 = 8*j**3 - 27*j**2 + 48*j. Let r(x) be the second derivative of 7*x**5/20 - 7*x**4/3 + 47*x**3/6 + 2*x. Let z(k) = 3*r(k) - 2*v(k). Solve z(s) = 0.
0, 3
Let k be ((-250)/(-20) - 9) + 0 + 1/(-2). Let c = 6 + -6. Determine y, given that 0*y + 0 + c*y**k + 4/3*y**4 - 4/3*y**2 = 0.
-1, 0, 1
Suppose -17*q = -12*q - 20. Factor 20*x**2 + 12*x**q - 28*x**3 - 39*x - 45*x + 80*x.
4*x*(x - 1)**2*(3*x - 1)
Let f(v) be the first derivative of 2*v**3/21 + 4*v**2/7 - 10*v/7 - 526. Let f(i) = 0. Calculate i.
-5, 1
Let m(g) = -2*g**2 + 3*g + 2. Let d be m(2). Suppose -2*q + q + 4*q = d. Factor 0*r + 2/9*r**2 + q.
2*r**2/9
Factor -779*d - 339*d + 96*d - 300 - 38*d - 35*d**2.
-5*(d + 30)*(7*d + 2)
Let d be 3/30 - (-1950)/500. Let -2/5*s**d - 54/5*s + 0 - 54/5*s**2 - 18/5*s**3 = 0. What is s?
-3, 0
Let x(j) = 9*j - 17. Let p be x(3). Factor -p*v**4 + 16*v**5 - 9*v**5 - 12*v**5.
-5*v**4*(v + 2)
Let d = -965/8 + 2899/24. Find s such that 0*s**2 + d*s**3 - 1/2*s + 1/3 = 0.
-2, 1
Let y(b) be the first derivative of -1/12*b**4 + 4/9*b**3 + 0*b - 2/3*b**2 + 11. Find m such that y(m) = 0.
0, 2
Suppose -10*n = -9*n - 4. Factor 2*u**n - 67*u**5 - 17*u**4 + 20*u**2 + 62*u**5.
-5*u**2*(u - 1)*(u + 2)**2
Suppose -251 = -35*z - 181. Determine p so that 2/7*p**3 + 16/7*p + 2*p**z - 32/7 = 0.
-4, 1
Let x(k) be the second derivative of -k**4/48 - k**3/8 + 5*k**2/4 - 33*k - 3. Suppose x(a) = 0. What is a?
-5, 2
Let i(j) = -2*j**2 - j + 1. Suppose 0 = 5*p + n - 119, p + 0*n + 3*n = 21. Let f(k) = 17*k**2 - k - 8. Let s(r) = p*i(r) + 3*f(r). Let s(t) = 0. Calculate t.
0, 9
Find g, given that -2/5*g**2 + 2/5*g + 12 = 0.
-5, 6
Let d(t) be the third derivative of t**6/600 + t**5/150 - 7*t**4/120 + 2*t**3/15 - 15*t**2 - t. Factor d(s).
(s - 1)**2*(s + 4)/5
Let q = 711 - 706. Let j(x) be the third derivative of 0*x + 0*x**3 + 0 + 0*x**6 + 1/18*x**4 - 1/30*x**q + 1/315*x**7 - 4*x**2. Factor j(z).
2*z*(z - 1)**2*(z + 2)/3
Let q = -6545 + 6547. What is b in 1/5*b - 4/5*b**4 - 6/5*b**q + 9/5*b**3 + 0 = 0?
0, 1/4, 1
Let g(b) be the first derivative of -3*b**4/4 - 13*b**3 + 3*b**2/2 + 39*b + 48. Determine n, given that g(n) = 0.
-13, -1, 1
Let k(x) be the first derivative of 5/6*x**6 + 5*x**2 - 35/3*x**3 + 4 + 0*x + 45/4*x**4 - 5*x**5. Solve k(w) = 0 for w.
0, 1, 2
Let k = 376/33 + -6749/99. Let g = k - -57. Solve -g*l**2 - 4/9*l - 2/9 = 0 for l.
-1
Let a(s) be the first derivative of -s**6/3 - 2*s**5/5 + 3*s**4 + 8*s**3/3 - 8*s**2 + 63. Suppose a(o) = 0. Calculate o.
-2, 0, 1, 2
Let t(p) be the third derivative of p**7/105 + 3*p**6/20 + p**5/2 + 7*p**4/12 + 104*p**2 + 2*p. Solve t(k) = 0 for k.
-7, -1, 0
Let v be (-12)/(-10) + (1110/(-840))/(15/12). Determine h, given that 0 - 1/7*h**4 + v*h**2 - 1/7*h + 1/7*h**3 = 0.
