first derivative of -m**6/2 + 6*m**5/5 + 9*m**4/4 - 8*m**3 + 6*m**2 + 49. Determine c, given that i(c) = 0.
-2, 0, 1, 2
What is c in 52/3*c**3 + 98/3*c + 0 + 149/3*c**2 + 1/3*c**4 = 0?
-49, -2, -1, 0
Let c be 3502/8 - 1/(-4). Solve 8*j - 8*j**4 + 8*j**2 - 442*j**3 + c*j**3 - 2*j**5 - 2*j = 0.
-3, -1, 0, 1
Let w(i) be the second derivative of i**7/21 - i**6/15 - 8*i**5/5 + 8*i**4/3 - 6*i + 25. Determine v, given that w(v) = 0.
-4, 0, 1, 4
Let t(r) be the third derivative of 4*r**2 + 0*r + 0*r**3 + 0 + 1/270*r**5 - 1/108*r**4. Factor t(h).
2*h*(h - 1)/9
Let v(s) = 16*s**2 + 11*s - 1. Let a(m) = 31*m**2 + 21*m - 1. Let j be (-15)/(-25)*1*15. Let u(p) = j*v(p) - 4*a(p). Solve u(t) = 0 for t.
-1, 1/4
Let d be 296/(-36) - 4/(-18). Let i be 14*(-4)/d + -3. Suppose -4*a**2 + a + 0*a**4 + 2*a**i + 2 + a**5 - 3*a**3 + a**3 = 0. What is a?
-2, -1, 1
Let h(w) = 2*w**3 + 14*w**2 + 50*w + 24. Let g(q) = -2*q**3 - 14*q**2 - 53*q - 24. Let a(o) = -6*g(o) - 7*h(o). Solve a(z) = 0.
-3, -2
Suppose 28 = 25*u - 24*u. Factor 3*g**3 + 126*g + 33*g**2 - 111*g + 47 + 90*g + u.
3*(g + 1)*(g + 5)**2
Let v(u) be the first derivative of -u**5/80 + u**4/6 - 2*u**3/3 + 22*u + 25. Let h(c) be the first derivative of v(c). Factor h(d).
-d*(d - 4)**2/4
Let j(v) be the third derivative of -v**6/120 + v**5/60 - 16*v**2 + 1. Find h such that j(h) = 0.
0, 1
Let d(s) be the third derivative of s**6/180 + s**5/90 - s**4/18 + 10*s**2 - 2. Suppose d(c) = 0. Calculate c.
-2, 0, 1
Suppose -4*n - 4*u + 16 + 12 = 0, 0 = -3*n + 5*u + 5. Let s(b) be the first derivative of -b**2 + 1 - n*b**2 - 8*b - 6 + b**4. What is o in s(o) = 0?
-1, 2
Solve 2 + 31/3*p - 19/3*p**3 + 5/3*p**4 + 1/3*p**2 = 0 for p.
-1, -1/5, 2, 3
Let i = 2039 - 2039. Let v(q) be the second derivative of 1/135*q**6 + 8/27*q**3 + 0*q**5 + i - 1/9*q**4 - 6*q - 1/3*q**2. Factor v(c).
2*(c - 1)**3*(c + 3)/9
Let x(t) be the first derivative of t**3/3 - 23*t**2/2 - 24*t - 196. Factor x(q).
(q - 24)*(q + 1)
Let u(a) = -a**3 + 9*a**2 - 10*a - 25. Let v be u(7). Factor 4/11*z**v + 0*z - 2/11 + 6/11*z**2.
2*(z + 1)**2*(2*z - 1)/11
Suppose -5*p + 19 = 2*o + o, -o = -2*p + 1. Let y(m) be the second derivative of 0 + 1/3*m**4 + 3/2*m**3 + p*m + m**2. Factor y(k).
(k + 2)*(4*k + 1)
Let h(v) be the second derivative of -v**9/5040 + v**8/6720 - 2*v**4/3 - 12*v. Let q(i) be the third derivative of h(i). Factor q(f).
-f**3*(3*f - 1)
Suppose 2*b = -10, 18*s - 5 = 20*s + b. Factor 4/7*c**3 + s*c + 0 + 4/7*c**2.
4*c**2*(c + 1)/7
Let p(x) be the first derivative of -x**5/3 + 11*x**4/6 - 28*x**3/9 + 4*x**2/3 - 116. What is l in p(l) = 0?
0, 2/5, 2
Let o(s) be the second derivative of s**7/1680 - s**6/96 + s**5/20 + 5*s**4/12 + 9*s. Let v(b) be the third derivative of o(b). Factor v(l).
3*(l - 4)*(l - 1)/2
What is o in -115/3*o**3 - 10/3 - 55/3*o**4 - 115/3*o**2 - 10/3*o**5 - 55/3*o = 0?
