b such that s(b) = 0.
-6
Suppose 4*f = 4*s, -2*s + 12 = 15*f - 13*f. Let d(g) be the first derivative of -7 - 3/14*g**2 - 2/7*g**s - 3/28*g**4 + 0*g. Determine t, given that d(t) = 0.
-1, 0
Let c(t) be the second derivative of -4/15*t**4 - 20*t + 0*t**2 + 2/75*t**6 + 0 - 2/105*t**7 + 4/25*t**5 + 0*t**3. Find v such that c(v) = 0.
-2, 0, 1, 2
Let o(f) be the first derivative of f**4/18 + 88*f**3/27 + 295*f**2/9 + 56*f - 1113. Factor o(q).
2*(q + 1)*(q + 7)*(q + 36)/9
Suppose 2*w = 3*o - 19, -3 = 4*o + 4*w + 5. Let b(v) be the first derivative of -20 + 5/3*v**o - 10*v**2 + 20*v. Let b(q) = 0. Calculate q.
2
Suppose 4/7*c**3 + 297/7*c**2 + 74/7*c + 0 = 0. What is c?
-74, -1/4, 0
Let x(i) = -12*i**2 + 1352*i + 7252. Let p(d) = -2*d**2 + 194*d + 1036. Let o(t) = -20*p(t) + 3*x(t). Factor o(y).
4*(y + 7)*(y + 37)
Let b(j) = -j**3 + 24*j**2 - 10*j - 224. Let x be b(16). Let c = x - 3327/2. Solve -5/2*g + c*g**3 + g**2 - 3 = 0 for g.
-3, -1, 2
Let j be -8 + (-4265)/(-550) - (-2 - -1). Let b = j + 1/22. Factor 12/5*p + 3/5*p**2 - p**3 + b.
-(p - 2)*(p + 1)*(5*p + 2)/5
Let k(i) be the second derivative of i**6/35 - 3*i**5/14 - 3*i**4/2 - 23*i**3/7 - 24*i**2/7 - 6*i + 336. Let k(a) = 0. What is a?
-1, 8
Suppose -7*c = -2*c - 60. Let i(n) = -n**2 + 11*n + 21. Let t be i(c). Suppose 5*r**2 - t + 26 - 10*r - 12 = 0. What is r?
1
Let m(b) be the third derivative of -621/40*b**5 + 0*b**3 - 13/20*b**6 - 1/140*b**7 + 0*b - 92*b**2 + 729/8*b**4 + 0. Factor m(h).
-3*h*(h - 2)*(h + 27)**2/2
Let n(x) be the first derivative of 0*x + 63 + 5/6*x**6 + 2*x**5 + 0*x**3 + 0*x**2 + 5/4*x**4. What is f in n(f) = 0?
-1, 0
Let y(x) be the first derivative of 3*x**5/5 + 45*x**4/4 + 48*x**3 - 96*x**2 + 4112. Factor y(h).
3*h*(h - 1)*(h + 8)**2
Let q(v) be the first derivative of 0*v**2 + 2/27*v**3 + 0*v + 4/27*v**6 + 1/3*v**4 + 2/5*v**5 - 61. Factor q(u).
2*u**2*(u + 1)**2*(4*u + 1)/9
Factor -181092*w + 131561*w**2 - 523000*w**3 - 342541*w**2 - 70268*w + 625*w**4 - 417220*w**2 - 33520.
5*(w - 838)*(5*w + 2)**3
Factor -4/7*l**4 + 34/7*l**2 + 24/7 - 52/7*l + 1/7*l**5 - 3/7*l**3.
(l - 2)**3*(l - 1)*(l + 3)/7
Let k(r) = 29*r**3 + 12*r**2 - 21*r - 40. Let j(o) = -53*o**3 - 24*o**2 + 43*o + 80. Let f(v) = -6*j(v) - 11*k(v). Factor f(t).
-(t - 8)*(t - 5)*(t + 1)
Let s(x) = -x**2 - 6*x + 4. Let v be s(0). Suppose -v*t - 3*p = -t, 4*t = 2*p. Let -1/4*r**3 + t*r - 1/4*r**2 + 0 = 0. What is r?
-1, 0
Suppose 0 = -4*w - 2*k + k + 16, 0 = -4*k + 16. Suppose w = -v - p, 2*p + 7 = -4*v - p. Factor 8*z - 2*z**v + 3 + 4*z**2 + 3 + 0.
2*(z + 1)*(z + 3)
Let p(s) be the second derivative of 5*s**7/42 - 2*s**6 - 107*s**5/4 - 35*s**4/2 + 1030*s**3/3 + 900*s**2 + 846*s. Suppose p(w) = 0. Calculate w.
