Suppose -10 - 9 = -5*o - 3*m, 4*m = 12. Factor 0*w + w + w**o - s*w.
w*(w - 1)
Let l(n) = -n**2 - 5*n + 6. Let y be l(-6). Determine w so that 4*w**2 + 7*w**3 + 5*w**4 + y*w**5 - w**4 - w**3 + w + w**5 = 0.
-1, 0
Let q(k) be the third derivative of 0*k + 3*k**2 - 3/70*k**7 - 3/10*k**5 + 0 + 1/5*k**6 + 0*k**4 + 1/2*k**3. Factor q(m).
-3*(m - 1)**3*(3*m + 1)
Let w(x) be the second derivative of x**7/8820 - x**6/2520 - x**4/12 + 2*x. Let r(o) be the third derivative of w(o). Factor r(t).
2*t*(t - 1)/7
Let m(z) be the second derivative of z**7/273 - 2*z**6/195 - z**5/65 + 2*z**4/39 + z**3/39 - 2*z**2/13 + 4*z. Solve m(i) = 0 for i.
-1, 1, 2
Let b(z) be the third derivative of z**8/2016 + z**7/252 + z**6/120 - z**5/90 - z**4/18 - 25*z**2. Factor b(f).
f*(f - 1)*(f + 2)**3/6
Suppose -50*r**3 - 70*r**2 + 8*r**2 - 48*r - 21*r**4 - 13*r**2 - 12 - 3*r**5 - 7*r**3 = 0. What is r?
-2, -1
Let y be (1 - 1) + -4 - (2 + -6). Let p(v) be the first derivative of 0*v**4 + y*v**3 + 0*v**2 + 2 - 2/25*v**5 + 1/15*v**6 + 0*v. What is r in p(r) = 0?
0, 1
Let 8*m**3 + 8*m**2 - 16*m - 3*m**4 + 0*m**5 + 4*m**3 + m**4 - 2*m**5 = 0. Calculate m.
-2, 0, 1, 2
Let v be (-30)/(-18) - 6/4. Let x(i) be the third derivative of -1/60*i**5 + 1/24*i**4 + v*i**3 - i**2 + 0 + 0*i - 1/120*i**6. Factor x(q).
-(q - 1)*(q + 1)**2
Let d(i) be the first derivative of -7*i**4 + 20*i**3/3 + 32*i**2 + 16*i - 14. Factor d(w).
-4*(w - 2)*(w + 1)*(7*w + 2)
Let u(i) be the first derivative of -i**7/840 - i**6/240 + i**5/80 + i**4/24 - i**3/6 - i**2/2 - 5. Let x(b) be the second derivative of u(b). Factor x(d).
-(d - 1)**2*(d + 2)**2/4
Let t(z) be the third derivative of z**8/13440 + z**7/2520 + z**6/1440 - 5*z**4/24 - 4*z**2. Let i(q) be the second derivative of t(q). Factor i(m).
m*(m + 1)**2/2
Factor -10*h**2 + 22*h**2 - 2*h**3 + 0*h**3 - h**3.
-3*h**2*(h - 4)
Let y = 18 - 18. Let m(x) be the first derivative of -1/2*x**4 + 0*x**3 + 0*x**2 - 1 + y*x. Factor m(b).
-2*b**3
Let z = -275 - -1933/7. Factor z*i - 8/7 - 2/7*i**2.
-2*(i - 2)**2/7
Factor 0*p + 0*p**3 + 2/9*p**2 - 1/9*p**4 - 1/9.
-(p - 1)**2*(p + 1)**2/9
Let g(w) be the third derivative of -w**11/110880 - w**10/25200 - w**9/20160 + w**5/15 - 6*w**2. Let b(j) be the third derivative of g(j). Factor b(d).
-3*d**3*(d + 1)**2
Let k(l) be the second derivative of -l**6/15 - 7*l**5/10 - 5*l**4/2 - 3*l**3 + 67*l. Determine w, given that k(w) = 0.
-3, -1, 0
Let p(h) be the third derivative of -1/175*h**7 + 0 + 2/75*h**5 - 1/15*h**3 + 5*h**2 + 0*h - 1/30*h**4 + 1/150*h**6. Solve p(d) = 0.
-1, -1/3, 1
Suppose h - 4*h = -x + 5, -4*h = 4*x - 100. Let n = x - 119/6. Let -n*v**3 + 0 + 1/3*v**2 - 1/6*v = 0. Calculate v.
0, 1
Let t = -539 - -2697/5. Solve -4/5*p**2 + 0 - t*p**3 - 2/5*p = 0 for p.
