+ 1)*(5*b + 2)/7
Let y(x) be the third derivative of x**6/80 + 3*x**5/40 + x**4/8 - 5*x**2. Suppose y(r) = 0. Calculate r.
-2, -1, 0
Let w(y) = y**4. Let a(k) = -5*k**3 + 5*k**2 + 5*k. Let j(u) = -a(u) + 5*w(u). Find q, given that j(q) = 0.
-1, 0, 1
Let h(s) = s - 2. Let c = 4 + 1. Let i be h(c). Factor 0*m - m + m**2 + 2 + m**i - 3.
(m - 1)*(m + 1)**2
Factor w**3 + 74*w**2 - 36*w**2 + 3*w**4 - 38*w**2 + 2*w**5.
w**3*(w + 1)*(2*w + 1)
Let n(h) be the third derivative of 1/60*h**4 + 0*h**3 + 0*h - 1/300*h**6 - h**2 + 0 + 0*h**5. Factor n(j).
-2*j*(j - 1)*(j + 1)/5
Solve 2/7*g**3 + 6/7*g**5 + 0 + 0*g - 2/7*g**2 + 10/7*g**4 = 0.
-1, 0, 1/3
Let b(h) be the first derivative of -1/5*h**5 + 7/2*h**2 + 5/4*h**4 - 3*h**3 - 2*h - 2. Suppose b(p) = 0. What is p?
1, 2
Let p(y) be the second derivative of y**4/12 + y**2 + 3*y. Let x be p(0). Determine c, given that -4*c**2 - x + 6*c - c + 11*c**2 = 0.
-1, 2/7
Let k(j) be the second derivative of -j**4/54 - 2*j**3/27 - 27*j. Solve k(m) = 0.
-2, 0
Let z(o) be the second derivative of o**7/14 + 3*o**6/10 + 9*o**5/20 + o**4/4 - 7*o. Let z(d) = 0. What is d?
-1, 0
Suppose -28 = -3*c + f, -5*f = 3*c + 2*c - 80. Let y = 15 - c. Suppose 2/3*i - 1/3*i**y + 0*i**3 + 0 + i**2 = 0. Calculate i.
-1, 0, 2
Suppose 0 = -5*k - 4*w - 8, -5*w + 7*w = 5*k - 4. Find m, given that k*m**2 - 3/2*m**3 + 3/2*m - 3/4 + 3/4*m**4 = 0.
-1, 1
Let j be -8 - -4 - -64*1. Factor 60 - 2*s**4 - j + 2*s**2 + 2*s**3 - 2*s.
-2*s*(s - 1)**2*(s + 1)
Let x(o) = o**3 + 2*o**2 - 5*o. Let d(n) = n**3 - n**2 + n. Let s(z) = -2*d(z) - x(z). Let s(p) = 0. Calculate p.
-1, 0, 1
Solve 10*n**2 - 10*n**2 + 2*n**3 - 3*n + n**3 = 0.
-1, 0, 1
Let q(u) be the second derivative of -u**4/12 + u**3/6 + 16*u. Factor q(r).
-r*(r - 1)
Suppose 6*p = -5 + 11. Let g(l) be the first derivative of -1/9*l**2 + 0*l - p + 2/27*l**3. What is v in g(v) = 0?
0, 1
Suppose 3*p + 276 = 4*s, 4*s + 2*p = 7 + 249. Suppose -v = -4*v + s. Factor 3 + 3*r**4 + 20*r**2 + v*r**3 + 12*r - 10*r**3 - 2*r**2.
3*(r + 1)**4
Let c be (-111)/225*2 - -1. Let x(h) be the third derivative of 0 - 3*h**2 + 1/60*h**4 - c*h**5 + 1/300*h**6 + 0*h**3 + 0*h. Determine j, given that x(j) = 0.
0, 1
Let j(m) be the third derivative of -m**6/240 - m**5/80 - m**4/96 - 14*m**2. Factor j(n).
-n*(n + 1)*(2*n + 1)/4
Factor -3/8*w**4 + 0*w**2 + 0 + 0*w + 9/8*w**3.
-3*w**3*(w - 3)/8
Suppose 5*t + 2*d = 4*d - 8, -3*d = 5*t - 12. Let g(s) be the second derivative of t*s**3 + 0 + 1/4*s**2 + s - 1/24*s**4. Find o such that g(o) = 0.
-1, 1
Let t(s) = -s**3 - 2*s**2 - 7*s + 6. Let v(p) = p - 1. Let u(n) = t(n) + 6*v(n). Factor u(b).
-b*(b + 1)**2
Let q(f) be the third derivative of 4*f**6/165 + 4*f**5/55 + 3*f**4/44 + 3*f**2. Factor q(x).
