rst derivative of -9 - 2/35*l**5 + 1/7*l**4 + 0*l - 2/21*l**3 + 0*l**2. Factor n(k).
-2*k**2*(k - 1)**2/7
Suppose -20*l = -23*l. Let t(i) be the third derivative of 1/24*i**4 + l + 0*i**3 + 0*i + 1/60*i**5 - i**2. Let t(a) = 0. What is a?
-1, 0
Suppose -4*n + 2*q = -3*q - 1, 20 = -5*n + 2*q. Let f(x) = 4*x**3 + 6*x**2 - 10*x. Let k(l) = l**3 - l. Let c(y) = n*k(y) + f(y). Suppose c(b) = 0. Calculate b.
0, 1, 2
Let u be (27/(-15))/((-5)/75). Find x, given that -4*x**2 + 0*x**3 - 6*x**2 - 8*x**2 - 12 - u*x - 3*x**3 = 0.
-4, -1
Let k(w) be the second derivative of -w**6/840 + w**5/420 + w**4/42 - 2*w**3/21 - 4*w**2 - 2*w. Let z(j) be the first derivative of k(j). Factor z(o).
-(o - 2)*(o - 1)*(o + 2)/7
Suppose g + 0 = 4. Let b be g/(-14)*42/(-18). What is n in 2/3*n**2 + b*n - 2/3 - 2/3*n**3 = 0?
-1, 1
Suppose 5*i = -w - 0 + 6, 0 = -4*w + 2*i + 24. Let s(x) be the third derivative of 0*x**3 + 1/720*x**w + 1/360*x**5 - 3*x**2 + 0*x - 1/72*x**4 + 0. Factor s(k).
k*(k - 1)*(k + 2)/6
Let p(k) be the second derivative of k**4/42 - k**3/7 + 2*k**2/7 + k. Let p(v) = 0. What is v?
1, 2
Let c be 3 - (0/(-4) + 1). Let k be 11/6 + 1/2. Factor 0*d + 0 + k*d**4 + 5/3*d**3 - 2/3*d**c.
d**2*(d + 1)*(7*d - 2)/3
Let v(l) be the second derivative of 3*l**5/40 - l**3/4 + 9*l. Suppose v(x) = 0. Calculate x.
-1, 0, 1
Let n(w) = -w**3 + 8*w**2 + 6*w + 27. Let o be n(9). Let g(v) be the third derivative of -1/120*v**5 + o*v + 0*v**3 - v**2 + 0 + 1/72*v**4. Factor g(j).
-j*(3*j - 2)/6
Let g = 158 - 153. Factor -4/3*p - 10/3*p**4 - 14/3*p**2 - 2/3*p**g - 6*p**3 + 0.
-2*p*(p + 1)**3*(p + 2)/3
Factor 6*r - 3 - 10*r**2 + 3 + 6*r**2.
-2*r*(2*r - 3)
Suppose 16/7*r - 32/7 + 2/7*r**3 + 2*r**2 = 0. What is r?
-4, 1
Let i(y) be the third derivative of 1/12*y**4 + 0*y**3 - 2/15*y**6 + 0*y + y**2 - 1/12*y**5 + 0 - 3/70*y**7. Factor i(a).
-a*(a + 1)**2*(9*a - 2)
Let z(g) be the second derivative of 5/6*g**4 + 1/10*g**5 + 7/3*g**3 + 3*g**2 + 0 - 9*g. Let z(k) = 0. What is k?
-3, -1
Let x(c) be the first derivative of c**3/15 - c**2/10 - 14. Factor x(v).
v*(v - 1)/5
Suppose -4*z + k = 4, -7 = 4*z + 4*k - 23. Let z*d + 0 - 1/2*d**2 = 0. Calculate d.
0
Let t(g) = -8. Let q(c) = -15. Let r(m) = 6*q(m) - 11*t(m). Let n(s) = s**3 + s**2 - s + 6. Let w(z) = -2*n(z) - 7*r(z). Determine a so that w(a) = 0.
-1, 1
Let c(q) be the first derivative of -1/5*q**5 + 1/3*q**3 + 1/2*q**2 + 0*q + 3 - 1/4*q**4. Factor c(s).
-s*(s - 1)*(s + 1)**2
Factor -4*v**2 + 2*v**2 - 12*v - 2*v + 26*v - 18.
-2*(v - 3)**2
Let p be ((-3)/354)/(1 - 2). Let u = 937/826 + p. Suppose -u - 24/7*c - 18/7*c**2 = 0. Calculate c.
-2/3
Solve -87*s**4 + 66*s**4 + 0*s**2 + 0*s**2 - 9*s**3 = 0.
-3/7, 0
Let k(c) be the first derivative of c**4/2 + 4*c**3/3 + c**2 - 7. Factor k(z).
