ird derivative of -r**5/90 + r**4/18 + r**3/3 - 33*r**2. Suppose n(j) = 0. What is j?
-1, 3
Factor -12/7*x**3 + 0 - 2/7*x**5 - 2/7*x + 8/7*x**2 + 8/7*x**4.
-2*x*(x - 1)**4/7
Suppose -n + 0 + 10 = 0. Suppose 5*u - n = 2*a, -2*a = -4*u + 2 + 4. Factor -5*v**2 + 5*v**3 + 2*v**2 + v - v**u - 2*v**3.
-v*(v - 1)**3
Factor -5*t - 10*t + 21*t**2 - 4 - 2.
3*(t - 1)*(7*t + 2)
Let q = 479/9 + -53. Suppose q*d**2 - 2/9*d**4 + 2/9*d**5 + 0*d - 2/9*d**3 + 0 = 0. Calculate d.
-1, 0, 1
Suppose -4*k = -k. Let w = -2 + 4. Factor k*j**3 - 4*j**3 + 6*j**3 + w*j**2.
2*j**2*(j + 1)
Let n(c) be the second derivative of c**7/147 + 2*c**6/105 - c**4/21 - c**3/21 + 22*c. Factor n(s).
2*s*(s - 1)*(s + 1)**3/7
Let q(z) = z**3 - 27*z**2 - 6*z - 6. Let d(n) = 3*n**3 - 56*n**2 - 13*n - 13. Let i(p) = 6*d(p) - 13*q(p). Factor i(u).
5*u**2*(u + 3)
Suppose -8 = -2*q + q. Let i(v) = -21*v + 1. Let l be i(-1). Factor -24*x - q - 9*x - l*x**2 + 5*x - 5*x**3.
-(x + 2)**2*(5*x + 2)
Let v(o) = o**2 - 5*o - 10. Let p be v(7). Determine z so that -2*z**4 - 40*z**3 - 10*z**p - 28*z**2 - 8*z - 8*z**2 = 0.
-2, -1, -1/3, 0
Let i(y) be the second derivative of -1/10*y**5 - 8/105*y**6 + 0*y**3 + 0 - 1/21*y**4 + y - 1/49*y**7 + 0*y**2. Factor i(w).
-2*w**2*(w + 1)**2*(3*w + 2)/7
Let n(d) be the second derivative of -d**5/100 - d**4/60 + d**3/15 + 39*d. Suppose n(s) = 0. What is s?
-2, 0, 1
Let z(u) be the third derivative of -9/80*u**5 + 0*u + 0 + 0*u**4 + u**2 + 0*u**3 - 1/280*u**7 + 3/80*u**6. Let z(v) = 0. What is v?
0, 3
Let b(l) be the second derivative of -l**8/3360 - l**7/840 + l**6/360 - l**4/6 + 3*l. Let u(h) be the third derivative of b(h). Factor u(s).
-s*(s + 2)*(2*s - 1)
Let v = 109/372 - -5/124. Solve 2/3*w**2 + 0 + 0*w**3 + 1/3*w - 2/3*w**4 - v*w**5 = 0.
-1, 0, 1
Let t = 11 + -8. Solve a**2 - 2*a**2 + t*a**3 + 4*a**2 = 0.
-1, 0
Let z be (-2)/6 + 294/18. Determine u so that 16 - z + u**3 = 0.
0
Let i(r) = -r + 5. Let u be i(4). Let s(y) = -y + 1. Let d(p) = p**2 + 3*p - 4. Let k(t) = u*d(t) + 5*s(t). Determine v, given that k(v) = 0.
1
Suppose 0 = -c - n, 27 = 5*c - n - 3*n. Suppose -2*r + 9 = r. Find t such that t + t**4 - 2*t + c*t - r*t**3 - t**2 + t**5 = 0.
-2, -1, 0, 1
Suppose 0 = -3*f - y + 6, 6*f + 4*y = 3*f - 3. Suppose -5*l = -f*l - 4. Factor -u - 3*u**4 + u + u**2 - l*u**3.
-u**2*(u + 1)*(3*u - 1)
Let x be 23/(-6)*-8 - (-24 + 28). Factor -8/3*i**2 - x*i**4 + 12*i**5 + 0 + 52/3*i**3 + 0*i.
4*i**2*(i - 1)**2*(9*i - 2)/3
Suppose -o = -7 + 4. Let u(t) be the third derivative of -1/12*t**4 - 1/30*t**6 + 0*t**o + 0*t + 1/10*t**5 + 0 + t**2. Factor u(d).
-2*d*(d - 1)*(2*d - 1)
Let q = 103/261 - 5/29. Determine b so that 8/9 - 14/9*b**2 - 2/9*b**3 + 2/3*b**4 + q*b**5 + 0*b = 0.
