((-56)/20 + 3)/((-9)/(-15)). Determine d so that 2/3*d - y*d**2 + 0 = 0.
0, 2
Let z(d) be the second derivative of d**6/10 + 21*d**5/80 + 3*d**4/16 + 23*d. Suppose z(q) = 0. Calculate q.
-1, -3/4, 0
Let a = 60 - 298/5. Let d(g) = g**3 - 5*g**2 - 16*g + 16. Let l be d(7). Solve -2/5*b + 0 - a*b**l = 0.
-1, 0
Let i(b) be the third derivative of b**5/30 + 5*b**4/6 - 11*b**3/3 - 2*b**2 + 12. Solve i(t) = 0.
-11, 1
Find n, given that -n**3 + 5/4*n**2 + 0 - 1/2*n + 1/4*n**4 = 0.
0, 1, 2
Factor -8/3 + 2*x**2 - 2/3*x**3 + 0*x.
-2*(x - 2)**2*(x + 1)/3
Solve 16*q**3 - 3*q - 7*q**5 + 88*q**2 - 4*q - 5*q - 16*q**4 + 3*q**5 - 72 = 0 for q.
-3, -1, 1, 2
Let c be 5*4 - 36/48. Let h = -19 + c. Factor h*z + 0 - 1/4*z**2.
-z*(z - 1)/4
Let d(c) = -c + 6. Suppose 2*g = 6 + 2. Let w be d(g). Factor 6*m**3 - 5*m**3 - 2*m + 6*m**w - 5*m**3.
-2*m*(m - 1)*(2*m - 1)
Let i(o) = -o**2 - o. Let t be i(-1). Suppose t*v - 3 = -v. Suppose -f - f**3 + 4*f**4 + 2*f - f**2 - v*f**2 = 0. Calculate f.
-1, 0, 1/4, 1
What is q in -12/7*q**3 + 0 - 15/7*q**2 - 6/7*q - 3/7*q**4 = 0?
-2, -1, 0
Suppose 3*j + 15 = 0, 3*s + j - 4*j = 15. Suppose s = -0*i + 4*i. What is c in -1/2*c**3 + 1/2*c + 1/2*c**2 - 1/2*c**4 + i = 0?
-1, 0, 1
Let n(s) = -s**2 - s. Let u(b) = 4*b**2 - 7*b + 1. Let h(f) = -3*n(f) + 3*u(f). Factor h(o).
3*(o - 1)*(5*o - 1)
Let n(k) be the second derivative of 0*k**2 + 1/189*k**7 + 0 + 3*k + 1/135*k**6 - 1/54*k**4 + 0*k**3 - 1/90*k**5. Factor n(t).
2*t**2*(t - 1)*(t + 1)**2/9
Suppose -17 = -3*c + 2*w - 3*w, -5*c + 25 = w. Let f be c/(2/2 + 13). Determine h, given that 6/7*h + 6/7*h**2 + f + 2/7*h**3 = 0.
-1
Let d(l) = 6*l**3 - 16*l**2 + 32*l - 4. Let a(j) = 7*j**3 - 16*j**2 + 32*j - 5. Let h(y) = 4*a(y) - 5*d(y). Factor h(v).
-2*v*(v - 4)**2
Let k = -306/5 + 62. Let f be (6/(-12))/((-3)/12). Factor f*m**4 - k*m**2 + 0*m + 6/5*m**3 + 0.
2*m**2*(m + 1)*(5*m - 2)/5
Let b(r) be the second derivative of r**5/20 - r**4/24 - r**3/3 + 3*r**2/2 + r. Let g(x) be the first derivative of b(x). Factor g(t).
(t - 1)*(3*t + 2)
Let r(u) be the first derivative of 8*u**7/35 + u**6/5 - 7*u**5/20 + u**4/8 + u**2 + 3. Let x(q) be the second derivative of r(q). Factor x(w).
3*w*(w + 1)*(4*w - 1)**2
Let f(v) be the first derivative of -v**5/10 + 11*v**4/32 + 9*v**3/8 - 13*v**2/8 - v - 16. Solve f(o) = 0.
-2, -1/4, 1, 4
Factor -8/9*n + 8/9*n**2 - 2/9*n**3 + 0.
-2*n*(n - 2)**2/9
Let a(m) be the first derivative of 3*m**5/40 + 5*m**4/16 + m**3/2 + 3*m**2/8 + 2*m + 3. Let q(w) be the first derivative of a(w). What is n in q(n) = 0?
-1, -1/2
Let j be 6/2*(-3 - 65/(-21)). Factor 0*a + j - 2/7*a**2.
-2*(a - 1)*(a + 1)/7
Let y(u) be the first derivative of 0*u + 3 - 1/3*u**3 - 1/12*u**4 - 1/3*u**2. Let y(z) = 0. What is z?
