 31*f**4 - 32*f**4 + 3*f - f**3 - 2*f + w*f**2 - 2 = 0. What is f?
-2, -1, 1
Let f(z) be the third derivative of -z**8/6720 - z**7/2520 - z**4/24 + 8*z**2. Let t(l) be the second derivative of f(l). Find m, given that t(m) = 0.
-1, 0
Determine n so that 0*n**4 + 0 + 0*n - 2/9*n**3 + 0*n**2 + 2/9*n**5 = 0.
-1, 0, 1
Suppose -5*c - 49 = -8*c + n, 2*c = -4*n + 56. Let a be (4/c)/(96/108). Factor -1/2*r + a + 1/4*r**2.
(r - 1)**2/4
Let x be (-3)/2*4/(-2). Determine o, given that 2*o**4 + 3*o**x - 9*o**2 + 2*o**2 - 12*o - 4 + 0 = 0.
-2, -1, -1/2, 2
Let s(c) be the third derivative of 3/8*c**4 + 2/35*c**7 - 1/20*c**6 - 1/5*c**5 + 0 - 15*c**2 + 0*c - 1/112*c**8 + 0*c**3. Solve s(q) = 0 for q.
-1, 0, 1, 3
Let n(f) be the first derivative of -2*f**5 + 0*f**2 - 5/6*f**6 + 4 + 0*f + 0*f**3 - 5/4*f**4. Factor n(a).
-5*a**3*(a + 1)**2
Let c(y) = 6*y**2 - y**2 + 60*y - 90 - 4*y**2. Let u(w) = 12*w - 18. Let p = 29 - 40. Let m(b) = p*u(b) + 2*c(b). Find d such that m(d) = 0.
3
Suppose -5*m + 44 = 2*r, 4*r + 13*m = 10*m + 32. Factor -2/13*d**r + 20/13*d - 18/13.
-2*(d - 9)*(d - 1)/13
Let i(c) be the second derivative of c**8/140 + c**7/105 - c**6/90 + 2*c**3/3 + 11*c. Let o(y) be the second derivative of i(y). Factor o(z).
4*z**2*(z + 1)*(3*z - 1)
Factor 6/5*i**4 + 24/5*i**2 + 0 - 24/5*i**3 + 0*i.
6*i**2*(i - 2)**2/5
Suppose 5*z - 6 = -2*r - 0, 0 = -z + 2*r + 6. Factor -4*i**5 + 10*i**2 + 4*i**4 + 4*i**2 + 20*i**3 - z*i**2.
-4*i**2*(i - 3)*(i + 1)**2
Let y(l) = 36*l**5 + 140*l**4 - 100*l**3 - 420*l**2 + 420*l - 72. Let p(h) = -h**4 - h**3 + h**2. Let s(z) = -4*p(z) - y(z). Solve s(a) = 0 for a.
-3, 2/9, 1
Factor -351*y + 72*y - 39*y - 150*y - 340*y - 40804 - 4*y**2.
-4*(y + 101)**2
Solve 12*y + 3*y + 0*y - 5*y**2 - 62 + 152 = 0.
-3, 6
Suppose -g - 7 = 4*w - 20, 0 = -4*g + 2*w + 106. Let k be 10/3 + -28 + g. Factor 2/3*a + 0 - k*a**2 - 1/3*a**3.
-a*(a - 1)*(a + 2)/3
Let n(u) be the second derivative of -25/48*u**4 + 35/24*u**3 + 0 - 15/8*u**2 - 19*u + 1/16*u**5. Let n(g) = 0. What is g?
1, 3
Suppose -r - r = -46. Factor -7 + r + 5*q**3 + 15*q - 1 + 30 - 25*q**2.
5*(q - 3)**2*(q + 1)
Let h = -70 + 143/2. Let z be (3/14)/((-34)/(-238)). Suppose -z*w - 7/2*w**2 + 5/2*w**4 + 1 + h*w**3 = 0. Calculate w.
-1, 2/5, 1
Let m(r) be the third derivative of -r**9/141120 + r**7/3920 - r**6/840 + r**5/60 + r**4/4 - 54*r**2. Let n(u) be the third derivative of m(u). Factor n(w).
-3*(w - 1)**2*(w + 2)/7
Let v(u) be the first derivative of -28 + 38/3*u**3 + 162*u - 1/2*u**4 - 99*u**2. Solve v(g) = 0 for g.
1, 9
Let k be (-11925)/(-1275) - (1 - -8). Suppose 10/17*o + k*o**2 - 4/17 = 0. What is o?
-2, 1/3
Let x be (12/8)/((-6)/(-28)). Let m = x + -4. Let 0*o**4 - 9*o**2 + 2*o**4 + 6*o**3 - m*o**4 = 0. Calculate o.