-2, -1, 1
Suppose 11 = -4*g + 3. Let w be (1/6)/(g/(-8)). What is x in -16/3*x + 32/3*x**2 + w = 0?
1/4
Let n(t) be the first derivative of t**6 - 16*t**5/5 + 7*t**4/2 - 4*t**3/3 + 7. Factor n(k).
2*k**2*(k - 1)**2*(3*k - 2)
Let i(h) = -h**2 - 1 - 3*h - 2*h + 4*h. Let y(q) = 4*q**2 + 4*q + 1. Let t be -1*(-3)/(-3) + -2. Let w(g) = t*i(g) - y(g). Determine s, given that w(s) = 0.
-2, 1
Suppose v + 3*x - 5 = -1, 5*v + x = 20. Factor 2*w - v*w + 2*w**2 + 3*w - 3*w**2.
-w*(w - 1)
Let f(x) be the first derivative of -x**6/42 + x**4/14 - x**2/14 - 5. What is h in f(h) = 0?
-1, 0, 1
Let i(b) be the second derivative of -b**6/30 + 3*b**5/40 - b**4/24 - 5*b. Find y, given that i(y) = 0.
0, 1/2, 1
Let r(f) = 13*f**3 + 11*f**2 - 29*f + 5. Let s(x) = -2*x**3 + 2*x**3 + 10*x - 2 - 4*x**2 - 4*x**3. Let j(c) = 4*r(c) + 11*s(c). Factor j(g).
2*(g - 1)*(2*g + 1)**2
Let -2*j**3 - 12 + 0*j**3 - 2*j**2 + 12 = 0. Calculate j.
-1, 0
Factor 0*m**2 - 1/3*m**3 + 0 + 0*m - 1/3*m**4.
-m**3*(m + 1)/3
Factor 7 + 0 - 4*s**2 - 6 + 3.
-4*(s - 1)*(s + 1)
Let h(g) be the second derivative of -g**6/6 + g**5 - 5*g**4/4 - 22*g. Factor h(r).
-5*r**2*(r - 3)*(r - 1)
Let q be (-34)/(-10) + (-4)/10. Suppose s - q = -0. Factor s*j + j + 2*j - 2*j**3 + 4.
-2*(j - 2)*(j + 1)**2
Factor 2/3*n - 2*n**2 + 0 + 2*n**3 - 2/3*n**4.
-2*n*(n - 1)**3/3
Let u = 140 + -698/5. Factor -2/5*z**2 + 0*z + u.
-2*(z - 1)*(z + 1)/5
Let k = -2 - -8. Suppose -o = -3*s + 20, 8*o - 3*o = s - 30. Factor -4*y**3 + 4*y**2 - 2*y**5 - 2*y**4 - 2 + 2*y**3 + k*y**3 - 2*y + 0*y**s.
-2*(y - 1)**2*(y + 1)**3
Let y = 0 - -3. Let s(g) be the first derivative of -1/8*g**4 + 1/4*g**2 + 1/6*g**y - 2 - 1/2*g. Factor s(l).
-(l - 1)**2*(l + 1)/2
Suppose -250*u = -247*u - 6. Let i(g) be the second derivative of -1/2*g**u - 1/24*g**4 - 2*g + 1/4*g**3 + 0. Let i(p) = 0. What is p?
1, 2
Solve -3/7*b**2 + 0 + 9/7*b = 0 for b.
0, 3
Let z(r) be the first derivative of -4*r**6/21 - 32*r**5/35 - 25*r**4/14 - 38*r**3/21 - r**2 - 2*r/7 - 24. Factor z(l).
-2*(l + 1)**3*(2*l + 1)**2/7
Suppose 3*r + 9 = v + 4*v, -3*r - 6 = -4*v. Factor q**3 + 0*q**r - q + 2*q**2 - 2*q**3.
-q*(q - 1)**2
Let y(b) be the second derivative of b**5/4 + 5*b**4/4 + 5*b**3/3 + 32*b. Let y(v) = 0. Calculate v.
-2, -1, 0
Factor 15/4*w**3 + 0 + 3/4*w**5 - 3/2*w**2 - 3*w**4 + 0*w.
3*w**2*(w - 2)*(w - 1)**2/4
Let x(u) be the third derivative of -1/210*u**7 - 5*u**2 + 0 + 0*u**4 + 0*u + 0*u**3 - 1/120*u**5 + 1/80*u**6. Suppose x(r) = 0. Calculate r.
0, 1/2, 1
Let a = -6 - -8. Factor -x**4 + 2*x**3 - 2 + 0 + 3 - a*x.
-(x - 1)**3*(x + 1)
Let y = -6 - -11. Suppose -18*n - y - 3*n**3 - 1 + n + 2*n - 12*n**2 = 0. Calculate n.