-2, -1, 0
Let t(y) = -5*y**2 - 40*y. Let c(l) = l**2 + 10*l. Let g(m) = -15*c(m) - 4*t(m). Factor g(k).
5*k*(k + 2)
Let d(b) be the second derivative of -2*b**6/15 - 4*b**5/5 - b. Determine z so that d(z) = 0.
-4, 0
Let u(a) be the first derivative of a**3/5 + 21*a**2/5 + 147*a/5 - 45. Find p, given that u(p) = 0.
-7
Factor -4*y**2 + 7*y**2 + 45*y - 15*y**3 - 53*y**2 - 4 + 24.
-5*(y - 1)*(y + 4)*(3*y + 1)
Let j(k) be the second derivative of 0 + 1/75*k**5 - 1/2*k**3 + 3*k + 0*k**2 - 1/15*k**4 - 1/900*k**6. Let c(b) be the second derivative of j(b). Factor c(y).
-2*(y - 2)**2/5
Let r be (-304)/(-10)*15/3. Suppose -3*w = -584 + r. Factor 1 + 23*d + 64*d**3 + 10*d**4 + 31 + w*d**2 + 105*d.
2*(d + 2)**3*(5*d + 2)
Let m(j) be the second derivative of 7*j**4/6 - 8*j**3/3 + j**2 + 9*j. Factor m(t).
2*(t - 1)*(7*t - 1)
Suppose 7*a = 17*a - 20. Suppose 0*l**4 + 0 + a*l**3 + 0*l - 4/3*l**2 - 2/3*l**5 = 0. Calculate l.
-2, 0, 1
Let a be (2/6*0)/1. Let m be (-1)/((-2)/8 + a). What is p in p**3 - p**m + p**2 - 2*p**3 - p + 2*p**3 = 0?
-1, 0, 1
Let o(u) = -20*u**2 + 32*u - 12. Let c(b) = 8*b**2 - 13*b + 5. Let w(d) = 12*c(d) + 5*o(d). Factor w(v).
-4*v*(v - 1)
Let i(r) be the first derivative of -r**5/40 + r**4/24 + r**3/6 + r - 5. Let d(a) be the first derivative of i(a). Determine n so that d(n) = 0.
-1, 0, 2
Let 3/5*t - 3/5*t**5 + 0 - 6/5*t**4 + 6/5*t**2 + 0*t**3 = 0. What is t?
-1, 0, 1
Let a(z) = -8*z**2 - 2*z. Let f(b) = -b**2. Let l(y) = -a(y) + 6*f(y). Factor l(r).
2*r*(r + 1)
Suppose 4*v + 0*j = j, -j = -5*v. Suppose 14/3*p**3 - 26/3*p**4 + v + 2/3*p**2 - 2/3*p + 4*p**5 = 0. Calculate p.
-1/3, 0, 1/2, 1
Let o(p) be the second derivative of -1/6*p**4 + 0*p**3 + 1/15*p**6 + 5*p + 0*p**5 + 0*p**2 + 0. Solve o(q) = 0.
-1, 0, 1
Let c = 78 + -74. Factor 3/4*p + 0*p**2 + 0 + 0*p**c + 3/4*p**5 - 3/2*p**3.
3*p*(p - 1)**2*(p + 1)**2/4
Let a(p) be the third derivative of -p**7/525 + p**5/150 - 7*p**2. Factor a(k).
-2*k**2*(k - 1)*(k + 1)/5
Let q(j) = -j**2 - 8*j + 2. Let k be q(-8). Let p - 8*p**5 + 12*p**4 + 17*p**5 + k - 46*p**4 + 46*p**3 - 24*p**2 = 0. Calculate p.
-2/9, 1
Let y(c) be the second derivative of c**4/12 - c**2/2 + 2*c. Factor y(k).
(k - 1)*(k + 1)
Suppose 2*x = 5*q + 13, -3*x = -4*x - q + 3. Determine g so that g**2 - g**2 + g**2 - x*g**2 = 0.
0
Let d(o) be the second derivative of 0*o**2 + 0*o**4 - 1/2*o**3 + 3/20*o**5 + 0 + 2*o. Factor d(c).
3*c*(c - 1)*(c + 1)
Suppose 12/23*b**2 + 0*b + 2/23*b**3 + 0 = 0. Calculate b.
-6, 0
Let s(z) = z**3 - 3*z**2 - 5*z - 2. Let w be s(4). Let t be 21/6 + 3/w. Factor -3*x**2 + 7*x**2 - 3*x**2 - 2*x**t + x**4.
x**2*(x - 1)**2
Let a(d) be the third derivative of -7/144*d**4 - 1/144*d**6 - 1/40*d**5 - 1/1260*d**7 - 2*d**2 + 0*d + 0 - 1/18*d**3. Find w, given that a(w) = 0.
