2 + 0*m**2 + 5*m - 10*m**2 + 11.
-5*(m - 2)*(m + 1)
Let k(g) be the first derivative of 0*g - 8/5*g**5 - 2 - 8/3*g**3 + 3*g**4 + g**2 + 1/3*g**6. Find d such that k(d) = 0.
0, 1
Let g = 9 - 5. Factor -h**2 - g - 2*h + h**2 - 3*h**2 + 5*h**2.
2*(h - 2)*(h + 1)
Factor 1 - 1/2*v**2 - 1/2*v.
-(v - 1)*(v + 2)/2
Let g(y) be the second derivative of y**7/7560 - y**6/2160 + y**4/4 - 3*y. Let u(h) be the third derivative of g(h). Factor u(v).
v*(v - 1)/3
Let h(s) be the third derivative of -2197*s**8/1848 + 676*s**7/231 - 65*s**6/132 - 71*s**5/33 - 35*s**4/33 - 8*s**3/33 + 22*s**2. What is t in h(t) = 0?
-2/13, 1
Let k(a) be the second derivative of 0 + 1/3*a**2 - 1/30*a**5 - 3*a - 1/18*a**4 + 1/9*a**3. Find n, given that k(n) = 0.
-1, 1
Let a(w) be the second derivative of w**7/168 - w**6/60 + w**5/80 + 7*w. Let a(f) = 0. Calculate f.
0, 1
Let i = 11 - 17. Let v = 10 + i. Let k**v + 2*k**2 + 4*k**3 + 0*k**4 + k**4 = 0. Calculate k.
-1, 0
Let s(w) = w**3 - 8*w**2 + 2*w - 16. Let k be s(8). Determine z so that k - 2/7*z - 2/7*z**4 - 6/7*z**3 - 6/7*z**2 = 0.
-1, 0
Factor 0*u - 12/7*u**3 + 0 - 9/7*u**4 + 12/7*u**2.
-3*u**2*(u + 2)*(3*u - 2)/7
Let n(q) = -q**3 - 3*q**2 + 3*q - 4. Let y be n(-4). Let t be 4/(2 + 0/(-4)). Factor y*f + 2/5*f**3 + 0 - 2/5*f**t.
2*f**2*(f - 1)/5
Let x(o) be the first derivative of -3*o**4/10 - 14*o**3/15 - o**2 - 2*o/5 + 11. Find q, given that x(q) = 0.
-1, -1/3
Let g(z) be the first derivative of -z**6/10 + z**5/25 + 3*z**4/20 - z**3/15 + 3. Determine w, given that g(w) = 0.
-1, 0, 1/3, 1
Suppose -5/3*q**3 + 10/3*q + 5/3*q**2 + 0 = 0. Calculate q.
-1, 0, 2
Let p = 84884/297 + 317/27. Let z = p - 297. Factor 2/11*t**3 - z*t**2 + 0 + 4/11*t.
2*t*(t - 2)*(t - 1)/11
Let o(r) be the second derivative of r**5/80 - r**4/16 + 5*r. Factor o(n).
n**2*(n - 3)/4
Let p(b) be the first derivative of 1/10*b**6 - 3 + 3/4*b**4 - 12/25*b**5 + 0*b**2 + 0*b - 2/5*b**3. Find j such that p(j) = 0.
0, 1, 2
Determine k so that 0*k**2 - 4*k**2 - 1 + 5*k + 3*k**2 - 5 = 0.
2, 3
Let t be 4/(0 + -4) + 2. Let o be (t/2)/(7/28). Find b such that -18/5*b**4 + 39/5*b**3 - 36/5*b**o + 3/5*b**5 + 0 + 12/5*b = 0.
0, 1, 2
Determine n so that n**2 + n + 4*n - 4*n = 0.
-1, 0
Let n(a) = a**2 + 4*a + 3. Let r(t) be the first derivative of -t**3/3 + t + 6. Let x(i) = n(i) - r(i). Factor x(c).
2*(c + 1)**2
Suppose -11*d = 14*d - 29*d. Suppose -8*c**2 - 2/3*c**5 + d - 26/3*c**3 - 8/3*c - 4*c**4 = 0. What is c?
-2, -1, 0
Let s(f) be the first derivative of -f**5/10 + f**4/4 - f**3/6 - 3*f + 2. Let u(t) be the first derivative of s(t). Factor u(w).
-w*(w - 1)*(2*w - 1)
Let j(g) = 2*g**3 - 6*g**2 - 2*g - 6. Let q(c) = -c**3 + 5*c**2 + c + 5. Let d(o) = -5*j(o) - 6*q(o). Determine z, given that d(z) = 0.
