- m*x**2 = 0. What is x?
-1, 1/3, 2
Let t(z) be the first derivative of -2 + 1/3*z + 1/6*z**2 - 1/9*z**3 - 1/12*z**4. Factor t(u).
-(u - 1)*(u + 1)**2/3
Let f(n) be the third derivative of n**6/780 - 7*n**5/390 + 11*n**4/156 - 5*n**3/39 - 12*n**2. Factor f(v).
2*(v - 5)*(v - 1)**2/13
Let z be ((-4)/10)/(1/(-10)). Factor 2/3*f**2 + 0*f + 0 + 4/3*f**3 + 2/3*f**z.
2*f**2*(f + 1)**2/3
Let p(s) be the second derivative of -1/60*s**5 + s**2 + 1/12*s**4 + 0 - 2*s - 1/6*s**3. Let x(l) be the first derivative of p(l). Factor x(g).
-(g - 1)**2
Let w(n) = 2*n**2 + 4*n + 2. Let t be w(-2). Let k(x) be the first derivative of -2/5*x - 1/10*x**4 + 2/15*x**3 + 1/5*x**t - 1. Suppose k(b) = 0. What is b?
-1, 1
Let w(v) be the second derivative of -v**5/30 + v**4/9 + v**3/9 - 2*v**2/3 + v. Factor w(o).
-2*(o - 2)*(o - 1)*(o + 1)/3
Factor 0 + 2*f**3 + 2*f**2 + 2/3*f**4 + 2/3*f.
2*f*(f + 1)**3/3
Let o(f) be the first derivative of f**5/5 - 3*f**4/4 + f**3 - f**2/2 + 30. What is a in o(a) = 0?
0, 1
Let w = 1/307 - -127/55260. Let s(m) be the third derivative of 0 + 1/72*m**4 + 0*m + 0*m**3 + w*m**5 - 2*m**2. Solve s(x) = 0.
-1, 0
Find p, given that -4 + 7*p**3 + 21*p**3 - 76*p**2 + 20 + 32*p = 0.
-2/7, 1, 2
Let k(r) be the first derivative of -r**7/35 + 2*r**6/75 + 3*r**5/50 - r**4/15 - 3*r - 2. Let j(o) be the first derivative of k(o). Let j(l) = 0. What is l?
-1, 0, 2/3, 1
Let u be (-13)/(-1 + (-1 - -3)). Let v be u/(-4) - (-2)/(-8). Let 0*q**2 - 3*q**2 + 0*q**3 - 1 - q**3 - v*q = 0. Calculate q.
-1
Determine c, given that 10/19*c**2 - 14/19*c - 2/19*c**3 + 6/19 = 0.
1, 3
Let k(o) be the second derivative of -o**4/3 + 4*o**3/3 + 6*o**2 + o. Factor k(u).
-4*(u - 3)*(u + 1)
Let h(l) be the first derivative of -l**6/108 - l**5/90 + l**4/54 + l**2 + 3. Let u(y) be the second derivative of h(y). Factor u(g).
-2*g*(g + 1)*(5*g - 2)/9
Let t = 122/3 - 40. Find c such that 0*c + 0 + t*c**2 = 0.
0
Let u(k) be the first derivative of -k**3 - 15*k**2/2 - 12*k + 7. Factor u(h).
-3*(h + 1)*(h + 4)
Suppose b - 1 = 2*y - 9, -3*b - 8 = -2*y. Factor 48/5*k**2 + b - 18/5*k**3 + 2/5*k**4 - 32/5*k.
2*k*(k - 4)**2*(k - 1)/5
Let a(w) be the first derivative of 22/3*w**3 - 1 - 29/2*w**4 - 4*w + 6*w**5 + 5*w**2. Find s, given that a(s) = 0.
-2/5, 1/3, 1
Let u be 1*1/3*2. Let d be ((-28)/(-6))/(-2) - -3. Find i, given that 0 - d*i**5 + 4/3*i**2 + u*i - 4/3*i**4 + 0*i**3 = 0.
-1, 0, 1
Let b(y) = y**3 - 5*y - 4. Let a(x) = -5*x**3 + 26*x + 21. Let p(k) = 2*a(k) + 11*b(k). Factor p(i).
(i - 2)*(i + 1)**2
Let d(a) be the third derivative of a**6/40 + a**5/40 - a**4/8 - a**3/4 - 2*a**2. Solve d(l) = 0 for l.
-1, -1/2, 1
Let t(h) be the second derivative of 1/15*h**5 + 8/9*h**3 - 1/180*h**6 - 1/3*h**4 + h**2 - h + 0. Let b(w) be the first derivative of t(w). Factor b(q).
-2*(q - 2)**3/3
Let f(p) be the second derivative of -p**6/1440 + p**5/80 - 3*p**4/32 - p**3/2 - 9*p. Let x(b) be the second derivative of f(b). Find z, given that x(z) = 0.
