vative of -p**5/18 + p**4/12 + 2*p**3/9 - p**2 + 4. Let o(c) be the second derivative of v(c). Factor o(b).
-2*(b - 1)*(5*b + 2)/3
Suppose -5*s + 19 - 9 = 0. Let 2*n**2 - 8*n**2 + s*n**2 - 4*n = 0. What is n?
-1, 0
Let y(x) = 1 + 3*x**2 - 4*x**2 + 2 - x. Let s be y(0). Factor 2*b**3 + 2*b + 0*b**3 - 4*b**s.
-2*b*(b - 1)*(b + 1)
Let t be ((-4)/3)/((-20)/30). Let -3*d**t - d**3 - 3*d**2 + 8*d**2 = 0. What is d?
0, 2
Suppose -26 + 6 = 5*o - 4*z, 2*o - 4*z + 20 = 0. Suppose o = -a - 4*a. Solve h**3 + 0 - 1/2*h**4 - 1/2*h**2 + a*h = 0 for h.
0, 1
Let n(p) = -p**4 + p**3 + p**2 - p + 1. Let c(a) = a**4 - 7*a**3 + 11*a**2 - 5*a + 2. Let m(b) = -c(b) + 2*n(b). Solve m(s) = 0 for s.
0, 1
Let i(z) be the third derivative of 0*z**3 + 1/165*z**5 + 0 - 1/660*z**6 - 1/132*z**4 + 0*z + 6*z**2. Find o, given that i(o) = 0.
0, 1
Let a(u) be the third derivative of 1/40*u**6 - 1/8*u**4 - u**2 + 0*u + 0*u**5 + 0 + 0*u**3. Solve a(r) = 0.
-1, 0, 1
Let f be (-204)/5*(-60)/(-18). Let q be f/(-30) - (-12)/(-9). Factor 2*s**4 - 2/5*s**5 + 8/5*s**2 - q*s**3 + 0 + 0*s.
-2*s**2*(s - 2)**2*(s - 1)/5
Let p(d) = -10*d**4 - 35*d**3 + 160*d. Let j(a) = 11*a**4 + 36*a**3 - 160*a. Let g(f) = 5*j(f) + 6*p(f). Factor g(l).
-5*l*(l - 2)*(l + 4)**2
Let q(x) be the first derivative of -x**6/21 + 2*x**5/35 + x**4/7 - 4*x**3/21 - x**2/7 + 2*x/7 - 7. Factor q(r).
-2*(r - 1)**3*(r + 1)**2/7
Let b(w) be the first derivative of -w**4/22 + 2*w**3/33 + 7. Determine k, given that b(k) = 0.
0, 1
Let g be 1 + 3/6*6. Let a be (-22)/(-6) + (g - 7). Factor -4/3*n**2 + a + 2/3*n**4 + 0*n**3 + 0*n.
2*(n - 1)**2*(n + 1)**2/3
Suppose 5/2*b**2 - 15/2*b**3 + 0 + 0*b = 0. What is b?
0, 1/3
Let b(t) be the third derivative of -3*t**5/200 + 7*t**4/240 + t**3/30 + 13*t**2. Factor b(z).
-(z - 1)*(9*z + 2)/10
Let n(h) be the first derivative of 0*h + 0*h**2 - 2/3*h**3 + 1 - 1/2*h**4. Solve n(i) = 0 for i.
-1, 0
Suppose 0 + 0*v - 2/21*v**2 + 8/7*v**3 - 24/7*v**4 = 0. Calculate v.
0, 1/6
Let j(z) be the third derivative of -z**5/180 - z**4/36 - 32*z**2. Factor j(s).
-s*(s + 2)/3
Let p(j) be the third derivative of 2*j**7/105 - j**6/6 + 44*j**2. Factor p(o).
4*o**3*(o - 5)
Let c(u) be the third derivative of u**8/320 + u**7/168 - u**6/15 + u**5/10 + 5*u**4/24 + 4*u**2. Let m(w) be the second derivative of c(w). Factor m(q).
3*(q - 1)*(q + 2)*(7*q - 2)
Let o(g) be the first derivative of g**6/2 - 6*g**5/5 + 2*g**3 - 3*g**2/2 + 1. Let o(x) = 0. Calculate x.