2*z*(z + 1)**2
Let b(p) be the second derivative of 4*p - 1/54*p**4 + 1/9*p**2 + 1/27*p**3 + 0 - 1/90*p**5. Factor b(z).
-2*(z - 1)*(z + 1)**2/9
Let h(d) = 3*d**3 - 10 + 12 + 0*d**3 - 2*d**3 - 15*d**2 + 14*d. Let f be h(14). Factor 1/4*b**3 + 0*b - 1/4*b**4 + 0*b**f + 0.
-b**3*(b - 1)/4
Let q(i) be the second derivative of i**6/135 - i**5/45 + i**4/54 + 7*i. Factor q(m).
2*m**2*(m - 1)**2/9
Let z(d) = d + 6. Let u = -38 + 34. Let t be z(u). Let 1/3*c**3 + 0*c + 2/3*c**t + 0 = 0. What is c?
-2, 0
Let f = -115 + 118. Factor 6/7*u**f + 0 + 2/7*u**4 + 4/7*u**2 + 0*u.
2*u**2*(u + 1)*(u + 2)/7
Let u be 52/24 + (-3)/18. Let a(d) be the first derivative of -2 - 1/2*d**u - 1/3*d**3 + 2*d. Factor a(o).
-(o - 1)*(o + 2)
Let i(p) be the first derivative of p**8/16 + 8*p**7/35 + 11*p**6/40 + p**5/10 + p**2 - 5. Let c(b) be the second derivative of i(b). Factor c(d).
3*d**2*(d + 1)**2*(7*d + 2)
Let g(z) be the third derivative of 2*z**7/105 - z**5/15 - 2*z**2. Factor g(x).
4*x**2*(x - 1)*(x + 1)
Let c = -63 - -94. Suppose 2*s + 2*s + 3*a = -7, -3*s = -5*a - c. Find r, given that 3*r**s + 2 + r - 5*r - r**2 = 0.
1
Suppose -q + 1 = -5*q + 5*p, -5*q = -2*p - 20. Suppose -4*u + u = -q. Factor 2/3*b**u + 0 + 4/3*b.
2*b*(b + 2)/3
Let g be 1/(3/((-12)/(-2))). Suppose 5*d - 60 = 5*w, -g*w - w = 2*d - 24. Factor 4 - 6*v + v**5 + 8*v - 8*v**3 + 8*v**4 + v**5 - d*v**2 + 4*v**5.
2*(v - 1)*(v + 1)**3*(3*v - 2)
Let 15*g**2 + 10*g - 19*g**2 - 6*g = 0. What is g?
0, 1
Let g(j) be the first derivative of -3*j**4/20 + 3*j**3/5 - 3*j**2/5 + 5. Let g(c) = 0. Calculate c.
0, 1, 2
Let 5*p**2 + 40*p - 10*p - 5*p**3 + 124 - 124 = 0. What is p?
-2, 0, 3
Let y(p) be the third derivative of p**6/240 + p**5/60 + p**4/48 + 9*p**2. Factor y(f).
f*(f + 1)**2/2
Let b be 7/((-294)/(-26)) - 2/6. Determine m, given that b*m - 8/7*m**2 + 0 + 6/7*m**3 = 0.
0, 1/3, 1
Let h(b) = -2*b**2 - 5*b + 2. Let y be (-1)/(2/(-12)*1). Let s(k) = 0 + 2 - 2*k**2 - 78*k + 72*k. Let c(w) = y*h(w) - 5*s(w). What is v in c(v) = 0?
-1, 1
Suppose 2*s + 30 - 6 = 0. Let j be (2/s)/((-9)/27). Factor -1/2*g**4 + 0 - 1/2*g + 1/2*g**3 + j*g**2.
-g*(g - 1)**2*(g + 1)/2
Let q = 1 + 1. Let -q*r**2 - 1 + 2*r**3 - 2 + 3 = 0. What is r?
0, 1
Let n be (2/6*0)/(0 - 2). Let f(o) be the second derivative of -2*o + 1/3*o**3 + 1/4*o**4 + n - 1/2*o**2. Factor f(p).
(p + 1)*(3*p - 1)
Let n be (-8)/(68/(-16) - -4). Let z = 32 - n. Find d such that -2/5*d**2 + 0 + z*d + 2/5*d**3 = 0.
0, 1
Let n(t) be the first derivative of -2*t**6/3 + 3*t**4 + 8*t**3/3 + 11. Let n(i) = 0. Calculate i.
-1, 0, 2
Let k be 11/(-44) - 449/(-4). Suppose -k*y + 112*y + y**2 = 0. Calculate y.