-1, 0
Let c(w) be the first derivative of -w**2 + 4/5*w**5 + 1/3*w**6 - 4/3*w**3 + 0*w**4 + 0*w + 4. Factor c(u).
2*u*(u - 1)*(u + 1)**3
Let j(b) be the first derivative of -2*b**5/15 + 4*b**3/9 - 2*b/3 - 5. Factor j(s).
-2*(s - 1)**2*(s + 1)**2/3
Let j = -54 - -54. Factor j - 2/7*q**4 - 8/7*q**3 - 8/7*q**2 + 0*q.
-2*q**2*(q + 2)**2/7
Let m(p) be the third derivative of p**5/120 - p**4/24 + p**3/12 + 29*p**2. Find k such that m(k) = 0.
1
Let f(j) be the second derivative of -j**4/4 + 3*j**2/2 - 2*j. Solve f(t) = 0.
-1, 1
Let i(j) be the third derivative of 0*j + 0*j**3 - 1/120*j**5 + 1/480*j**6 + 0 - j**2 + 1/96*j**4. Let i(a) = 0. What is a?
0, 1
Let s = 103/654 - -1/109. Factor 1/6*i**2 + 0 + s*i.
i*(i + 1)/6
Let n(s) be the second derivative of 1/10*s**5 - 1/2*s**2 - 1/6*s**3 - 1/42*s**7 + 3*s + 1/6*s**4 - 1/30*s**6 + 0. Solve n(y) = 0 for y.
-1, 1
Let h(k) be the third derivative of -k**8/1680 - k**7/420 + k**5/60 + k**4/24 - k**3/3 + k**2. Let a(u) be the first derivative of h(u). Factor a(v).
-(v - 1)*(v + 1)**3
Let p be 64/(-2)*3/6. Let t be (-8)/p + 1/(-2). Solve -2/9*u**4 + 4/9*u**3 + t*u + 0 + 0*u**2 = 0 for u.
0, 2
Factor 3*x**2 - x + 17 - 5 - 7*x - 4*x.
3*(x - 2)**2
Let u(b) be the first derivative of 2*b**6/3 + 58*b**5/15 + 15*b**4/2 + 16*b**3/3 + 4*b**2/3 + 18. Solve u(i) = 0.
-2, -1/2, -1/3, 0
Suppose -4*w - 4*n + 13 = -11, 0 = 3*w - n - 2. Factor -1/2*g**w + 0 - 7/4*g**3 + 0*g.
-g**2*(7*g + 2)/4
Let n(o) be the second derivative of o**5/50 - o**4/15 - o**3/5 + 12*o. Factor n(r).
2*r*(r - 3)*(r + 1)/5
Suppose -5*n = -17 + 2. What is h in -5*h**5 - 5 + 6 + 2*h**2 + 5*h - 3*h**4 + 4*h**5 - 2*h - 2*h**n = 0?
-1, 1
Let d(u) be the second derivative of -27*u**6/20 - 81*u**5/20 - 9*u**4/2 - 2*u**3 + 3*u. Factor d(i).
-3*i*(3*i + 2)**3/2
Suppose 0 = -2*c - 0*c + 10. Suppose c*g - 2*g - 3*m - 18 = 0, 4*m = -g - 9. Solve d**3 - 2*d**5 + 0*d**5 - 6*d**g + 8*d**4 - 3*d**3 = 0.
0, 2
Let w(i) be the third derivative of 0 + 1/120*i**4 + 4*i**2 + 0*i**3 + 1/300*i**5 + 0*i. Suppose w(a) = 0. What is a?
-1, 0
Suppose 8 = a + 3*a. Suppose -29*g**3 + 2*g**2 - g + 2*g**4 - 2 + 10*g**4 + 18*g**a = 0. What is g?
-1/4, 2/3, 1
Suppose -2 = -5*f + 3*l + 2, 5*l = -f + 12. Factor -3*w**4 + 1 + 1 - 3*w**2 + w + f*w - 7*w**3.
-(w + 1)**3*(3*w - 2)
Let d(g) = 3*g**5 - 9*g**4 - g**3 + 13*g**2 - 6*g - 4. Let j(p) = -p**3 + p**2 - 1. Let a(w) = -d(w) + 4*j(w). Determine n, given that a(n) = 0.
-1, 0, 1, 2
Let l(u) be the second derivative of u**6/420 + u**5/105 + u**4/84 + u**2/2 - 2*u. Let v(y) be the first derivative of l(y). Let v(d) = 0. What is d?
-1, 0
Factor 2796 + 16*i - 4*i**3 - 2796.
-4*i*(i - 2)*(i + 2)
Let p be 24/10 + -1 + -1. Let j = -2 - -5. Factor 2/5*b - 2/5*b**j + 2/5 - p*b**2.