-2, -1, -1/2
Let q(u) be the third derivative of 0*u**3 - 1/60*u**5 + 0*u + 0 - 1/360*u**6 - 17*u**2 - 1/36*u**4. Factor q(t).
-t*(t + 1)*(t + 2)/3
Factor 24649/6 + 157/3*d + 1/6*d**2.
(d + 157)**2/6
Suppose z = -2*r + 4, -5*z + 2 = -r - 7. Suppose 4*d = -8 - 8, 0 = -c - 3*d - 9. Factor -11/2*y**c - 7/2*y**5 - y**z + 0 - 8*y**4 + 0*y.
-y**2*(y + 1)**2*(7*y + 2)/2
Let f(h) be the third derivative of -1/8*h**4 + 0*h**3 - 13*h**2 + 0*h - 3/20*h**5 - 3/40*h**6 + 0 - 1/70*h**7. Solve f(w) = 0 for w.
-1, 0
Let o(q) = -6 + 2*q**2 + 12 + q - 3*q**2 - 3. Let k be o(0). Let -4*v**2 - k*v**2 + 3 - 4*v**2 + 14*v**2 - 6*v = 0. Calculate v.
1
Let s = 165817/84 - 1974. Let g(c) be the third derivative of 0*c**4 + 5*c**2 + 0 - 1/10*c**6 + 0*c + 0*c**5 - s*c**8 - 8/105*c**7 + 0*c**3. Solve g(b) = 0.
-3, -1, 0
Let h be (4774/(-21))/(-31) - 7. Suppose 0*i + h*i**3 + 1/3*i**2 + 0 = 0. Calculate i.
-1, 0
Let w = -16443/5 - -3289. Let 2/15*o**4 + 0*o**3 + 0 - w*o**2 - 4/15*o = 0. Calculate o.
-1, 0, 2
Let s(d) be the second derivative of -d**7/210 + 11*d**6/120 - 19*d**5/60 + 3*d**4/8 - 14*d**2 + 8*d. Let a(u) be the first derivative of s(u). Factor a(k).
-k*(k - 9)*(k - 1)**2
Let o be (-8)/4 + 216/6. Suppose o*l = 20*l + 42. Factor 0 - 4/7*u**2 + 0*u - 4/7*u**l.
-4*u**2*(u + 1)/7
Let c(w) be the first derivative of 5*w**6/6 - 7*w**5/2 - 15*w**4/8 + 125*w**3/6 - 115*w**2/4 + 15*w - 15. Solve c(s) = 0 for s.
-2, 1/2, 1, 3
Let h = 13 - 8. Let a be -4*(-10)/(-8) - -6. Determine s, given that -a - 8*s - 3 - h - 4*s**2 + 5 = 0.
-1
Let x(o) be the first derivative of o**6/63 - 96*o**5/35 + 1152*o**4/7 - 24576*o**3/7 - 87. Suppose x(h) = 0. Calculate h.
0, 48
Let k(d) be the second derivative of 3*d**5/20 + 5*d**4/2 + 29*d. Suppose k(a) = 0. Calculate a.
-10, 0
Determine g, given that -69 + 80*g + 100 + 45*g**2 - 316*g**3 - 88 - 243 + 311*g**3 = 0.
-3, 2, 10
Let c(a) be the first derivative of -98*a**5/15 - 21*a**4 - 218*a**3/9 - 12*a**2 - 8*a/3 + 30. Determine p, given that c(p) = 0.
-1, -2/7
Let u(i) = i + 2. Let y be u(0). Suppose j = -5*z + 2, -3*z + 4 = y*j + 2*z. Factor 2/7*g**j - 6/7*g + 4/7.
2*(g - 2)*(g - 1)/7
Let i(o) be the second derivative of -o**7/42 - o**6/30 + o**5/10 - 2*o - 17. Suppose i(u) = 0. What is u?
-2, 0, 1
Let c(q) be the second derivative of q**6/21 + 3*q**5/70 - 5*q**4/42 - q**3/7 + 351*q. Let c(k) = 0. Calculate k.
-1, -3/5, 0, 1
Let a(k) be the second derivative of 19*k + 0*k**3 + 0 + 3/20*k**5 + 1/6*k**4 + 1/30*k**6 + 0*k**2. Factor a(w).
w**2*(w + 1)*(w + 2)
Suppose 5*s - 48 + 33 = 0. Factor 11*a**2 + 23*a - 9*a**3 + 3*a**s - 28*a.
-a*(a - 1)*(6*a - 5)
Let z be 18 + (2 - 2)/4. Let j be 1/9 - (-4)/z. Determine a, given that 0 + 0*a**3 + 1/3*a**4 - j*a**2 + 0*a = 0.
