culate r.
1
Let s(j) be the first derivative of 2*j**3/3 - 41*j**2 - 264*j - 2965. Solve s(m) = 0 for m.
-3, 44
Find a such that -16 - 20/3*a + 4/3*a**2 + 1/3*a**3 = 0.
-6, -2, 4
Let c be 15 + -2 + (-2 - 2) + 4. Let u be 15/(-10)*(c/(-12) + 1). What is v in -1/4*v**2 + u*v**5 + 1/4 - 1/2*v**3 + 3/8*v + 0*v**4 = 0?
-1, 1, 2
Let c(g) be the second derivative of -5*g**7/42 - 2*g**6 - 11*g**5 - 95*g**4/6 + 75*g**3/2 + 125*g**2 - g - 603. Determine m, given that c(m) = 0.
-5, -2, -1, 1
Let y(o) be the second derivative of -o**5/25 - 14*o**4/3 + 2*o**3/15 + 28*o**2 - 2053*o. Find g, given that y(g) = 0.
-70, -1, 1
Factor -2/3*b**2 + 3824/3 + 636*b.
-2*(b - 956)*(b + 2)/3
Let w be -1*11034/(-648) - 17. Let y(k) be the third derivative of 28*k**2 + w*k**4 - 1/3*k**3 + 0*k - 1/180*k**6 + 1/30*k**5 + 0. Let y(g) = 0. What is g?
-1, 1, 3
Suppose 77*y + 2*x = 81*y + 8, -5*y - 8 = -2*x. Let c(k) be the second derivative of y*k**2 + 0*k**3 + 1/3*k**4 + k**5 + 0 + 17*k. Factor c(j).
4*j**2*(5*j + 1)
Let i(j) be the first derivative of -j**5/180 + 37*j**4/36 - 1369*j**3/18 - 5*j**2/2 - 13*j + 109. Let n(p) be the second derivative of i(p). Factor n(z).
-(z - 37)**2/3
Solve 486/5 - 27/10*f**3 - 189/2*f - 1/10*f**4 + 297/10*f**2 = 0.
-36, 3
Let t = -370 + 1. Let s = 369 + t. Factor -2/7*b**2 - 6/7*b + s.
-2*b*(b + 3)/7
Factor -94*h**2 + 139*h**2 - 2*h**4 + 65*h**2 - 219*h**3.
-h**2*(h + 110)*(2*h - 1)
Let k be (462/539)/((-1)/7) + 92/12. Let x(m) be the second derivative of 17*m + 1/3*m**4 + 0 + k*m**3 + 0*m**2. Factor x(a).
2*a*(2*a + 5)
Let t be 11/(-4)*(305/(-330) - (-30)/36). Let a(n) be the third derivative of 0*n - 5*n**2 + 0 - t*n**4 - 3/20*n**5 + 1/2*n**3. Factor a(z).
-3*(z + 1)*(3*z - 1)
Factor -35/4*c**2 + 1/4*c**4 - 9/2*c - 4*c**3 + 0.
c*(c - 18)*(c + 1)**2/4
Let s(r) = -4*r - r - 10 - 6*r - r**2 + 19*r. Let h be s(6). Factor 14*l**3 + 93*l - 5*l**3 + 4*l**2 - 60*l**h - 18.
(l - 3)**2*(9*l - 2)
Let z be ((-40)/(-21))/(544/1904). Let -85/6*v + z - 5/6*v**3 + 25/3*v**2 = 0. Calculate v.
1, 8
Let f(p) be the second derivative of -p**5/90 - 49*p**4/54 + 50*p**3/27 - 479*p. Factor f(b).
-2*b*(b - 1)*(b + 50)/9
Let g(b) = 21*b + 149. Let v be g(-7). Factor 25*r + 6*r**v + 0*r + 27*r - 8*r**2 + 6*r.
-2*r*(r - 29)
Determine c, given that 1085764/7 + 4/7*c**2 + 4168/7*c = 0.
-521
Determine h so that -1/4*h - 1/4*h**5 + 9*h**2 - 9/2 - 9/2*h**4 + 1/2*h**3 = 0.
-18, -1, 1
Factor 56/5 - 18/5*t**2 - 8/5*t.
-2*(t + 2)*(9*t - 14)/5
Let m be -83 + 30955/350 - 1/((-70)/4). Find q, given that -q**2 + 6 + 1/2*q**3 - m*q = 0.
-3, 1, 4
Factor 9/8 + 8*s + 7/8*s**2.
(s + 9)*(7*s + 1)/8
Let u be (-2)/(-5)*331175/260. Let v = -508 + u. What is n in v + 1/2*n**2 - 2*n = 0?
