r.
-r*(r - 1)/6
Let b = 5 - 3. Determine n, given that 3*n**2 + 3*n**3 + b*n**3 + 2*n**4 - 5*n**2 - 5*n**5 = 0.
-1, 0, 2/5, 1
Let u(r) be the third derivative of r**6/40 + 12*r**2. Find c such that u(c) = 0.
0
Let u(b) be the first derivative of 3*b**4/7 + 2*b**3/21 - 6*b**2/7 - 2*b/7 - 5. Factor u(h).
2*(h - 1)*(h + 1)*(6*h + 1)/7
Let o(b) be the first derivative of b**8/672 - b**7/280 - b**6/240 + b**5/60 - b**3/24 - 3*b**2/2 + 1. Let m(a) be the second derivative of o(a). Factor m(q).
(q - 1)**3*(q + 1)*(2*q + 1)/4
Suppose -2*s - 4*r + 12 = -0*r, 0 = 3*r - 15. Let k = 8 + s. Factor 4/3*p**3 + 14/3*p - 4/3 - 16/3*p**2 - 2/3*p**5 + 4/3*p**k.
-2*(p - 1)**4*(p + 2)/3
Suppose -6 = -d + 2. Let p be (-4 + d)/(4/3). Factor 1/3*f**p + 0 + 2/3*f + f**2.
f*(f + 1)*(f + 2)/3
Let d(z) be the third derivative of -z**9/181440 - z**8/60480 + z**5/10 + 4*z**2. Let l(n) be the third derivative of d(n). Determine x, given that l(x) = 0.
-1, 0
Let s be ((-13)/(-13))/(-3*2/(-3)). Solve 4*q - 2 + s*q**3 - 5/2*q**2 = 0 for q.
1, 2
Let k(z) = 4*z**3 - 12*z - 3. Let r(o) = -6*o**3 + 18*o + 4. Let h(v) = -8*k(v) - 5*r(v). Factor h(g).
-2*(g - 2)*(g + 1)**2
Let m = -10 - -13. Factor -2*a**m - 2*a + 0*a + 4*a.
-2*a*(a - 1)*(a + 1)
Suppose 3*u - 4*c = u + 14, 2 = -2*c. Determine n, given that n**u + 3*n + n**5 - n - 4*n**3 = 0.
-1, 0, 1
Let y(z) be the first derivative of -3*z**6/10 - 48*z**5/25 - 69*z**4/20 + 6*z**3/5 + 42*z**2/5 + 24*z/5 - 7. Find k such that y(k) = 0.
-2, -1/3, 1
Let d(u) = u**2 - 2*u. Let i be d(3). Let f(z) be the first derivative of -1/3*z**3 + i - z**2 + 0*z - z**5 + 2*z**4. Determine y so that f(y) = 0.
-2/5, 0, 1
Factor -100*i**2 - 1446*i**4 + 115*i**3 + 2*i - i + 19*i + 1411*i**4.
-5*i*(i - 2)*(i - 1)*(7*i - 2)
Let v(a) = -165*a**3 + 51*a**2 + 186*a - 30. Let w(n) = 33*n**3 - 10*n**2 - 37*n + 6. Let y(s) = 4*v(s) + 21*w(s). Factor y(b).
3*(b - 1)*(b + 1)*(11*b - 2)
Let s be 6 - 51/15 - (-4)/10. Let n(o) be the first derivative of 0*o + 7/15*o**s - 2 - 1/5*o**2. What is y in n(y) = 0?
0, 2/7
Let o(z) be the second derivative of 1/42*z**4 + 0 + 1/70*z**5 - 1/21*z**3 - 1/7*z**2 + 3*z. Factor o(h).
2*(h - 1)*(h + 1)**2/7
Let n(c) be the first derivative of 1/8*c**2 - 1 - 1/16*c**4 + 1/4*c - 1/12*c**3. Factor n(l).
-(l - 1)*(l + 1)**2/4
Factor -8/7*c - 2/7*c**2 - 8/7.
-2*(c + 2)**2/7
Factor -21*w**4 - 14*w**4 - 32*w**2 + 4*w**5 + 11*w**4 + 48*w**3.
4*w**2*(w - 2)**3
Let i(y) be the second derivative of -y**7/2100 - y**6/450 + y**5/300 + y**4/30 + y**3/6 + y. Let f(r) be the second derivative of i(r). Factor f(a).
-2*(a - 1)*(a + 1)*(a + 2)/5
Suppose d - 8 = -3*g, 5*d - 6*g - 6 = -4*g. Let w(l) be the first derivative of 2*l - 2 + 7/2*l**d - 4/3*l**3. Factor w(n).
-(n - 2)*(4*n + 1)
Let u = 261 + -257. Factor 2/9*t**2 + 2/9*t**u + 0 + 0*t + 4/9*t**3.
