)/(-20)*o. Factor 2/5*c**4 + 1/5*c + 0*c**3 - 2/5*c**p + 0 - 1/5*c**5.
-c*(c - 1)**3*(c + 1)/5
Let r(f) be the second derivative of 0*f**2 - 9 - 2*f + 3/35*f**5 + 0*f**3 + 1/70*f**6 + 3/28*f**4. Determine w so that r(w) = 0.
-3, -1, 0
Suppose 322 = 169*p - 16. Find d such that 0*d**p + 0*d + 0 + 2/17*d**4 - 2/17*d**3 = 0.
0, 1
Suppose 125 + 435*n**4 - 127*n**2 + 117*n**2 - 35*n**5 - 210*n - 1550*n**3 + 55*n**5 + 1850*n**2 - 660*n = 0. What is n?
-25, 1/4, 1
Factor 710*x - 15*x**2 + 423*x**2 + 1920 - 184869*x**4 + 184870*x**4 - 2214*x - 42*x**3.
(x - 30)*(x - 4)**3
Factor 21878 + 11*y**3 + 20*y**2 - 9*y**3 - 28934 - 616*y.
2*(y - 18)*(y + 14)**2
Suppose -2/7*w**2 - 552/7 - 554/7*w = 0. Calculate w.
-276, -1
Let v(z) be the second derivative of -z**7/945 - z**6/540 + 4*z**5/135 + z**4/9 + 41*z**2/2 - 2*z + 27. Let n(i) be the first derivative of v(i). Factor n(m).
-2*m*(m - 3)*(m + 2)**2/9
Let r be 17/68 - ((-705)/(-12))/5. Let q = -199/18 - r. Factor 8/9*g + 8/9 - 2/3*g**2 - q*g**3 + 2/9*g**4.
2*(g - 2)**2*(g + 1)**2/9
Let s(k) be the second derivative of k**4/120 + 209*k**3/30 - 4*k - 462. Solve s(a) = 0.
-418, 0
Let a be 15/(-24)*(-12)/10. Let l be 12*(-2)/(-408) + (-2008)/(-544). Factor -9/2*j - l - a*j**2.
-3*(j + 1)*(j + 5)/4
Let u = 25422 + -97979/4. Let b = u + -923. Suppose -1/2*v**5 + 10*v - 4 - 19/2*v**3 - 1/4*v**2 + b*v**4 = 0. Calculate v.
-1, 1/2, 1, 4
Let v(d) = 20*d**2 + 184*d - 1059. Let a(c) = -11*c**2 - 100*c + 530. Let j(u) = -9*a(u) - 5*v(u). Factor j(x).
-(x - 15)*(x + 35)
Let j be (-6240)/(-28028) - (-50)/(-1225). Determine o, given that -10/11*o - 8/11 - j*o**2 = 0.
-4, -1
Let k(l) be the first derivative of 18*l**3 + 1/3*l**6 + 25/2*l**4 + 18/5*l**5 + 50 + 10*l**2 + 0*l. Factor k(h).
2*h*(h