-2, -1
Let o(f) = -2 + 5 - 4*f + 3*f - f**2. Let q be o(0). Find h such that -3*h**q + h**3 + h**4 + 5*h - 1 - 3*h = 0.
-1, 1
Let h(p) be the third derivative of -p**7/210 - p**6/120 + p**5/30 + 3*p**2. Factor h(k).
-k**2*(k - 1)*(k + 2)
Factor 13*c**2 + 21*c + 2*c**2 + 9 + 0 + 3*c**3.
3*(c + 1)**2*(c + 3)
Let a(k) be the second derivative of -k**4/24 - k**3/12 + 7*k. Factor a(z).
-z*(z + 1)/2
Let n = -16 - -16. Let r(b) be the third derivative of -1/30*b**5 - 2*b**2 + 0*b + 1/105*b**7 + n*b**3 - 1/6*b**4 + 1/30*b**6 + 0. What is y in r(y) = 0?
-2, -1, 0, 1
Let h(m) = m**2 + 7*m + 2. Let q be h(-7). Factor -2*l + 0*l**2 - l**q - 4*l + 4*l - 1.
-(l + 1)**2
Let s be (-6)/(-4) + 23/2. Let l = s - 11. Determine p so that -2/3*p - 2/3*p**3 + 0 + 4/3*p**l = 0.
0, 1
Suppose 0 - 1/5*j**4 - j**3 - 4/5*j - 8/5*j**2 = 0. What is j?
-2, -1, 0
Let c = -121 + 123. Let d(m) be the third derivative of 2/15*m**3 + 0*m + 0 + 1/60*m**4 - 1/300*m**6 + c*m**2 - 1/75*m**5. Factor d(j).
-2*(j - 1)*(j + 1)*(j + 2)/5
What is n in 20/7*n + 2/7*n**2 + 50/7 = 0?
-5
Let y = -6005 + 18167/3. Let j = y + -50. Factor -j*d + 2/3*d**3 + 2/3*d**2 - 2/3.
2*(d - 1)*(d + 1)**2/3
Let o = -2 + 4. Suppose -14/3*b - 2*b**o - 4/3 = 0. What is b?
-2, -1/3
Let s(d) be the second derivative of d**6/120 - d**5/8 + 37*d**4/48 - 5*d**3/2 + 9*d**2/2 - 2*d. Factor s(t).
(t - 3)**2*(t - 2)**2/4
Let u(i) be the second derivative of 0 + 1/70*i**5 + 1/21*i**3 + 0*i**2 + 1/21*i**4 - 6*i. Determine d so that u(d) = 0.
-1, 0
Let g(i) be the second derivative of -i**7/280 + i**6/40 - i**4/2 - i**3/2 - i. Let t(z) be the second derivative of g(z). What is c in t(c) = 0?
-1, 2
Let l(k) = 2*k**3. Let w be l(1). Let a(n) = 2*n**2 + 2*n + 3. Let c(p) = -3*p + 2*p + 9 - 11 - p**2. Let z(h) = w*a(h) + 3*c(h). Factor z(f).
f*(f + 1)
Let t(z) be the first derivative of 1/3*z**4 - 2/9*z**6 - 8/9*z**3 + 0*z**2 + 2/5*z**5 - 3 + 2/3*z. Suppose t(i) = 0. What is i?
-1, -1/2, 1
Let x(j) = j**4 - j**3 - j**2 + 1. Let k(c) = 4*c**5 - 17*c**4 - 19*c**3 + 45*c**2 + 84*c + 31. Let y(a) = -k(a) - 5*x(a). Factor y(g).
-4*(g - 3)**2*(g + 1)**3
Factor 0*i**2 - 5*i**3 + i**2 + 14*i**2 - 10*i.
-5*i*(i - 2)*(i - 1)
Solve -4/5*x**4 - 3/5*x**3 + 4/5*x**2 + 4/5*x + 0 - 1/5*x**5 = 0 for x.
-2, -1, 0, 1
Let a(s) be the second derivative of -4*s**6/15 - 3*s**5/5 - s**4/3 + 11*s. Factor a(w).
-4*w**2*(w + 1)*(2*w + 1)
Factor -3/2*d**3 + 3/2*d + 3 - 9/2*d**2 + 3/2*d**4.
3*(d - 2)*(d - 1)*(d + 1)**2/2
Let a be -8 + 5 - (0 + (-28)/8). Find t, given that -1/2*t + 1/2*t**3 + a*t**2 - 1/2 = 0.
-1, 1
Let h(s) be the first derivative of -s**5/20 + s**4/8 + s**3/4 - s**2/2 - s + 9. Let h(l) = 0. What is l?
-1, 2
Let y(p) be the first derivative of -4*p**3/3 + 10*p**2 - 16*