-5, -2, -1, 2, 18
Let l be ((-2)/2 - 14/(-9))/(991/29730). Determine d, given that -l*d**3 + 10*d**2 - 4 + 50/3*d - 6*d**4 = 0.
-3, -1, 2/9, 1
Solve 2753 + 48*z + 2718 - 18*z**2 - 5503 = 0.
4/3
Let z(r) be the third derivative of 1/15*r**5 + 150*r**3 + 4*r**2 + 5*r**4 + 0*r - 5. Let z(d) = 0. Calculate d.
-15
Factor 20972*p - 20966*p + 189*p**3 + 22*p**2 - 217*p**2.
3*p*(p - 1)*(63*p - 2)
Factor -3/4*t**2 - 12156507/4 - 6039/2*t.
-3*(t + 2013)**2/4
Let p(v) be the second derivative of -v**5/4 + 3125*v**4/12 + 5*v**3/6 - 3125*v**2/2 + 2*v + 562. Find y, given that p(y) = 0.
-1, 1, 625
Suppose 5*w = -3*o + 13, -7*o + 2*o = 5*w - 5. Suppose -36 = -5*l - 4*n, 0 = w*l - 4*l - n. Factor -l*p - 2*p + 0*p - 23*p**2 + 20*p**2.
-3*p*(p + 2)
Suppose -49 - 12 = -3*h - 4*x, -h = 3*x - 27. Suppose -20 = 10*g - h*g. Factor -2/3*n + 2/3*n**3 + 2/3*n**2 + 0 - 2/3*n**g.
-2*n*(n - 1)**2*(n + 1)/3
Let v = 502/45 - 6436/585. Factor 2/13*z**3 + 20/13 - v*z - 20/13*z**2.
2*(z - 10)*(z - 1)*(z + 1)/13
Let o(n) be the first derivative of -n**6/2 + 42*n**5/5 + 51*n**4/4 - 30*n**3 - 3658. Suppose o(y) = 0. Calculate y.
-2, 0, 1, 15
Let u(g) = 4*g - 10. Let n = 71 + -68. Let r be u(n). Factor 3*x + 2*x**3 + 2 + 122*x**r - 5*x**3 - x**4 - 123*x**2.
-(x - 1)*(x + 1)**2*(x + 2)
Let w be (-16)/(-72) + 1426/(-18) + -2. Let v = w - -84. Factor 3*f**2 - 11*f**5 + 23*f - 3*f**4 - 17*f + 14*f**5 - 9*f**v.
3*f*(f - 2)*(f - 1)*(f + 1)**2
Let o(f) be the first derivative of 826*f**3/39 - 1237*f**2/13 - 12*f/13 - 2037. Determine a so that o(a) = 0.
-2/413, 3
Let v(d) = d**5 + d**3 + d**2 + 3*d + 1. Let c(w) = 15*w**5 - 5*w**4 - 10*w**3 + 30*w**2 + 30*w + 10. Let i(q) = c(q) - 10*v(q). Factor i(u).
5*u**2*(u - 2)*(u - 1)*(u + 2)
Factor -42320*j + 0 + 4/5*j**4 - 1844/5*j**3 + 42688*j**2.
4*j*(j - 230)**2*(j - 1)/5
Solve 2/9*a**3 - 52/9*a**2 - 22/3*a + 36 = 0.
-3, 2, 27
Let p(n) = -17*n**2 + 19*n - 65. Let q(x) = -15*x**2 + 12*x - 66. Let f(m) = -6*p(m) + 7*q(m). Factor f(i).
-3*(i + 4)*(i + 6)
Let c = 43179 - 43177. Factor 3/7*o - 6/7 + 6/7*o**c - 3/7*o**3.
-3*(o - 2)*(o - 1)*(o + 1)/7
Let w(a) be the first derivative of -4*a**5/5 - 2*a**4 + 4*a**3 + 8*a**2 - 16*a + 6055. Factor w(d).
-4*(d - 1)**2*(d + 2)**2
Let u be (-360)/(-260) + 80/130. Factor 1/9*g**u + 50/9*g + 625/9.
(g + 25)**2/9
Let d(m) be the first derivative of 2*m**5/15 - 2*m**4 + 68*m**3/9 + 4*m**2 - 70*m/3 + 3623. Find o such that d(o) = 0.
-1, 1, 5, 7
Factor 23296*n - 50/3*n**4 - 4704 - 84848/3*n**2 - 4160/3*n**3.
-2*(n + 42)**2*(5*n - 2)**2/3
Suppose -713 + 745 = 8*p. What is k in 7/2*k - 1/4*k**p + 1/2*k**3 + 5/4 + 3*k**2 = 0?
-1, 5
Suppose -15*h + 871 = -254. Determine s, given that 765*s**2 + 291*s**3 + 540*s + 60 + 249*s**3 + 80*s**4 - 100*s**3 + h = 0.