-2, -1
Let s = 13 - 11. Let a(i) be the second derivative of s*i**3 - 7/12*i**4 + 2*i**2 - 3*i + 0. Determine h so that a(h) = 0.
-2/7, 2
Let t(a) = a. Let q be t(3). Let c(x) be the first derivative of 4*x**2 + 1 - 2/3*x**q - 8*x. Suppose c(o) = 0. What is o?
2
Let c(w) be the third derivative of w**5/210 + w**4/28 + 2*w**3/21 - 12*w**2. Find x, given that c(x) = 0.
-2, -1
Suppose 0 = -2*q + 2, 2*z + 0*z = -2*q + 18. Let n = -31/4 + z. Factor -n*j**3 + 0*j + 0 - 1/4*j**2.
-j**2*(j + 1)/4
Let o(j) be the third derivative of -j**6/180 - j**5/6 - 25*j**4/12 - 125*j**3/9 - 3*j**2. Solve o(q) = 0 for q.
-5
Let m(a) be the second derivative of 2*a**7/21 - 4*a**6/5 + 13*a**5/5 - 4*a**4 + 8*a**3/3 + 3*a. Find u such that m(u) = 0.
0, 1, 2
Let z(q) = 3*q**2 - q + 2. Let a = -14 + 8. Let u(d) = -3*d**2 + d - 3. Let n(p) = a*z(p) - 4*u(p). Factor n(y).
-2*y*(3*y - 1)
Suppose 5*o = -4*j - 7, -3*j + 1 = 2*j + 3*o. Suppose r**j + 2*r + 0*r**3 - r**4 - r - r**3 = 0. Calculate r.
-1, 0, 1
Let w = 271/10 - 128/5. Let z(a) be the second derivative of 3*a**3 - 4*a + 9/10*a**6 + 0 - w*a**2 - 3/10*a**5 - 2*a**4 - 2/7*a**7. Let z(p) = 0. Calculate p.
-1, 1/4, 1
Let p(o) be the second derivative of -o**4/8 - o**3/2 - 25*o. Factor p(b).
-3*b*(b + 2)/2
Suppose -4*p + 4 = -4*j, -2*p + 3*j = 8*j + 5. Find w such that -1/5*w**2 + 1/5*w**3 + 0*w + p = 0.
0, 1
Let v(w) = w**2 + 4*w. Let s be v(-4). Let x(t) be the second derivative of 2*t**2 + 1/20*t**5 - t - 1/4*t**4 + s*t**3 + 0. Factor x(p).
(p - 2)**2*(p + 1)
Let l(x) be the first derivative of x**6/540 - x**5/54 + 2*x**4/27 - 4*x**3/27 + x**2/2 + 3. Let i(t) be the second derivative of l(t). Factor i(u).
2*(u - 2)**2*(u - 1)/9
Let f(g) = 4*g**2 - 8*g + 2. Let z(y) = -12*y**2 + 24*y - 5. Let x(a) = 7*f(a) + 2*z(a). Factor x(l).
4*(l - 1)**2
Suppose 0*j + 0*j**2 + 1/2*j**3 - 5/2*j**4 + 0 + 2*j**5 = 0. What is j?
0, 1/4, 1
Let q = 47/51 + -10/17. Let w = q + 1/6. Determine a, given that w*a**3 + 1/2 + 3/2*a**2 + 3/2*a = 0.
-1
Let r = -104/99 + 16/9. What is h in -2/11*h**3 + 8/11*h**2 + 0 - r*h = 0?
0, 2
Factor 14/9*j - 2*j**2 - 2/9*j**4 + 10/9*j**3 - 4/9.
-2*(j - 2)*(j - 1)**3/9
Let a be 2 + (-1 + -3 - -4). Let f(b) be the third derivative of -2*b**a + 0 + 0*b**4 + 0*b**3 + 0*b + 0*b**5 - 1/120*b**6. Factor f(z).
-z**3
Let c = 14/29 + -10/261. Suppose -c*l**2 + 0 + 0*l - 2/9*l**3 = 0. What is l?
-2, 0
Determine f, given that 7*f**5 - f**4 - 4*f**5 + 2*f - 5*f**3 - 3*f**2 + 3*f**2 + f**2 = 0.
-1, -2/3, 0, 1
Let s(v) be the third derivative of -v**5/60 - 7*v**4/24 + v**2. Let y be s(-6). Determine x, given that 0*x**5 + 0*x - 8*x**4 - x + 3*x**5 + y*x**3 = 0.
-1/3, 0, 1
Let b(j) = -j**3 + 5*j**2 + 3*j + 18. Let p be b(6). Solve p - 2/3*n - 2/3*n**2 = 0.
-1, 0
Let w(d) be the second derivative of -d**5/10 - 29*d. Solve w(u) = 0 for u.
0
Let j be -1 - (-1 + -2) - 2. Let a(k) be the third d