-1, 0, 1
Let p(f) be the first derivative of -2*f**3/21 + 10*f**2/7 - 18*f/7 + 857. Factor p(r).
-2*(r - 9)*(r - 1)/7
Let t(u) = -u - 3. Let p be t(-5). Let i(o) = 4*o - 2*o**2 + 3 - 8*o + o**p. Let d(k) = 7*k**2 + 25*k - 19. Let w(z) = 6*d(z) + 39*i(z). Factor w(y).
3*(y - 1)**2
Let q be 86/12 - 4 - (-1)/(-6). Factor 22*c**q - 17*c**3 - 5*c + 5*c**2 + 3 - 3 - 5.
5*(c - 1)*(c + 1)**2
Factor 0*t**2 + 0 + 2/5*t**4 + 0*t - 1/5*t**5 + 3*t**3.
-t**3*(t - 5)*(t + 3)/5
Suppose 14*s = 11*s - 45. Let w be 93/180 + s/12 + 1. Factor -2/15 + 0*r**2 + w*r + 2/15*r**4 - 4/15*r**3.
2*(r - 1)**3*(r + 1)/15
Suppose 3*s - 11 + 5 = 0. Let t(g) be the first derivative of -s - 6*g - 2/3*g**3 - 4*g**2. Factor t(w).
-2*(w + 1)*(w + 3)
Let i = 20 + -18. Let k(w) be the third derivative of -1/6*w**3 + 0*w + 1/12*w**4 + 0 - w**i - 1/60*w**5. Factor k(b).
-(b - 1)**2
Let r(m) be the first derivative of -1/9*m**3 + m**2 - 19 - 3*m. Find a, given that r(a) = 0.
3
Let f(d) be the third derivative of 0*d + 1/2*d**4 + 2/35*d**7 - 2/15*d**5 + 0 - 1/84*d**8 + 21*d**2 - 2/3*d**3 - 1/15*d**6. Factor f(c).
-4*(c - 1)**4*(c + 1)
Suppose 2*k**2 - 25 - 51 + 15*k + 4 + k**2 = 0. Calculate k.
-8, 3
Let v be (0 - 3/5)/((-189)/840). Let k(q) be the second derivative of 0 + 1/6*q**4 - 6*q + 16*q**2 + v*q**3. Factor k(w).
2*(w + 4)**2
Let h(t) be the second derivative of -t**7/98 - t**6/7 - 117*t**5/140 - 37*t**4/14 - 34*t**3/7 - 36*t**2/7 + 63*t + 7. Determine k, given that h(k) = 0.
-3, -2, -1
Let d be 10/(-35) - (-1686)/21. Factor -15*j**2 + 7*j**2 + 60*j**3 + 12*j + 45*j**3 + d*j**2.
3*j*(5*j + 2)*(7*j + 2)
Factor 1552*k - 54 - 253*k**2 - 190*k**2 - 112*k + 38*k**2 - 1226.
-5*(9*k - 16)**2
Let x = 50 + -8. Find g, given that 3 - 24*g + 24 - 45*g**2 + x*g**2 = 0.
-9, 1
Suppose 0 = 10*o + 5*o - 90. Let w(i) be the third derivative of -1/4*i**4 - 4*i**2 + 1/40*i**o + 1/20*i**5 + 0*i**3 + 0 + 0*i. Factor w(k).
3*k*(k - 1)*(k + 2)
Let s(y) = y**3 - 25*y**2 - 27*y - 1594. Let v be s(28). Let 9/2 - 15/2*a + 3/2*a**3 + 3/2*a**v = 0. Calculate a.
-3, 1
What is s in -8/11*s + 8/11*s**2 + 6/11*s**3 + 0 - 4/11*s**4 - 2/11*s**5 = 0?
-2, 0, 1
Let f(q) be the first derivative of 2/33*q**3 - 2/55*q**5 - 2 + 0*q + 0*q**2 + 0*q**4. Suppose f(x) = 0. What is x?
-1, 0, 1
Let v(o) be the first derivative of -o**3 + 3*o - 11. Factor v(n).
-3*(n - 1)*(n + 1)
Let p(h) be the first derivative of h**6/360 + h**5/45 + h**4/18 + h**2 + 21. Let w(g) be the second derivative of p(g). Factor w(j).
j*(j + 2)**2/3
Let k(s) be the second derivative of 4*s**2 - 7*s + 1/280*s**6 + 15/56*s**4 + 0 + 9/14*s**3 + 1/20*s**5. Let l(f) be the first derivative of k(f). Factor l(t).
3*(t + 1)*(t + 3)**2/7
Let g(r) = 11 - 8*r + r**3 + 20 + 5*r + 26*r**2 - 23*r. Let b be g(-27). Factor 0 - 2*l**3 + l + 1/2*l**2 - 3/2*l**b.