2*x*(4*x + 3)**2/11
Suppose -3*p = -32 + 8. Suppose -4*q - 12 = -p*q. Factor 0 + 1/2*o**2 - 1/4*o - 1/4*o**q.
-o*(o - 1)**2/4
Factor 7*c**2 + 22 - 30 - 44*c + 20.
(c - 6)*(7*c - 2)
Suppose -2*o + o + 1 = 4*i, 0 = -i - 4*o + 4. Let d(z) be the first derivative of 3 + i*z + 1/12*z**3 - 1/16*z**4 + 0*z**2. Factor d(w).
-w**2*(w - 1)/4
Let u(o) be the first derivative of o**7/840 + o**6/120 + o**5/60 + 4*o**3/3 - 5. Let w(m) be the third derivative of u(m). Solve w(b) = 0.
-2, -1, 0
Factor -5*a**2 + 3*a + 48 - 8 - 28*a - 10*a.
-5*(a - 1)*(a + 8)
Let t = -33 - -22. Let p = t - -34/3. Factor -1/3 - p*b**2 - 2/3*b.
-(b + 1)**2/3
Let k(c) be the second derivative of -c**7/42 - 7*c**6/45 - 11*c**5/60 + 4*c**4/9 + 2*c**3/3 + 22*c - 1. Determine q so that k(q) = 0.
-3, -2, -2/3, 0, 1
Let g be 108/(-60) + (4/2)/1. Factor g*h**2 + 4/5 - 4/5*h.
(h - 2)**2/5
Let k(y) be the second derivative of -y**6/420 - y**2/2 - 3*y. Let t(g) be the first derivative of k(g). Factor t(z).
-2*z**3/7
Let w(m) be the first derivative of 4*m**3/3 + 2*m**2 - 17. Find j, given that w(j) = 0.
-1, 0
Let a(z) be the first derivative of -1/60*z**5 - 3*z + 1/18*z**3 + 3 + 0*z**4 + 0*z**2. Let i(k) be the first derivative of a(k). Factor i(t).
-t*(t - 1)*(t + 1)/3
Factor 14*n**3 + 16 + 24*n**2 + 25*n - 10*n**3 + 11*n.
4*(n + 1)**2*(n + 4)
Let h(f) be the second derivative of -f**7/210 - f**6/50 - f**5/50 - f. Solve h(n) = 0 for n.
-2, -1, 0
Factor 0 + 1/4*c**2 + 0*c + 1/4*c**3.
c**2*(c + 1)/4
Let g(x) = -x**3 - 2*x**2 + 2*x - 1. Let u be g(-3). Let s(o) be the first derivative of 1/12*o**3 + 1/8*o**2 - u - 1/2*o. Find m, given that s(m) = 0.
-2, 1
Let d(c) = -c**2 + 7*c - 4. Let z be d(6). Factor -3*f**z - f - 6*f**2 + 8*f**2.
-f*(f + 1)
Let j(c) be the second derivative of -c**4/12 - 2*c**3/3 - 33*c. Solve j(d) = 0 for d.
-4, 0
Suppose -b - 4*a = 13, 3*b - 5*a - 19 = 10. Let z(j) be the third derivative of -j**2 + 0 - 1/120*j**6 + 1/12*j**4 + 0*j - 1/60*j**5 + 0*j**b. Factor z(k).
-k*(k - 1)*(k + 2)
Let g(a) = a**4 - a**3 + a**2. Let i(s) = -6*s**4 + 5*s**3 - 8*s**2 + 2*s. Let n(z) = -14*g(z) - 2*i(z). Factor n(k).
-2*k*(k - 2)*(k - 1)*(k + 1)
Let l(n) be the third derivative of -1/30*n**5 + 0 - 1/15*n**6 - 1/84*n**8 + 0*n + 4*n**2 + 0*n**4 - 1/21*n**7 + 0*n**3. Let l(g) = 0. What is g?
-1, -1/2, 0
Let c(q) be the first derivative of 3*q**4/8 - q**3 + 3*q**2/4 - 16. Factor c(j).
3*j*(j - 1)**2/2
Let s(x) be the second derivative of x**7/70 - 3*x**5/50 + x**3/10 - 6*x. Factor s(w).
3*w*(w - 1)**2*(w + 1)**2/5
Let q = -16 + 16. Let v(u) be the second derivative of -1/42*u**7 + 0*u**3 + q + 0*u**4 + 0*u**2 + 2/15*u**6 - 1/5*u**5 + 2*u. Solve v(z) = 0 for z.
0, 2
Let z(c) be the third derivative of -c**8/1848 + c**7/1155 + c**6/660 - c**5/330 + 9*c**2. Let z(x) = 0. What is x?