-1, 0, 1
Let u(w) = -w**3 - 5*w**2 + 18*w + 30. Let i be u(-7). Find z such that -9/2*z**i + 3/2*z**3 + 0 + 3*z = 0.
0, 1, 2
Determine h, given that 4/5*h**2 + 2/5*h**4 + 0*h + 0 - 6/5*h**3 = 0.
0, 1, 2
Find i such that -1372 + 139*i + 0*i**3 + 3*i**3 + i**3 + 449*i - 84*i**2 = 0.
7
Let o = 268/645 + -2/129. Determine l, given that -1/5 - 1/5*l**2 + o*l = 0.
1
Factor 3*j**4 + 0*j**2 + 0*j + 0 - 3*j**3 - 3/4*j**5.
-3*j**3*(j - 2)**2/4
Let l(p) = -p**2 + 9*p - 6 + 2*p - p - 1. Let b be l(9). Factor 0*s**b + 1/3*s**4 + 2/3*s**3 - 2/3*s - 1/3.
(s - 1)*(s + 1)**3/3
Let w(p) = -2*p - 12. Let t be w(-8). Factor k**2 - 3*k**4 + 6*k**t + 2*k**3 - 2*k**4.
k**2*(k + 1)**2
Suppose -1/4*t**3 + 0 + 0*t**2 + 1/4*t = 0. What is t?
-1, 0, 1
Let x(w) be the first derivative of -w**2 + 2*w + 1. Let s be x(0). Suppose 1/2*h**3 + 2 + 5/2*h**s + 4*h = 0. What is h?
-2, -1
Let m(b) be the first derivative of -b**5/90 + b**4/9 - 4*b**3/9 - 7*b**2/2 + 7. Let j(y) be the second derivative of m(y). Factor j(i).
-2*(i - 2)**2/3
Let m(v) be the first derivative of -1/5*v**6 + 7/5*v**2 - 3 - 16/25*v**5 + 4/5*v + 4/5*v**3 - 2/5*v**4. Let m(b) = 0. What is b?
-1, -2/3, 1
Let x(p) = 2*p**4 - 5*p**3 - 2*p**2 + 8*p. Let a(z) = z**4 - z**2 + z. Let w(o) = -6*a(o) + 2*x(o). Determine u so that w(u) = 0.
-5, -1, 0, 1
Let z be ((-265)/(-10))/(1/2). Let t = z + -28. Let 12*y**2 - t*y**5 - 39*y**3 + 160/3*y**4 - 4/3*y + 0 = 0. Calculate y.
0, 1/3, 2/5, 1
Let h be (-2)/(-6)*14/28. Let r(b) be the first derivative of -1/2*b**2 - 1 - h*b**3 - 1/2*b. Solve r(d) = 0 for d.
-1
Let p(n) be the first derivative of -n**4/2 - 8*n**3/3 - 4*n**2 + 4. Find z, given that p(z) = 0.
-2, 0
Factor -4*b - 2/9*b**2 - 18.
-2*(b + 9)**2/9
Factor 50/7*u**2 + 60/7*u + 18/7.
2*(5*u + 3)**2/7
Let 57*u**3 + 133*u**4 - 18 - 85*u**4 - 57*u - 69*u**4 + 39*u**2 = 0. Calculate u.
-1, -2/7, 1, 3
Determine a, given that 9*a**2 + 3*a**2 + 7*a**2 - 3*a**3 - 36*a - a**2 + 24 = 0.
2
Let k(x) be the second derivative of -2/3*x**3 - x - x**2 + 1/2*x**4 + 0. Let k(u) = 0. Calculate u.
-1/3, 1
Suppose 46 = 5*a - 5*w + 16, -2*w = 4*a - 12. Let h = a + -1. Factor r**2 + 0 + 1/2*r**h + 1/2*r.
r*(r + 1)**2/2
Let x(o) be the first derivative of 49*o**3/3 + 42*o**2 + 36*o + 8. Factor x(g).
(7*g + 6)**2
Let n = -78/217 + 20/31. Factor -2/7 + 4/7*w**2 - n*w**4 + 2/7*w + 2/7*w**5 - 4/7*w**3.
2*(w - 1)**3*(w + 1)**2/7
Factor 10/9*u + 2/9*u**2 + 8/9.