-1, 0, 1
Let h(a) be the first derivative of -6 + 0*a + 3/2*a**2 - 1/8*a**4 + 1/10*a**3 + 1/25*a**5. Let b(d) be the second derivative of h(d). Factor b(f).
3*(f - 1)*(4*f - 1)/5
Let x = 70 - 63. Suppose -x*v = v. Solve v*a - 2/7*a**3 + 0 - 2/7*a**2 = 0 for a.
-1, 0
Let q(w) be the second derivative of w - 5/7*w**2 - 11/14*w**3 - 9 + 1/12*w**4. Determine n so that q(n) = 0.
-2/7, 5
Let o(h) = -h**3 + h**2 - 1. Let w(r) = -5*r + 4*r + 12*r**2 + 5 - 19*r**2 + 4*r**3. Let s be 2/(-5) + 7/5. Let v(y) = s*w(y) + 5*o(y). Factor v(f).
-f*(f + 1)**2
Let l(m) = -8*m**5 + m**4 - 36*m**3 - 7*m**2 - 7*m - 7. Let z(s) = 2*s**5 + 12*s**3 + 2*s**2 + 2*s + 2. Let n(x) = 2*l(x) + 7*z(x). Factor n(d).
-2*d**3*(d - 3)*(d + 2)
Let m(o) be the third derivative of -o**5/300 + 23*o**4/120 - 11*o**3/15 - 10*o**2 - 12*o. Factor m(z).
-(z - 22)*(z - 1)/5
Let l(c) = -c**2 + 7*c - 1. Let n be l(7). Let w(q) = -q**2 - 1. Let r(k) = -11*k + 31*k + 5 + k**2 + 14*k**2. Let h(a) = n*r(a) - 20*w(a). Factor h(i).
5*(i - 3)*(i - 1)
Suppose r + 2*i = 9, 0 = -3*r + 2*i - 1 + 12. Suppose -3 - 7*y**2 + 5 + r*y**2 - 8*y**3 + 8*y = 0. Calculate y.
-1, -1/4, 1
Suppose -3*t + 8 = -2*r, 0 = 5*r - 20*t + 25*t - 30. Determine z so that -15/7*z**r - 9/7*z - 1/7 + 25/7*z**3 = 0.
-1/5, 1
Suppose -4*o + 10 = -i, -372*o + 6 = -3*i - 368*o. Suppose 0*u + 1/2*u**i - 1/2 = 0. Calculate u.
-1, 1
Let g(v) be the first derivative of v**7/63 - 2*v**6/45 + v**5/30 + 6*v + 1. Let k(p) be the first derivative of g(p). Factor k(x).
2*x**3*(x - 1)**2/3
Let t be ((-456)/(-95))/(3/(-40)). Let o = t + 66. Factor -25/2*j**o + 5*j - 1/2.
-(5*j - 1)**2/2
Let p(z) = z**3 - 18*z**2 + 17*z + 2. Suppose 0*s - 5*l + 27 = s, -5*l - 41 = -3*s. Let c be p(s). Factor -3*h + 120 + 3*h**c - 120.
3*h*(h - 1)
Let r(y) be the third derivative of y**8/1176 - 2*y**7/735 - 109*y**2. Solve r(o) = 0 for o.
0, 2
Suppose -4*s = -3*i - 11, -5*i = s - 3 + 6. Determine c, given that 0*c + 2/5*c**s + 0 + 0*c**3 - 2/5*c**4 = 0.
-1, 0, 1
Let d(u) = -20*u**3 + 125*u - 120. Let t(o) = 5*o**3 - 31*o + 30. Let p(m) = 4*d(m) + 15*t(m). What is s in p(s) = 0?
-3, 1, 2
Let o be (1/20)/((-7)/(-42)). Factor 1/5 - o*u + 0*u**2 + 1/10*u**3.
(u - 1)**2*(u + 2)/10
Suppose -5*v + 667 = 3*b, 0*b + 4*b = v - 115. Let n = 397/3 - v. Factor 0 - 20/3*o**4 - 12*o**3 - 28/3*o**2 - n*o**5 - 8/3*o.
-4*o*(o + 1)**3*(o + 2)/3
Let f(r) = r**4 + 2*r**3 - 5*r**2 + 2. Let c(h) = h**4 + 2*h**3 - 6*h**2 + 2*h + 1. Let i(s) = -4*c(s) + 6*f(s). Factor i(u).
2*(u - 1)**2*(u + 2)**2
Factor -69*s**2 - 84 + 27/2*s**3 + 130*s - 1/2*s**4.
-(s - 21)*(s - 2)**3/2
Let m be 1/42*7*9/6. Find z, given that 0*z + m*z**5 + 0 + 1/2*z**2 -