1, 3
Suppose b - 87 = -5*w, -3*b - 66 = -2*w - 310. Let 10*l - 43*l**4 - 15*l**2 - 34*l**4 + b*l**4 = 0. Calculate l.
-2, 0, 1
Let l(x) be the third derivative of -x**8/1344 + x**7/210 + 43*x**6/480 + 19*x**5/120 - 13*x**4/8 - 9*x**3 - 145*x**2. Suppose l(k) = 0. Calculate k.
-3, -2, 2, 9
Let f(q) be the third derivative of q**5/60 + q**4/24 - q**3/2 + 2*q**2. Let g be f(-4). Find t, given that -t**2 - 8*t - 5*t - g + 8*t - t = 0.
-3
Let r(w) be the first derivative of 1/2*w**4 + 120*w + 251 + 28*w**2 - 62/3*w**3. Let r(f) = 0. Calculate f.
-1, 2, 30
Let m = 83208 - 83208. Find z, given that 1/3*z**3 - 1/6 + m*z**2 + 1/6*z**4 - 1/3*z = 0.
-1, 1
Let a(f) be the third derivative of -f**8/3360 + f**7/630 + 7*f**6/360 + f**5/15 - 5*f**4/24 + 58*f**2. Let x(t) be the second derivative of a(t). Factor x(o).
-2*(o - 4)*(o + 1)**2
Let u(w) = -21*w**4 - 71*w**3 + 228*w**2 - 31*w + 7. Let h(f) = 49*f**4 + 165*f**3 - 526*f**2 + 72*f - 16. Let a(m) = -7*h(m) - 16*u(m). Factor a(p).
-p*(p - 1)*(p + 4)*(7*p - 2)
Find n, given that 1/5*n**5 - 39/5*n**4 + 178/5*n**3 + 0 + 136/5*n - 276/5*n**2 = 0.
0, 1, 2, 34
Factor 201*s + 9*s**3 - 11760 - 1986*s - 10*s**3 + 153*s**2 + 273*s - 2*s**3.
-3*(s - 28)**2*(s + 5)
Let p = -3835 - -3839. Let k(m) be the first derivative of -1/14*m**p + 1/21*m**6 + 0*m**2 + 2/35*m**5 - 14 - 2/21*m**3 + 0*m. Factor k(s).
2*s**2*(s - 1)*(s + 1)**2/7
Let s(j) be the first derivative of j**5/5 + j**4 - 49*j**3 + 49*j**2 + 2744*j - 3697. Factor s(n).
(n - 7)**2*(n + 4)*(n + 14)
Suppose 0 = -5*k + 2*k - 2*g + 8, 5*k + 5*g - 15 = 0. What is h in -19*h + 5*h**2 - h**3 + 15*h - h**k = 0?
0, 2
Let w = 36308 - 36306. Factor 3/8*g**w + 9/2 - 3*g.
3*(g - 6)*(g - 2)/8
Let d(f) = 3*f**3 + 251*f**2 + 2275*f + 3595. Let y(r) = 2*r**3 + 126*r**2 + 1138*r + 1798. Let s(m) = -2*d(m) + 5*y(m). Factor s(o).
4*(o + 2)*(o + 15)**2
Let w(j) be the first derivative of j**7/2100 + j**6/100 + 23*j**5/300 + j**4/4 + 20*j**3 + 146. Let p(h) be the third derivative of w(h). Solve p(x) = 0.
-5, -3, -1
Suppose 72 = 112*z + 67 - 331. Let i(k) be the third derivative of -1/27*k**z - 1/54*k**4 + 0*k + 0 + 33*k**2 + 4/45*k**5. Factor i(c).
2*(4*c - 1)*(6*c + 1)/9
Let d(r) be the first derivative of -r**3/5 + 3*r**2/10 + 144*r - 2497. Solve d(z) = 0.
-15, 16
Let g(n) = -10*n**2 - 2*n. Let k(x) = -22*x**2 - 2404*x + 4808. Let r(c) = -4*g(c) + 2*k(c). Find j such that r(j) = 0.
-1202, 2
Factor 360*n + 870 - 129*n**4 + 30 + 125*n**4 - 40*n**3 - 64*n**2.
-4*(n - 3)*(n + 3)*(n + 5)**2
Suppose 7*h = -1 + 15. What is v in -46*v - 85*v**2 - 10*v - v**3 - h*v**3 + 61*v**2 + 8*v = 0?
-4, 0
Let -2216/11*g - 2/11*g**2 - 613832/11 = 0. Calculate g.
-554
Let u = 104/1571 - -12048/7855. Let 0 + 2*v**2 - u*v**4 + 3/10*v**3 + 1/2*v**5 - 2/5*v = 0. What is v?