0, 3
Let z(t) be the second derivative of t**8/2800 - t**7/3150 - t**6/75 + 2*t**5/75 - 11*t**4/6 + 44*t. Let a(n) be the third derivative of z(n). Factor a(y).
4*(y - 2)*(y + 2)*(3*y - 1)/5
Let w(y) be the second derivative of -2/3*y**3 + 0 + y**2 - 1/6*y**5 - 7/12*y**4 + 2*y. Let m(a) be the first derivative of w(a). Factor m(g).
-2*(g + 1)*(5*g + 2)
Let g be (2/16)/(182/728). Find z such that 0 - g*z - 1/2*z**2 = 0.
-1, 0
Let u(d) be the second derivative of 7*d**6/15 + 9*d**5/10 - 2*d**4 - 4*d**3/3 - 14*d - 3. Determine c, given that u(c) = 0.
-2, -2/7, 0, 1
Determine a, given that -8*a**3 + 5*a - 6*a**3 + 16*a**3 - 7*a**3 - 35*a**2 + 35 = 0.
-7, -1, 1
Factor 105 - 26*i**2 - 74*i - 190 + 97.
-2*(i + 3)*(13*i - 2)
Let 9*g**2 + g + 2*g**3 - 9*g + 12 - 13*g**2 - 2*g = 0. Calculate g.
-2, 1, 3
Suppose -7*k + 6*k + 265 = 0. Determine w so that -2 + k*w**3 - 15*w - 10*w**2 + 2 - 260*w**3 = 0.
-1, 0, 3
Let o = -1004 - -1010. Let a(c) be the first derivative of -2/3*c**3 + 5/4*c**2 - c + 1/8*c**4 - o. Factor a(z).
(z - 2)*(z - 1)**2/2
Let g be (-226)/(-2)*(-6 + 5). Let y = g + 115. Factor -8/5 + 4/5*n**3 - 4/5*n + 8/5*n**y.
4*(n - 1)*(n + 1)*(n + 2)/5
Let m(z) be the second derivative of -3*z**6/10 + 11*z**5/20 + 4*z**4/3 - 2*z**3/3 - 13*z. Solve m(x) = 0 for x.
-1, 0, 2/9, 2
Let m(z) be the third derivative of 3*z**6/100 + 146*z**5/25 + 289*z**4/15 + 128*z**3/5 + 186*z**2. Factor m(o).
2*(o + 96)*(3*o + 2)**2/5
Let z be 0/((-2 + 3)*-2). Let d(g) be the third derivative of 1/450*g**5 + z + 0*g + 4/45*g**3 - 3*g**2 + 1/45*g**4. Factor d(t).
2*(t + 2)**2/15
Suppose 2*u + 0 + 8 = 0, 4*a - 28 = u. Solve a*m**2 - 9*m**2 - 2 - 8*m - 4 - m = 0 for m.
-2, -1
Let c be (2*20)/(0 - -2). Suppose -o + c = 3*o. Find b, given that 0*b**2 + 0 + 1/8*b**o + 9/8*b**3 + 3/4*b**4 + 0*b = 0.
-3, 0
Suppose -4*q = -4*s - 4, -q - q - 4*s = 4. Let o(u) be the second derivative of 2*u**2 + 0 + q*u**4 - 2/15*u**6 + 4/3*u**3 - 2/5*u**5 + u. Factor o(i).
-4*(i - 1)*(i + 1)**3
Let q = 778 - 778. Let s = 2/279 - -544/1953. Factor q - 40/7*d**2 + s*d**5 + 36/7*d**3 + 16/7*d - 2*d**4.
2*d*(d - 2)**3*(d - 1)/7
Let u = -37 - -40. Let i(z) be the first derivative of z**u + 9/2*z**2 - 3 + 9*z + 1/12*z**4. Factor i(y).
(y + 3)**3/3
Let y(g) = 4*g**3 + 6*g**2 - 12*g - 1. Let v(i) = -4*i**3 - 7*i**2 + 13*i + 2. Let s(l) = -6*v(l) - 8*y(l). Factor s(k).
-2*(k - 1)*(k + 2)*(4*k - 1)
Let w be (36/(-28))/3 + (24640/(-882))/(-32). Let -2/3*u**5 + 2/9*u - 2/9 + 4/3*u**2 - 10/9*u**4 + w*u**3 = 0. What is u?
-1, 1/3, 1
Suppose 2*h + 3*q - 164 = -q, 85 = h - q. Let m = 88 - h. Factor 0 - 8/7*j**3 - 4/7*j + 10/7*j**2 + 2/7*j**m.