-3, -1, -3/4
Let s be 114/627 - (-2)/(-132). Let j(g) be the first derivative of 0*g - 1/27*g**3 - 1/5*g**5 + 0*g**2 + s*g**4 - 23. Solve j(c) = 0.
0, 1/3
Suppose 827*u**2 - 224 + 839*u**2 - 564*u - 1676*u**2 = 0. What is u?
-56, -2/5
Let s(l) be the third derivative of -l**5/40 - 13*l**4/8 - 169*l**3/4 + 2*l**2 + 290. Factor s(r).
-3*(r + 13)**2/2
Let r be 132/(-315) + 10/75 - (-12576)/5502. What is v in -529/2*v + 0 - 9/2*v**3 - 69*v**r = 0?
-23/3, 0
Factor -46/3*r**2 - 2/3*r**3 + 184/3 + 8/3*r.
-2*(r - 2)*(r + 2)*(r + 23)/3
Let y(o) be the third derivative of 1/20*o**5 + 0 - 5*o**2 - 2*o + 1/4*o**4 + 0*o**3 - 3/40*o**6. Find q such that y(q) = 0.
-2/3, 0, 1
Suppose -4*d = -4*h - 32, 24 = 5*d - 3*h - 12. Let t = 24 + d. Factor 27*w**4 - 27*w**3 + 21*w**5 + 14 - 34 + 8 - 72*w - t*w**3 - 123*w**2.
3*(w - 2)*(w + 1)**3*(7*w + 2)
Let d(o) be the second derivative of -66*o - 1/3*o**3 - 1/12*o**4 - 2 + 1/40*o**5 + 1/120*o**6 + 0*o**2. Suppose d(t) = 0. What is t?
-2, 0, 2
Let v(k) be the first derivative of -8/9*k - 4/9*k**2 - 200 + 1/18*k**4 + 2/27*k**3. Determine o, given that v(o) = 0.
-2, -1, 2
Let p(x) be the second derivative of x**5/100 + 59*x**4/60 - 2*x**3 - 9*x - 72. Solve p(v) = 0.
-60, 0, 1
Let i(m) = -2*m**3 + 910*m**2 + 35568*m + 34656. Let z(a) = -a**3 + 303*a**2 + 11856*a + 11552. Let j(q) = 3*i(q) - 8*z(q). Determine r, given that j(r) = 0.
-76, -1
Let d(r) = 2*r**2 - 70*r + 50. Let x(j) = -j**2 + 36*j - 27. Let o(a) = 4*d(a) + 9*x(a). Factor o(g).
-(g - 43)*(g - 1)
Let n be (-112)/(-20)*10/(-4)*(39 + -711). Suppose 36*i**2 + 1008*i + n + 3/7*i**3 = 0. Calculate i.
-28
Suppose 17*i = 6*i + 990. Let d be 645/189 - (-40)/i. Suppose 18/7*q**2 + 24/7 - 60/7*q + d*q**3 = 0. What is q?
-2, 2/3
Suppose 8*c - 2*k = 5*c + 85, -2*k = -5*c + 135. Suppose c*r = -33 + 108. Determine m so that 1/4*m**r + m**2 + 1/2 + 5/4*m = 0.
-2, -1
Let w(o) = -129*o**3 - 153765*o**2 - 43908*o - 90. Let q(h) = 37*h**3 + 43932*h**2 + 12545*h + 25. Let j(s) = -18*q(s) - 5*w(s). Let j(l) = 0. What is l?
-1045, -2/7, 0
Let c(y) = -4*y**3 + 77*y**2 - 256*y - 13. Suppose 8 - 62 = -9*a. Let n(d) = -d**3 + 19*d**2 - 64*d - 3. Let v(o) = a*c(o) - 26*n(o). Find r such that v(r) = 0.
0, 8
Factor 3/4*p**2 - 1575/4*p - 789/2.
3*(p - 526)*(p + 1)/4
Let f be -2 - -1*(-5 - (-4 + -1)). Let t be f/16 - (-97)/776. Solve 0*p + t - 3/5*p**2 = 0 for p.
0
Let g(q) be the second derivative of q**4/16 - 197*q**3/4 + 294*q**2 + 2769*q. Suppose g(w) = 0. Calculate w.
2, 392
Let p(u) be the first derivative of u**6/2520 - 13*u**5/840 - 11*u**3 - 34. Let i(v) be the third derivative of p(v). Factor i(w).
w*(w - 13)/7
Suppose -q = -4*g - 3*q + 4, -4*g + 24 = -3*q. Suppose -g*z**3 - 48 + 96 + 7*z**3 - 52*z = 0. What is z?
-4, 1, 3
Let k(a) = 6*a**2 + 7*a + 5. Let p b