3
Let v be (3/9)/(1/9). Let l(c) = -3 + v + c + 0. Let r(t) = -3*t**2 - 3. Let b(p) = -6*l(p) + r(p). Factor b(z).
-3*(z + 1)**2
Factor 3/2*o**2 - 18*o + 54.
3*(o - 6)**2/2
Suppose -328*r = -326*r - 4. Factor -1/6*a**r + 0*a + 0.
-a**2/6
Factor 0 + 8/15*n + 2/15*n**3 + 8/15*n**2.
2*n*(n + 2)**2/15
Let i(j) be the third derivative of -j**5/300 - j**4/60 - j**2. Let i(g) = 0. Calculate g.
-2, 0
Let r be 12/7 - 2/(-7). Factor -2*f + 5*f**2 + 3 - r*f**2 - 4*f**2.
-(f - 1)*(f + 3)
Let a be (0 + (-2)/(-3))*6. Let d be (-2)/a*12/(-2). Determine h so that -3*h + 1 + 3*h**2 - h**3 + d*h**2 - 3*h**2 = 0.
1
Let o(v) be the second derivative of -3*v**4/2 - 13*v**3/3 - 4*v**2 - 38*v. Factor o(i).
-2*(i + 1)*(9*i + 4)
Let i(j) be the second derivative of j**7/2940 - j**6/1260 - j**3/6 + 2*j. Let w(q) be the second derivative of i(q). Suppose w(p) = 0. Calculate p.
0, 1
Suppose 3*a + 3*g - 2*g = 3, 2*g = 2*a - 2. Let y = a + 4. Factor 1/3*n**y - 4/3*n**2 + 2*n**3 - 4/3*n**4 + 1/3*n + 0.
n*(n - 1)**4/3
Let w be 5/((-5)/2) + 0. Let k = w - -6. Determine x, given that -2*x + 2*x**4 + 2*x**3 - 4*x**3 + k*x - 2*x**2 = 0.
-1, 0, 1
Suppose x = 2*x. Let v be 3 + (1 - 1) + x. Factor 7*o**2 - 5*o**2 - o**v + 2*o**3.
o**2*(o + 2)
Suppose 0 = -2*x - 5*i + 23 + 10, -4*i + 12 = -2*x. Factor 4*c**2 + 2*c**2 - c**x - 4*c**2 + c**3.
-c**2*(c - 2)*(c + 1)
Suppose 3 + 1 = o. Let q(c) be the first derivative of -8*c + 4 + 1/2*c**o - 10/3*c**3 + 8*c**2. Factor q(i).
2*(i - 2)**2*(i - 1)
Let u(t) = 4*t**3 - 5*t**2 - 4*t + 2. Suppose -2*s = 3*s - 15. Let y(g) = -4*g**3 + 4*g**2 + 4*g - 2. Let i(l) = s*y(l) + 2*u(l). Factor i(b).
-2*(b - 1)*(b + 1)*(2*b - 1)
Let m be -2*(-12 + 3 - -1). Let b be (-2)/7 - m/(-7). Suppose -8/9 - 2/9*r**b + 8/9*r = 0. What is r?
2
Let z = 9 - 37. Let d be 4/14 - 34/z. Factor 0 + 0*s - 1/2*s**2 - 1/2*s**5 - d*s**3 - 3/2*s**4.
-s**2*(s + 1)**3/2
Let k(d) be the second derivative of 1/6*d**3 + 0*d**2 + 1/4*d**4 + 0 + 3/20*d**5 + 1/30*d**6 - d. Solve k(h) = 0.
-1, 0
Let d(q) = 3*q**2 + q + 1. Let i(o) = 4*o**2 + 2*o + 1. Let m(s) = -7*d(s) + 5*i(s). Suppose m(b) = 0. What is b?
1, 2
Factor -27*z + 2 + 6*z**3 + 1 + 9 - 3*z**4 + 9*z**2 + 3*z.
-3*(z - 2)*(z - 1)**2*(z + 2)
Let m(k) be the second derivative of 0*k**3 + 0*k**4 + 0*k**2 + 7*k + 0 + 1/126*k**7 + 1/45*k**6 + 1/60*k**5. Factor m(y).
y**3*(y + 1)**2/3
Let y(a) be the third derivative of 0*a + 1/360*a**6 - 1/9*a**3 - 1/24*a**4 - 7*a**2 + 0*a**5 + 0. Determine h so that y(h) = 0.
-1, 2
Let q(t) = -11*t**3 - 17*t**2 + 5*t - 5. Let w(u) = -5*u**3 - 8*u**2 + 2*u - 2. Let l(f) = -2*q(f) + 5*w(f). Determine d so that l(d) = 0.