-1, 0, 1
Let x(n) be the first derivative of -n**4/14 - 8*n**3/21 - 5*n**2/7 - 4*n/7 - 4. Find h, given that x(h) = 0.
-2, -1
Factor 2/3*j**3 - 4/3*j + j**2 - 1/3*j**4 - 4/3.
-(j - 2)**2*(j + 1)**2/3
Let y be 1045/200 - 6/10. Let w = -19/8 + y. Suppose -1/2*x**2 + 1/4 + x + w*x**4 - 3*x**3 = 0. What is x?
-1/3, 1
Find p, given that -4 + 0*p**2 - 8*p + 3*p**2 + 4*p**2 - 11*p**2 = 0.
-1
Let c(h) be the first derivative of h**5/80 - h**4/48 - h**3/24 + h**2/8 - 3*h + 4. Let b(l) be the first derivative of c(l). Factor b(z).
(z - 1)**2*(z + 1)/4
Let s(x) be the first derivative of 2/11*x**5 + 6/11*x**4 + 0*x**2 - 2 + 0*x + 8/33*x**3. Factor s(b).
2*b**2*(b + 2)*(5*b + 2)/11
Suppose 75*d - 87*d = 0. Factor 0 - 2/5*k**3 + 2/5*k + d*k**2.
-2*k*(k - 1)*(k + 1)/5
Let l(a) be the first derivative of -a**3 + 63*a**2 - 1323*a - 62. Factor l(y).
-3*(y - 21)**2
Let p be (-2 - -2)*((-1 - -2) + 0). Let l(u) be the first derivative of -1/3*u**3 + p*u + 0*u**2 - 3. Determine i so that l(i) = 0.
0
Let d(l) be the third derivative of -l**5/360 - l**4/48 + l**3/9 + l**2 + 7*l. Solve d(b) = 0 for b.
-4, 1
Let p(n) be the second derivative of 2*n - 1/24*n**7 + 7/40*n**5 + 1/12*n**4 - 7/24*n**3 - 1/60*n**6 + 0 - 1/4*n**2. What is o in p(o) = 0?
-1, -2/7, 1
Let m(d) = -8*d**5 - 23*d**4 - 31*d**3 - 24*d**2 - 5*d. Let t(l) = 39*l**5 + 114*l**4 + 156*l**3 + 120*l**2 + 24*l. Let k(g) = -24*m(g) - 5*t(g). Factor k(q).
-3*q**2*(q + 2)**3
Factor -15/2*p**2 - 6*p + 6 + 9/2*p**3.
3*(p - 2)*(p + 1)*(3*p - 2)/2
Let q(d) be the first derivative of 7*d**4/32 + 19*d**3/24 + d**2/2 - d/2 + 6. Factor q(c).
(c + 1)*(c + 2)*(7*c - 2)/8
Let u(l) be the second derivative of -l**6/135 - l**5/45 - l**4/54 - 8*l. Factor u(p).
-2*p**2*(p + 1)**2/9
Let w be (-8)/(-36) + (-10)/216. Let f = w - -2/27. Solve -f*l**3 + 0 - 1/4*l**2 + 0*l = 0.
-1, 0
Let d = -6 - -8. Let o(p) = p**3 + 6*p**2 - 26*p + 9. Let w be o(-9). Suppose w + 18/7*a**5 + 2/7*a**d + 0*a + 30/7*a**4 + 2*a**3 = 0. Calculate a.
-1, -1/3, 0
Let d(t) be the first derivative of -t**4/2 - 2*t**3/3 + t**2 + 2*t - 49. Determine m so that d(m) = 0.
-1, 1
Let t(d) = -d**3 + 12*d**2 - 11*d - 3. Let x(q) = -8*q**3 + 108*q**2 - 100*q - 28. Let g(w) = -28*t(w) + 3*x(w). Determine p so that g(p) = 0.
0, 1, 2
Let p(v) be the first derivative of 0*v + 1/2*v**2 - 1 - 1/3*v**3. Find k, given that p(k) = 0.
0, 1
Let l(o) be the third derivative of o**8/112 + o**7/35 - o**5/10 - o**4/8 + 6*o**2. Factor l(i).
3*i*(i - 1)*(i + 1)**3
Suppose 3*g + 15 = 8*g. Factor 0*q + 0*q**2 + 0 + 0*q**g + 1/2*q**4.
q**4/2
Let y be (-165)/(-25) - 3/(-5). Solve 14/5*q**3 - 2/5*q**4 - 16/5 + 8*q - y*q**2 = 0.
1, 2
Let y(d) = 3*d**4 - 2*d**3 + 4*d**2 - 2*d - 1. Let t = 16 - 49. Let s