-2*(b - 1)*(b + 1)**2/5
Suppose 4*k + 2*v = -0*k + 20, -4*k + 3*v = 0. Suppose 2*d + 3*j + 5 = -4, -6 = -k*d + 2*j. Solve z + d*z + 8*z**4 + 8*z**2 + z + 12*z**3 + 2*z**5 = 0 for z.
-1, 0
Suppose -l = m - 6, -2*l + 0 + 8 = 0. Suppose 2*t - 2 - 2 = 0. Solve t*f**4 - m*f**2 + 2*f**3 - f + f - 2*f**5 = 0 for f.
-1, 0, 1
Let k(u) be the first derivative of -u**7/420 + u**5/20 - u**4/6 + 2*u**3 - 7. Let h(s) be the third derivative of k(s). Let h(o) = 0. What is o?
-2, 1
Suppose -i - 31 = -33. Let f(v) be the third derivative of 0*v - 1/24*v**3 - 1/80*v**5 - 1/480*v**6 + 4*v**i - 1/32*v**4 + 0. Find q such that f(q) = 0.
-1
Factor -19*d**3 + 3 + 2*d**2 + 18*d**3 - 5 + d.
-(d - 2)*(d - 1)*(d + 1)
Let h(z) be the third derivative of 0*z + 1/36*z**4 + 5*z**2 + 0 + 1/270*z**5 + 0*z**3. Find w, given that h(w) = 0.
-3, 0
Let v(t) be the first derivative of 3*t**5/5 - 3*t**4/2 + 3*t**2 - 3*t + 3. Suppose v(d) = 0. Calculate d.
-1, 1
Suppose -3*a - 25 = -4*u + 21, 48 = 4*u - 2*a. Determine n, given that 3*n**3 + u*n**2 - 13*n**2 - 3*n = 0.
-1, 0, 1
Let i(d) be the second derivative of 0*d**2 + 0 + 1/2*d**3 + 9/20*d**5 - d**4 - 2*d. Factor i(g).
3*g*(g - 1)*(3*g - 1)
Let t(w) = w**2 + 2*w + 1. Let m be t(-1). Suppose 3*h - 10 = -2*q, 4*h + m*q - 12 = -2*q. Determine l, given that 0*l**2 + l**h + 2*l**3 + l**4 - 4*l**3 = 0.
0, 1
Let d(s) be the third derivative of s**6/60 - s**4/12 + 4*s**2. Find j such that d(j) = 0.
-1, 0, 1
Let t(j) be the third derivative of 1/100*j**5 + 0*j - 2*j**2 - 1/5*j**3 - 1/40*j**4 + 0. Factor t(h).
3*(h - 2)*(h + 1)/5
Let h(v) = v**3 - 12*v**2 + 10*v + 13. Let o be h(11). Suppose -3 = 4*d + q, 5*q = o*d + q - 12. Factor -1/5*n**2 + 1/5 + d*n.
-(n - 1)*(n + 1)/5
Let s(w) be the second derivative of w**7/5040 + w**6/1440 - w**4/12 - 2*w. Let q(o) be the third derivative of s(o). Let q(c) = 0. What is c?
-1, 0
Let k(v) = 8*v**2 - 8*v - 7. Let s(z) = -z**2 + z + 1. Let w(i) = 5*k(i) + 35*s(i). Let w(d) = 0. Calculate d.
0, 1
Let y(j) = j - 2. Let a be y(6). Suppose 0 = -2*u + a + 2. Factor 3*r + 0*r + r**u - r - 3*r**3.
-2*r*(r - 1)*(r + 1)
Let t(i) be the third derivative of 11*i**5/300 - 3*i**4/40 - i**3/15 + 38*i**2. Factor t(a).
(a - 1)*(11*a + 2)/5
Let l(v) be the second derivative of -v**4/21 + v**3/7 - v**2/7 - 5*v. Factor l(t).
-2*(t - 1)*(2*t - 1)/7
Let c be -1*9/(-7 - -4). Let h(a) be the second derivative of 1/8*a**2 - 3/80*a**5 - 1/48*a**4 + c*a + 1/8*a**3 + 0. Determine r, given that h(r) = 0.
-1, -1/3, 1
Let v(m) = -3 + 6*m - 5*m - 2*m**2 - 4*m**2 + 8*m. Let l(u) = 7*u**2 - 10*u + 3. Let f(s) = 3*l(s) + 4*v(s). Factor f(h).
-3*(h - 1)**2
Factor 578/5 + 2/5*o**2 + 68/5*o.
2*(o + 17)**2/5
Let y(b) be the second derivative of 10*b + 0 - 1/8*b**3 + 0*b**2 + 1/1