2*j*(j - 2)*(j - 1)**2/7
Let f(m) = m**2 - 5*m - 4. Let z be f(-1). Let h be z/((12/(-42))/(9/(-21))). Solve -4/7*r - 16/7*r**4 - 8/7*r**2 + 0 + 4*r**h = 0.
-1/4, 0, 1
Let c be ((-4)/15)/((-5)/(250/40)). Solve c*i**2 + 2/3*i - 1/3*i**3 + 0 = 0.
-1, 0, 2
Let z(h) be the second derivative of 2/33*h**3 + 0 + 1/110*h**5 - 1/22*h**4 + 0*h**2 + 5*h. Suppose z(m) = 0. What is m?
0, 1, 2
Let f(n) be the third derivative of -1/315*n**7 + 1/45*n**5 + 1/180*n**6 + 0*n**3 + 0*n + 0*n**4 + 0 - 5*n**2. Let f(l) = 0. What is l?
-1, 0, 2
Let a be ((-1)/50*-5)/((-16)/(-40)). Factor a*o**4 + 0 - 1/4*o**3 + 1/4*o - 1/4*o**2.
o*(o - 1)**2*(o + 1)/4
Let a(b) = b**2 + 69*b - 70. Let d be a(1). Suppose 2/15*p**3 + d + 4/15*p - 2/5*p**2 = 0. Calculate p.
0, 1, 2
Suppose 23 = 7*a - 5. Determine j so that -4*j**2 - a*j + 5*j**2 - 4*j**2 + j + 6 = 0.
-2, 1
Let p(j) be the first derivative of -j**4/30 - 4*j**3/15 - 4*j**2/5 - 46*j + 31. Let l(d) be the first derivative of p(d). Let l(b) = 0. Calculate b.
-2
Factor -6/19*l**3 + 0 - 8/19*l + 26/19*l**2.
-2*l*(l - 4)*(3*l - 1)/19
Let g(n) be the second derivative of -10*n**7/21 + 8*n**6/3 + 43*n**5/4 + 145*n**4/12 + 5*n**3 - n - 140. What is i in g(i) = 0?
-1, -1/2, 0, 6
Let h(t) be the first derivative of 0*t + 1/3*t**4 + 2/15*t**5 + 21 + 0*t**2 + 2/9*t**3. Let h(u) = 0. Calculate u.
-1, 0
Let v be (6/10)/1 - 8/30. Let r(t) be the first derivative of 5/8*t**4 + v*t**3 + 0*t**2 + 1/12*t**6 + 3 + 2/5*t**5 + 0*t. Factor r(f).
f**2*(f + 1)**2*(f + 2)/2
Let d = -2086 - -2089. Let r(k) be the first derivative of -6 - 2/3*k**2 + 0*k - 2/9*k**d. Factor r(v).
-2*v*(v + 2)/3
Let h be (-504)/210 + (-24)/(-10). Determine i so that 3/2*i**2 + 3/2*i**3 + h - 3*i = 0.
-2, 0, 1
Let n be 1/((-3)/66*2). Let w = -8 - n. Factor -26 - 81*j - 189*j + 41*j**w - 291*j**3 - 28 - 450*j**2.
-2*(5*j + 3)**3
Factor 8*u**3 + 185 - 28*u + 52*u**2 - 185.
4*u*(u + 7)*(2*u - 1)
Let t(b) be the second derivative of b**8/3360 + b**7/210 + b**6/40 + b**5/15 + 5*b**4/3 - 23*b - 2. Let a(c) be the third derivative of t(c). Factor a(v).
2*(v + 1)**2*(v + 4)
Let x = 1 + -1. Suppose 14 = 4*r + 6. Let -7*m**r - 8*m + 3*m**2 + x*m**2 = 0. Calculate m.
-2, 0
Suppose 8*q - 32 = 16. Suppose -q*w = 2*w - 24. Find g such that 2/7*g + 2/7*g**4 - 2/7*g**w - 2/7*g**2 + 0 = 0.
-1, 0, 1
Let w = 1473/5278 - -5/754. Solve 2/7 + 0*m - w*m**2 = 0 for m.
-1, 1
Let g = 693 - 687. Let z(q) be the third derivative of 1/165*q**5 - 1/132*q**4 - 1/660*q**6 + 0 + 0*q**3 + g*q**2 + 0*q. Solve z(d) = 0.
0, 1
Let i(j) be the third derivative of -19*j**7/5040 - j**6/720 - j**4/3 - 12*j**2. Let k(z) be the second derivative of i(z). Suppose k(n) = 0. What is n?
-2/19, 0
Let h = 134 + -124. Factor -4*k**3 + 2*k**4 - 3*k**2 + 4*k**4 + 11*k**2 - h*k**4.
-4*k**2*(k - 1)*(k + 2)
Suppose -3*b = 9*b - 36. Let m(n) be the second derivative of -1/12*n*