-2, 0
Let t(y) be the first derivative of y**9/13608 + y**8/7560 - 2*y**3/3 + 2. Let o(p) be the third derivative of t(p). Factor o(u).
2*u**4*(u + 1)/9
Let a(d) be the third derivative of -d**5/60 - d**4/24 + d**3/3 + 25*d**2. Solve a(k) = 0 for k.
-2, 1
Let s = -65 - -67. Solve -8/5 + 24/5*k - 26/5*k**s - 2/5*k**4 + 12/5*k**3 = 0 for k.
1, 2
Let c(x) = 11*x**4 + 12*x**3 - 5*x**2 - 17*x - 1. Let o(d) = 5*d**4 + 6*d**3 - 2*d**2 - 8*d - 1. Let f(q) = 2*c(q) - 5*o(q). Suppose f(y) = 0. What is y?
-1, 1
Let j(v) be the third derivative of -v**5/12 + 15*v**4/8 - v**2 - 21. Solve j(k) = 0 for k.
0, 9
Let b(k) be the third derivative of k**7/42 - k**5/6 + 5*k**3/6 + 29*k**2. What is c in b(c) = 0?
-1, 1
Let r(d) = 11*d**2 - 19*d**3 - 3 - 2*d + 6 + 21*d**3. Let p(b) = -2*b**3 - 10*b**2 + 2*b - 2. Let f(v) = -7*p(v) - 6*r(v). Find k such that f(k) = 0.
-2, -1, 1
Let i(g) be the third derivative of g**9/483840 - g**7/40320 + g**5/30 - 4*g**2. Let h(w) be the third derivative of i(w). Factor h(d).
d*(d - 1)*(d + 1)/8
Factor 0 - 2/5*m + 3/5*m**2 + 1/5*m**3 + 1/5*m**5 - 3/5*m**4.
m*(m - 2)*(m - 1)**2*(m + 1)/5
Let s(d) = -9*d**2 - 7*d + 5. Let r(g) = 4*g**2 + 4*g - 2. Let q(j) = 5*r(j) + 2*s(j). Factor q(n).
2*n*(n + 3)
Let r(y) be the first derivative of y**4/4 + 2*y**3/3 - y**2/2 - y - 4. Let o be r(-2). Factor 1/4*a**2 - a + o.
(a - 2)**2/4
Let 2/13*t**2 - 8/13*t + 6/13 = 0. Calculate t.
1, 3
Suppose -3*b = -3 - 3. Factor 0 - 1/5*a**5 - 1/5*a**4 + 0*a**3 + 0*a + 0*a**b.
-a**4*(a + 1)/5
Let t = 1 - 1. Let b(d) be the second derivative of 3/7*d**3 + 2/7*d**2 + 1/6*d**4 + t + d. Factor b(j).
2*(j + 1)*(7*j + 2)/7
Factor -3/7*o**4 + 0*o**3 - 3/7*o**5 + 0 + 0*o**2 + 0*o.
-3*o**4*(o + 1)/7
Suppose -5*p - m + 24 = 0, -m = -2*p - 6*m + 28. Let x = 13/3 + -4. Factor x*d**p + 0*d**2 - 2/3*d**3 + 2/3*d - 1/3.
(d - 1)**3*(d + 1)/3
Let i = -5 - -7. Let 0*w**i + 3*w**2 + 2*w - 4*w**2 - w**3 = 0. Calculate w.
-2, 0, 1
Suppose 2/3*u**3 - 2/3*u**5 - 2/3*u**2 + 0*u + 2/3*u**4 + 0 = 0. Calculate u.
-1, 0, 1
Factor -z**3 + 1/6*z**4 - 11/6*z - 7/3*z**2 - 1/2 + 1/6*z**5.
(z - 3)*(z + 1)**4/6
Suppose 4*k - 20 = -6*k. Solve -3/4*v**4 + 1/4*v**5 + 1/2*v**k + 1/2*v**3 - 3/4*v + 1/4 = 0 for v.
-1, 1
Let m(c) = -57*c**2 + 48*c. Let x(w) = 7*w**2 - 6*w. Let j(y) = 4*m(y) + 33*x(y). Find o, given that j(o) = 0.
0, 2
Factor 1/6 + 1/6*t**2 - 1/3*t.
(t - 1)**2/6
Let z be ((-76)/12 - -5)*18/(-8). Factor 3/2*n + 3*n**2 + 3/2*n**z + 0.
3*n*(n + 1)**2/2
Let z = 23 + -23. Factor 0 + z*n - 1/4*n**2 + 1/4*n**3.
n**2*(n - 1)/4
Let m(l) be the third derivative of l**7/42 - l**6/12 - l**5/12 + 5*l**4/12 - 12*l**2. Determine k, given that m(k)