2*t**2*(t + 1)**2/9
Let u be (-2)/(-7) - 396/(-84). Let 12*k**3 - 16*k**2 + 16*k**4 - 59*k + 5*k**5 + 4*k**5 - 5*k**u + 43*k = 0. Calculate k.
-2, -1, 0, 1
Suppose -2*t = -t. Let h be 2/3*(-6)/(-8). Suppose h*o + 1/2*o**2 + t = 0. What is o?
-1, 0
Let 3*b**3 - 3*b + b**2 - 2*b**2 + b**2 = 0. What is b?
-1, 0, 1
Let b(l) be the third derivative of 7/48*l**4 + 0*l - 2*l**2 - 1/30*l**5 - 1/60*l**6 - 1/6*l**3 + 0. What is v in b(v) = 0?
-2, 1/2
Factor -3*x**2 + 2*x**2 - 15*x - 5 + 15*x**3 + 6*x**2.
5*(x - 1)*(x + 1)*(3*x + 1)
Factor 1/5*m - 1/5*m**3 - 1/5*m**2 + 1/5.
-(m - 1)*(m + 1)**2/5
Let h be 1 + 0 + 1 + -2. Factor -9*p**2 + 2*p - 2 + h*p + 1 + 8*p**2.
-(p - 1)**2
Let p(a) be the first derivative of 2*a**6/5 + 33*a**5/25 + 3*a**4/4 - 2*a**3/5 - 7. Solve p(f) = 0.
-2, -1, 0, 1/4
Let y(w) be the second derivative of 0 + 2/15*w**3 + 1/30*w**4 - 5*w - 1/50*w**5 + 0*w**2. Factor y(q).
-2*q*(q - 2)*(q + 1)/5
Factor -9*a**3 - 21*a**5 + 36*a**4 - 156 + 156 - 6*a**2.
-3*a**2*(a - 1)**2*(7*a + 2)
Let h(z) = 2*z**2 + z. Let a(p) = p. Let x be (-8)/52 + 45/39. Let c(l) = x*h(l) + 3*a(l). What is o in c(o) = 0?
-2, 0
Let o be (12/(-9))/((-2)/15). Suppose -o = -n - 2. Determine w so that 4*w**2 + 6*w - n*w - 5*w**3 + 3*w**3 = 0.
0, 1
Let a = 372 - 1114/3. Let x be (-2)/(-10) - 10/(-75). Factor -1/3*y**2 - a*y - x.
-(y + 1)**2/3
Let o(t) be the first derivative of -2*t**3/3 - 8*t**2 - 35. Factor o(p).
-2*p*(p + 8)
Determine w so that -16*w - 36*w**3 + 32*w**3 - 48*w**4 + 20*w**5 + 45*w**2 + 3*w**2 = 0.
-1, 0, 2/5, 1, 2
Let t = 5 - 11. Let k be 3*-2*2/t. Factor 2*l**2 + 2*l**k - l**5 - 8*l**3 - 3*l**3 + 5*l**4 + 3*l**3.
-l**2*(l - 2)**2*(l - 1)
Let f(l) be the third derivative of -l**5/210 + l**4/84 - 9*l**2. Determine u so that f(u) = 0.
0, 1
Let k(s) = -s**3 - 4*s**2 + 5*s + 5. Let a be k(-5). Suppose a = 5*p - 10. What is l in 0*l**p + 0 + 2/5*l**4 + 0*l**2 + 0*l = 0?
0
Let a(z) be the third derivative of z**8/504 + z**7/315 - z**6/180 - z**5/90 - 16*z**2. Factor a(o).
2*o**2*(o - 1)*(o + 1)**2/3
Let j(t) be the first derivative of t**6/10 + 18*t**5/25 + 27*t**4/20 + 8. What is c in j(c) = 0?
-3, 0
Let x = -3555/7 + 509. What is p in 8/7 - 8/7*p**3 - 38/7*p**2 + 30/7*p**4 + x*p = 0?
-1, -2/5, 2/3, 1
Factor -12*v - 46*v**2 + 16*v**3 + v**3 - 75*v**5 + 10*v**2 + 90*v**4 + 16*v**3.
-3*v*(v - 1)**2*(5*v + 2)**2
Let o(t) be the second derivative of t - 8/9*t**2 + 4/9*t**3 + 1/90*t**5 - 1/9*t**4 + 0. Factor o(z).
2*(z - 2)**3/9
Let u(o) be the second derivative of -o**4/12 - o**3/3 - o**2/2 + 4*o. Factor u(f).
-(f + 1)**2
Let h = 2 + 2. Factor h*g**3 - 4*g**3 + g**4.
g**4
Suppose 5*j + 15 = 2*m, 3*j + 3 = 2*j. Factor m + 4/5*r + 2/5*r**2.