-1, 0, 1
Let n(f) = f + 7. Let q be n(-5). Find c, given that -4*c**2 - 4*c**3 + q*c**3 - 4*c + 0*c + 2*c = 0.
-1, 0
Let h(v) = -4*v**2 + 83*v - 479. Let i(r) = -2*r**2 + 42*r - 240. Let w(m) = -2*h(m) + 5*i(m). Factor w(p).
-2*(p - 11)**2
Let h(m) be the first derivative of -m**3/2 - 3*m**2 - 6*m - 10. Factor h(f).
-3*(f + 2)**2/2
Let f(y) be the first derivative of y**6/30 - 3*y**5/20 + y**4/4 - y**3/6 - 2*y + 2. Let q(s) be the first derivative of f(s). Suppose q(j) = 0. Calculate j.
0, 1
Let b(g) = 4*g**3 - 2*g**3 - 2*g**2 - 6*g - 2*g**2. Let p(o) = -o**3 + 3*o**2 + 4*o. Let f(z) = -5*b(z) - 8*p(z). Let f(n) = 0. Calculate n.
-1, 0
Let q = -661 - -661. Let z be (2/(-16))/(2/(-12)). Factor -z*w + q + 3/4*w**2.
3*w*(w - 1)/4
Suppose -2*p + 4*p - v = 0, -2*p + 3*v = 8. Let t(z) be the first derivative of z + 1/8*z**4 + 0*z**3 - 3/4*z**p + 1. Factor t(a).
(a - 1)**2*(a + 2)/2
Let h(t) be the second derivative of -t**7/630 - t**6/180 - t**5/180 + 3*t**2 - 7*t. Let q(w) be the first derivative of h(w). Factor q(g).
-g**2*(g + 1)**2/3
Let b(y) be the second derivative of y - 1/16*y**4 + 0*y**5 + 0 - 1/12*y**3 + 1/120*y**6 + 0*y**2. Factor b(s).
s*(s - 2)*(s + 1)**2/4
Let x(a) = 4*a - 2. Let h be x(2). Let l = 6 - h. Factor l + 7/4*k**5 + 0*k + 11/4*k**3 - 1/2*k**2 - 4*k**4.
k**2*(k - 1)**2*(7*k - 2)/4
Let s(p) be the first derivative of -2*p**5/55 - 13*p**4/22 - 40*p**3/11 - 112*p**2/11 - 128*p/11 + 16. Factor s(j).
-2*(j + 1)*(j + 4)**3/11
Let r be ((-8)/12)/(-10 - -1). Let f(u) be the second derivative of 0 + 1/54*u**4 - u + 0*u**2 + r*u**3. What is l in f(l) = 0?
-2, 0
Let p be (0/(-1))/(-1 - -2). Suppose -y = -p*y. Factor y*n**2 - n + 0*n**2 - n**2 + 2*n.
-n*(n - 1)
Let g(j) be the third derivative of 1/24*j**4 + 0*j**3 - 7*j**2 + 1/20*j**5 + 0 + 1/210*j**7 + 1/40*j**6 + 0*j. Determine q, given that g(q) = 0.
-1, 0
Let -16*i - 108*i**3 + 57*i**5 + 136*i**4 - 430*i**2 + 27*i**5 + 334*i**2 = 0. Calculate i.
-2, -1/3, -2/7, 0, 1
Let o(v) be the first derivative of 1/3*v**3 + 0*v + 0*v**2 - 3 - 1/5*v**5 + 0*v**4. Factor o(s).
-s**2*(s - 1)*(s + 1)
Factor 8 - 2/3*y**2 - 16/3*y + 2/3*y**3.
2*(y - 2)**2*(y + 3)/3
Suppose 0 = m - 3, -1 = -2*p + 5*m - 2*m. Suppose -4*h = 5*v - 96, p*h - 50 = -3*v + 18. Factor -4*n - 3*n**4 + 15*n**3 - 23*n**2 + 0*n**4 + v*n - n**2.
-3*n*(n - 2)**2*(n - 1)
Suppose -4/3*x - 6*x**3 + 0 - 14/3*x**2 - 2/3*x**5 - 10/3*x**4 = 0. What is x?
-2, -1, 0
Let s(i) be the second derivative of 0*i**2 + 1/2*i**4 + 3/20*i**5 + 0*i**3 - 1/10*i**6 - 6*i + 0. Factor s(p).
-3*p**2*(p - 2)*(p + 1)
Let r = 11 - 6. Let i be (-4 + r)/((-1)/(-3)). What is g in -2*g**5 - i*g**5 + 3*g**4 - 2*g**3 + 3*g**5 + g**5 = 0?
0, 1, 2
Let x(r) be the second derivative of r**7/3780 - r**6/540 + r**5/180 + r**4/4 + 3*r. Let m(l) be the third derivative of x(l). Solve m(a) = 0 for a.