-1, 0, 1/5, 2
Factor -456/5*z - 92/5 + 9/5*z**3 - 187/5*z**2.
(z - 23)*(z + 2)*(9*z + 2)/5
Let m = 37 - 71. Let t be (-72)/(-48)*(-1 - m/6). Let -4 - 4*a**2 - a**2 - 18*a - 10*a**2 + t*a**2 = 0. What is a?
-2, -1/4
Let u be (-2)/(-40) + 5/(-1000)*-10. Let c(z) be the first derivative of u*z**4 - 2/5*z**3 + 0*z + 2/5*z**2 + 39. Find y, given that c(y) = 0.
0, 1, 2
Suppose 35 = 5*x, -5*u + 38 = -0*x + 4*x. Let b(g) be the first derivative of -15 - 1/8*g**u + 0*g + 1/2*g**3. Let b(a) = 0. Calculate a.
0, 1/6
Suppose -3*t - 5*s + 5 + 11 = 0, 2*t - 4*s + 4 = 0. Suppose f = t*q - 3*f - 2, 1 = 2*q - 5*f. Factor 144*h - 138*h - 3*h**3 - 3*h**2 + 0*h**q.
-3*h*(h - 1)*(h + 2)
Let o(c) be the first derivative of -c**5/50 + 8*c**4/15 + 252*c - 212. Let h(x) be the first derivative of o(x). Suppose h(u) = 0. What is u?
0, 16
Let r(w) = 12*w**3 - 3729*w**2 + 7485*w - 3732. Let t(a) = -3*a**3 + 933*a**2 - 1871*a + 933. Let y(g) = -2*r(g) - 9*t(g). Factor y(p).
3*(p - 311)*(p - 1)**2
Solve 3234/5 + 3232/5*j - 2/5*j**2 = 0 for j.
-1, 1617
Let c = 1797621 + -1797618. Determine g so that 10 - 44*g + 37/5*g**c - 9/10*g**4 - 61/10*g**2 = 0.
-2, 2/9, 5
Let n(h) be the third derivative of -h**7/10 - 127*h**6/40 - 137*h**5/20 - 17*h**4/8 - 10587*h**2. Find c such that n(c) = 0.
-17, -1, -1/7, 0
Factor 562576*n**2 + 6*n**4 - 98176*n**2 + 142241172 - 2620*n**3 - 28992320*n - 4*n**4 + 61296748 + 3*n**4.
5*(n - 172)**3*(n - 8)
Let i(v) be the second derivative of -1/5*v**5 - 2*v**4 + 0*v**2 - 10/3*v**3 - 178*v + 0. Factor i(w).
-4*w*(w + 1)*(w + 5)
Let r(c) be the third derivative of -c**5/20 + 12*c**4 + 4*c**2 - 20. Factor r(j).
-3*j*(j - 96)
Determine m, given that -94/19 - 6*m - 20/19*m**2 = 0.
-47/10, -1
Let k be (-4)/16 + 105/20. Solve 21*n - 21*n - 11*n**k + 13*n**5 - 2*n**3 = 0 for n.
-1, 0, 1
Factor 352 + 68/7*z - 2/7*z**2.
-2*(z - 56)*(z + 22)/7
Let q(w) be the third derivative of 4*w**5/15 + w**4/6 - 12*w**3 - 3*w**2 - 50*w. Suppose q(z) = 0. Calculate z.
-9/4, 2
Suppose 9*d = -5 + 59. Suppose -3*a + 6 = -7*x + 2*x, 3*a - 2*x = d. Factor 4*s**a - 4*s - 5*s + 32*s**4 + 9*s + 22*s**3 + 14*s**5.
2*s**2*(s + 1)**2*(7*s + 2)
Let h = -93 + 95. Let r be 75/2 - 3/h. Find s, given that -r*s + 3*s**2 - 38*s + 65*s = 0.
0, 3
Let o = -40883 - -40887. Factor -2 - 17/3*w**2 - 1/3*w**o - 7/3*w**3 - 17/3*w.
-(w + 1)**2*(w + 2)*(w + 3)/3
Let g(z) = z**2 - 2*z. Let d(p) = -20*p**2 + 85*p. Let i(r) = d(r) + 15*g(r). Let j(t) = 10*t**2 - 110*t. Let w(q) = -5*i(q) - 3*j(q). Factor w(k).
-5*k*(k - 11)
Let b be (263/(-5) - -95) + 3*2. Find d, given that 2/5*d**2 - 44/5*d + b = 0.
11
Suppose -2*k = -4*f + 8, -640*k = -3*f - 643*k + 6. Let m(n) be the first derivative of 1/21*n**3 + 4/7*n**f + n + 12. Let m(s) = 0. Calculate s.
-7, -1