0
Let r(w) be the first derivative of w**5/10 + 2*w**4/3 + 4*w**3/3 - w + 1. Let z(v) be the first derivative of r(v). Factor z(j).
2*j*(j + 2)**2
Let u(f) be the first derivative of -2*f**5 - f**4/2 + 10*f**3/3 + f**2 + 3. Let u(r) = 0. What is r?
-1, -1/5, 0, 1
Let f(a) = 2*a**3 + 12*a**2 - 2*a - 4. Let t(m) = -6*m**3 - 35*m**2 + 6*m + 13. Let p(l) = -11*f(l) - 4*t(l). Solve p(r) = 0 for r.
-4, -1, 1
Let d(y) be the first derivative of -2*y**3/15 - y**2/5 - 7. Let d(g) = 0. What is g?
-1, 0
Let r(o) be the third derivative of -2*o**2 - 1/40*o**5 - 1/224*o**8 + 0 + 0*o**3 - 3/140*o**7 - 3/80*o**6 + 0*o + 0*o**4. Suppose r(l) = 0. Calculate l.
-1, 0
Let m(w) be the second derivative of 5/39*w**3 - 2/39*w**4 - 2*w + 0 - 2/13*w**2 + 1/130*w**5. Factor m(d).
2*(d - 2)*(d - 1)**2/13
Suppose 5*n + 15 = -7*u + 2*u, 0 = 2*u + 4*n + 16. Factor 2*m**u + 0 + 1/2*m.
m*(4*m + 1)/2
Let q be 6/10*((-56)/(-24) + 1). Suppose 2*v - 5*v = 0. Find p such that 1/2*p**q - 1/2*p**4 + v - 1/2*p**3 + 1/2*p = 0.
-1, 0, 1
Let v(y) be the second derivative of -y**6/15 + y**5/6 - y**4/12 - 3*y**2/2 + 3*y. Let j(c) be the first derivative of v(c). Suppose j(a) = 0. Calculate a.
0, 1/4, 1
Factor 3*m**3 - 3*m**3 + m**3 - 2*m**3.
-m**3
Let m(x) = -7*x + 4. Let d be m(7). Let b be (-8)/90*d/18. Factor 0 - b*u - 2/9*u**2.
-2*u*(u + 1)/9
Let f(d) be the second derivative of 0 - 3*d - 1/4*d**2 - 1/24*d**3 + 1/48*d**4. Suppose f(j) = 0. Calculate j.
-1, 2
Let n(t) be the second derivative of -t**8/3360 - t**7/420 - t**6/180 - t**4/12 - 2*t. Let b(w) be the third derivative of n(w). Solve b(v) = 0 for v.
-2, -1, 0
Suppose 3*x = -t - 4*t - 7, -4*x - 5*t - 6 = 0. Let s be 2 + x/(-3) + -1. Factor 1/3*f**4 - 2/3*f**3 + 1/3*f + 1/3 - s*f**2 + 1/3*f**5.
(f - 1)**2*(f + 1)**3/3
Let t = 39 - 35. Let s(y) be the second derivative of y - 2*y**2 - y**3 - 1/6*y**t + 0. Solve s(l) = 0 for l.
-2, -1
Let i(y) be the first derivative of y**4 - 4*y**3 + 4*y**2 + 3. Suppose i(w) = 0. Calculate w.
0, 1, 2
Let g(k) = k**3 - 8*k**2 - 7*k - 10. Let v be g(9). Suppose -4*b = -m - 0*m + v, b + 9 = 2*m. Factor -h**5 - 2*h**m - 9*h**3 + 8*h**3 + 0*h**5.
-h**3*(h + 1)**2
Factor 1/3*h**2 - 1/3 + 1/3*h**3 - 1/3*h.
(h - 1)*(h + 1)**2/3
Let g(x) be the third derivative of -x**9/945 + x**8/240 - x**7/315 - x**6/180 + 5*x**4/24 + 5*x**2. Let c(s) be the second derivative of g(s). Factor c(w).
-4*w*(w - 1)**2*(4*w + 1)
Suppose -2*l + 25 = -21. Suppose 5 = 4*d + 4*r + 1, -2*d = -5*r - l. Factor 2*u**d + 3*u**4 + u**5 - 4*u**4.
u**4*(u + 1)
Let g(z) be the third derivative of z**6/200 - z**5/100 - 3*z**2. Factor g(f).
3*f**2*(f - 1)/5
Let q(z) be the first derivative of 3*z**5/70 + z**4/6 - 4*z**2/7 + 6*z + 5. Let c(w) be the first derivative of q(w). Let c(a) = 0. What is a?
-2, -1, 2/3
Suppose 2*c - 8 = 2*r + 4, -8 = -c + 2*r. Factor 3/4*n**c + 9/4