-l*(l + 1)**2*(3*l - 2)/2
Let t(v) = -8*v**3 - 11*v**2 - 37*v - 29. Let h(o) = -2*o**3 - o**2 - o - 1. Let k(z) = 5*h(z) - t(z). Factor k(u).
-2*(u - 6)*(u + 1)*(u + 2)
Suppose -8*f**4 - 9*f + 6 - 77*f**4 + 3*f**3 - 193*f**3 - 20*f - 21*f**3 - 161*f**2 = 0. What is f?
-1, -3/5, 2/17
Let t(a) be the first derivative of -a**5/15 - a**4/6 + 4*a**3/3 + 2*a**2 - 6. Let f(q) be the second derivative of t(q). Factor f(d).
-4*(d - 1)*(d + 2)
Let r(a) be the first derivative of 11/120*a**5 - 5/48*a**4 - 2 + 3*a**2 - 1/6*a**3 + 0*a + 7/120*a**6. Let s(j) be the second derivative of r(j). Factor s(x).
(x + 1)*(2*x - 1)*(7*x + 2)/2
Let s be 6 + 0 + -3 + 1. Suppose s*f = f + 6. Determine a so that a + a - 3*a**f - 3 + 4*a = 0.
1
Let x = -105260/9 + 31158031/2664. Let h = x + -1/37. Factor -33/4*u**2 - 51/8*u**4 - 21/2*u**3 - 3*u - h - 3/2*u**5.
-3*(u + 1)**4*(4*u + 1)/8
Let d(x) = x**3 - 108*x**2 + 2706*x - 27006. Let n(s) = 2*s**3 - 219*s**2 + 5413*s - 54013. Let i(y) = 13*d(y) - 6*n(y). Factor i(r).
(r - 30)**3
Let h(d) be the third derivative of -2/3*d**3 + 0*d + 3/4*d**4 + 1/15*d**7 - 1/6*d**5 + 0 + 25*d**2 - 3/20*d**6. What is a in h(a) = 0?
-1, 2/7, 1
Let r(b) be the second derivative of -1/12*b**4 + 0*b**2 + 0 + 5*b + 2/3*b**3. Factor r(p).
-p*(p - 4)
Suppose 2/11*g**4 + 6/11*g**2 + 0 - 10/11*g**3 + 18/11*g = 0. Calculate g.
-1, 0, 3
Let w(h) = 12*h + 458. Let o be w(-38). Factor -3/5*b + 0 + 3/5*b**o.
3*b*(b - 1)/5
Solve -6*k + 39/5*k**2 + 108/5*k**3 - 12*k**5 + 0 - 21/5*k**4 = 0 for k.
-1, 0, 2/5, 5/4
Let k be 117/(-2106) + (22/18 - 1). Let f(t) be the first derivative of -4/3*t**3 - 8/3*t - 1 + k*t**4 + 3*t**2. Suppose f(p) = 0. Calculate p.
1, 4
Let m(u) be the second derivative of 98*u**6/3 - 119*u**5 + 1865*u**4/12 - 85*u**3 + 45*u**2/2 + 46*u + 4. Factor m(s).
5*(s - 1)**2*(14*s - 3)**2
Let h(n) be the first derivative of -n**6/150 - n**5/15 - 7*n**4/30 - 2*n**3/5 - 11*n**2/2 + 6. Let s(j) be the second derivative of h(j). Factor s(v).
-4*(v + 1)**2*(v + 3)/5
Let c(n) be the third derivative of 1/3*n**3 + 1/10*n**6 + 0 - 1/4*n**4 - 11*n**2 + 1/105*n**7 - 1/56*n**8 - 1/15*n**5 + 0*n. Solve c(j) = 0 for j.
-1, 1/3, 1
Let w be 1/(0 + 2/6). Let l be ((-16)/24)/((-6 + w)/18). Solve 2/3*b - 2/3*b**3 + 2*b**2 - 4/3 - 2/3*b**l = 0.
-2, -1, 1
Factor -334*u**2 - 71*u**2 - 553*u**2 - 360*u**3 - 345 - 92*u**2 - 1040*u - 5*u**4.
-5*(u + 1)**3*(u + 69)
Let v(z) be the third derivative of z**8/840 + z**7/175 - z**6/300 - z**5/50 - 20*z**2. Determine a, given that v(a) = 0.
-3, -1, 0, 1
Let h(o) be the third derivative of o**6/80 + 13*o**5/40 - 29*o**4/16 + 15*o**3/4 - 52*o**2 - 2*o. Determine x, given that h(x) = 0.
-15, 1
Let k(q) be the first derivativ