1
Let t(j) be the second derivative of j**9/45360 + j**8/20160 - j**7/7560 - j**6/2160 - j**4/12 + 4*j. Let o(c) be the third derivative of t(c). Factor o(s).
s*(s - 1)*(s + 1)**2/3
Let s be (-6)/4*(1 + -3). Suppose j - 8 = 2*i, -s = -3*j - 5*i + 4*i. Factor -t**3 + t + 4*t**2 - 4*t**j.
-t*(t - 1)*(t + 1)
Let q(t) = -14*t**3 - 40*t**2 - 40*t - 8. Let c(h) = 28*h**3 + 79*h**2 + 80*h + 16. Let i(d) = 6*c(d) + 13*q(d). Factor i(v).
-2*(v + 1)*(v + 2)*(7*v + 2)
Let u(w) be the first derivative of -3*w**5/5 + 3*w**3 - 3*w**2 + 46. Find p, given that u(p) = 0.
-2, 0, 1
Let o(b) = -b + 19. Let m be o(19). Factor -1/4*h**3 + m - 1/4*h**2 + 1/4*h**4 + 1/4*h.
h*(h - 1)**2*(h + 1)/4
Factor 9/2*f**5 + 10*f**4 + 0*f + 0 + 13/2*f**3 + f**2.
f**2*(f + 1)**2*(9*f + 2)/2
Let i(d) be the second derivative of d**7/21 - d**6/30 - 3*d**5/20 + d**4/12 + d**3/6 + 9*d. Factor i(z).
z*(z - 1)**2*(z + 1)*(2*z + 1)
Let z(l) = l + 7. Let j be z(-4). Let q(x) be the third derivative of 0*x**4 + 0 + 0*x + 1/120*x**5 + 0*x**j + 2*x**2. Factor q(y).
y**2/2
Let t(q) = 5*q**3 - 2*q + 3. Let h(d) = -d**2 - d. Let i(y) = -3*h(y) + t(y). Let n(s) = 24*s**3 + 14*s**2 + 4*s + 14. Let o(z) = 14*i(z) - 3*n(z). Factor o(p).
-2*p*(p - 1)*(p + 1)
Suppose -6 = -2*t - x - 67, -2*t = 5*x + 81. Let y be -2 - (-2 - (-32)/t). Factor y + 26/7*q**2 + 32/7*q + 6/7*q**3.
2*(q + 2)**2*(3*q + 1)/7
Let z = 15 + -12. Determine t, given that z*t**4 + t - 3*t**5 + t**4 + 2*t**3 - 4*t**2 + 0*t**4 = 0.
-1, 0, 1/3, 1
Let o(l) be the third derivative of l**7/105 - l**6/20 + l**5/10 - l**4/12 + 12*l**2. Factor o(n).
2*n*(n - 1)**3
Let t(g) = -3*g - g**2 + 2*g + 2*g**2. Let i(f) = -2*f**3 - 8*f**2 + 12*f - 2. Let v(b) = i(b) + 10*t(b). Factor v(k).
-2*(k - 1)**2*(k + 1)
Let h(c) be the second derivative of -4*c + 1/3*c**3 + 0 + 1/2*c**2 + 1/12*c**4. Factor h(k).
(k + 1)**2
Let x be (-5)/15 - (-28)/75. Let c(p) be the first derivative of 1/5*p - 2 + 1/10*p**4 - x*p**5 + 0*p**3 - 1/5*p**2. Factor c(l).
-(l - 1)**3*(l + 1)/5
Let c(m) be the first derivative of -m**3/15 + m**2/2 - 4*m/5 + 2. Determine k, given that c(k) = 0.
1, 4
Factor -3/4*y**4 + 3/4 + 0*y**2 + 3/2*y - 3/2*y**3.
-3*(y - 1)*(y + 1)**3/4
Let r(p) be the first derivative of 0*p**5 + 1/7*p**2 + 0*p + 0*p**3 - 3 - 1/7*p**4 + 1/21*p**6. Factor r(w).
2*w*(w - 1)**2*(w + 1)**2/7
Let w(m) be the third derivative of -m**7/42 - 11*m**6/24 - 11*m**5/4 - 25*m**4/24 + 125*m**3/3 - 27*m**2. Suppose w(u) = 0. What is u?
-5, -2, 1
Let n = 15 + -10. Solve -2*u**5 + 2*u**2 + 0*u - u**4 - 2*u**3 + 3*u**n - 1 + u = 0 for u.
-1, 1
Let v(y) = -y**3 + 7*y**2 + y - 4. Let k be v(7). Factor 4 - s**2 + s**k - 2*s**3 + s**4 - 4 + s