2*r*(r + 2)/5
Suppose 2 = 3*v - 2*v. Solve 7*j + 8*j - v*j**3 - 15*j + j**4 + j**2 = 0.
0, 1
Let n(d) be the third derivative of 4*d**7/735 - d**6/420 - 2*d**5/35 - 5*d**4/84 + 2*d**3/21 - 7*d**2. Solve n(b) = 0 for b.
-1, 1/4, 2
Suppose -d = -4*d + 9. Determine l, given that -2*l**3 + 3*l**3 - l**4 - 2*l**3 + 0*l**d = 0.
-1, 0
Let k(a) = a**5 + a**4 + a**2 + a. Let w(h) = 3*h**5 + h**4 - 4*h**3 + h**2 + 3*h. Let q(r) = -k(r) + w(r). Factor q(o).
2*o*(o - 1)**2*(o + 1)**2
Let b be (-7)/(3/(3 + -6)). Factor b - 7 + 3*c**3 - 3*c**5.
-3*c**3*(c - 1)*(c + 1)
Factor -4/7*g**3 + 0*g + 0*g**2 + 0.
-4*g**3/7
Suppose -14*g = -2*g. Let 3/5*l**3 + g*l**2 + 0 - 3/5*l = 0. Calculate l.
-1, 0, 1
Let l(k) be the first derivative of 3*k**4/2 - 2*k**3/3 - 5*k**2/2 + 5*k + 1. Let t(w) = -5*w**3 + 2*w**2 + 4*w - 4. Let n(o) = 4*l(o) + 5*t(o). Factor n(q).
-q**2*(q - 2)
Let q(c) = -2*c. Suppose -2*z = -p - 10, -14 = -p + 6*p - z. Let j be q(p). Factor -4*a**4 + 14*a**3 + 2 - 9*a**2 - j - 9*a**2 + 10*a.
-2*(a - 1)**3*(2*a - 1)
Let r(m) be the first derivative of 16/11*m**2 + 8/11*m - 2 + 14/55*m**5 + 19/22*m**4 + 50/33*m**3 + 1/33*m**6. Factor r(u).
2*(u + 1)**3*(u + 2)**2/11
Suppose 10 + 0 = -2*a. Let r be 2 - a/(15/(-6)). Factor 0*t**2 + r*t**3 - t**3 + t**2.
-t**2*(t - 1)
Let u(p) be the first derivative of 0*p**4 + 2/3*p + 0*p**2 + 1 - 4/9*p**3 + 2/15*p**5. Determine x, given that u(x) = 0.
-1, 1
Let n(d) be the third derivative of d**9/7560 - d**7/1260 - 5*d**4/24 + 6*d**2. Let l(s) be the second derivative of n(s). Find c, given that l(c) = 0.
-1, 0, 1
Let s(v) be the third derivative of -v**10/226800 + v**8/15120 - v**6/1080 - v**5/20 + 3*v**2. Let x(z) be the third derivative of s(z). What is n in x(n) = 0?
-1, 1
Let f(b) = -b + 10. Let n be f(-6). Suppose -21*i**3 - 196*i**4 + 30*i**2 + n*i**2 + 16 - 91*i**3 + 134*i**2 + 112*i = 0. Calculate i.
-1, -2/7, 1
Suppose 6 - 4*m**3 + 2*m**5 + 2*m**4 - 10 + 4 = 0. Calculate m.
-2, 0, 1
Factor -8/11*t - 9/11 + 1/11*t**2.
(t - 9)*(t + 1)/11
Let w(m) be the first derivative of m**7/4620 + m**6/660 + m**5/330 - 8*m**3/3 + 7. Let j(p) be the third derivative of w(p). What is k in j(k) = 0?
-2, -1, 0
Find o, given that 928/5*o**2 + 896/5*o**3 + 318/5*o + 36/5 = 0.
-3/8, -2/7
Let k(q) be the second derivative of -2*q**6/15 + q**5 - 3*q**4 + 14*q**3/3 - 4*q**2 + 9*q. Solve k(w) = 0 for w.
1, 2
Suppose -2*s + 2*q = 7*q - 14, 4*s = -5*q + 18. Factor -2*g**5 - s*g**5 + 9*g**4 + 9*g**3 + 7*g**5 + 3*g**2.
3*g**2*(g + 1)**3
Let r(j) be the second derivative of 0*j**2 - 4*j - 1/39*j**3 + 0 - 1/26*j**4 - 1/65*j**5. Factor r(c).
-2*c*(c + 1)*(2*c + 1)/13
Let f = 924 - 924. Factor 0*c - 2/11*c**3 + f + 2/11*c**2.
-2*c**2*(c - 1)/11
Let m(a) be the third derivative of 