2*(u + 1)*(u + 4)/9
Let x(d) be the third derivative of d**7/210 + d**6/30 + d**5/10 + d**4/6 + d**3/6 + 4*d**2. Factor x(g).
(g + 1)**4
Let u = 116/603 - -2/67. Factor 2/9*f**4 + 0*f + u*f**2 + 4/9*f**3 + 0.
2*f**2*(f + 1)**2/9
Let s(n) be the first derivative of 1/108*n**4 + 1/90*n**5 - 3/2*n**2 - 2 + 0*n**3 + 0*n. Let d(h) be the second derivative of s(h). Factor d(q).
2*q*(3*q + 1)/9
Let x(p) be the first derivative of -2*p**5/65 + 22*p**4/13 - 484*p**3/13 + 5324*p**2/13 - 29282*p/13 + 18. Suppose x(j) = 0. What is j?
11
Let b = 232711 + -50032698/215. Let g = b + 1/43. Factor 0*z**2 + 2/5*z**4 - 2/5 - 4/5*z + g*z**3.
2*(z - 1)*(z + 1)**3/5
Let z(m) be the first derivative of m**5/300 + m**4/20 + 3*m**3/10 - m**2 - 4. Let b(i) be the second derivative of z(i). Factor b(c).
(c + 3)**2/5
Let w(g) be the second derivative of 0 + 1/63*g**7 + 0*g**5 + g + 0*g**4 - 1/45*g**6 + 0*g**3 + 0*g**2. Suppose w(q) = 0. What is q?
0, 1
Let t(s) be the second derivative of -s**7/168 + s**5/40 - s**3/24 - 9*s. Solve t(p) = 0 for p.
-1, 0, 1
Let r = 6 - 6. Find k such that r - 4*k**2 - 2*k**3 + 0 + 0 = 0.
-2, 0
Let w(k) = -k**2 - 9*k - 6. Let v be w(-8). Find y, given that 2/3*y**v - 1/3*y - 1/3 = 0.
-1/2, 1
Let i(z) be the third derivative of z**5/420 + z**4/168 - z**3/21 - 18*z**2. Factor i(t).
(t - 1)*(t + 2)/7
Let q = 33/100 + -2/25. Suppose -3/4*p**2 + 1 - q*p**3 + 0*p = 0. Calculate p.
-2, 1
Let p = -13 + 18. Let j(r) = -r + 2. Let k(u) = u**2 - 2*u + 5. Let z(b) = p*j(b) - 2*k(b). Factor z(n).
-n*(2*n + 1)
Let d(i) = -i - 11. Let n be d(-12). Let o = n - -1. Find j, given that -2/3 - 2/3*j**o + 4/3*j = 0.
1
Let f(u) be the third derivative of 0 - 1/2*u**3 - 4*u**2 + 3/4*u**4 - 9/20*u**5 + 0*u. Factor f(j).
-3*(3*j - 1)**2
Let y = 264 - 1316/5. Factor -y - 8/5*w**2 + 2*w + 2/5*w**3.
2*(w - 2)*(w - 1)**2/5
Let k = 7 - 7. Let n(t) be the first derivative of k*t + 3/2*t**4 + 1 + t**2 - 8/3*t**3. Factor n(i).
2*i*(i - 1)*(3*i - 1)
Let f(n) be the second derivative of n**4/72 - n**3/9 + n**2/3 - 10*n. Factor f(g).
(g - 2)**2/6
Let r be ((-228)/133)/(2 - (-19)/(-7)). Factor 0 + 12/5*a - r*a**2 + 3/5*a**3.
3*a*(a - 2)**2/5
Let z(d) be the second derivative of -d**6/165 - d**5/55 + 2*d**3/33 + d**2/11 - 7*d. Let z(a) = 0. Calculate a.
-1, 1
Let l(i) be the third derivative of i**5/20 - i**4/12 + 4*i**2. Let l(r) = 0. What is r?
0, 2/3
Let r(k) be the first derivative of k**6/960 - k**4/16 - 7*k**3/3 - 2. Let n(c) be the third derivative of r(c). Factor n(f).
3*(f - 2)*(f + 2)/8
Let y(w) = -w**5 + w**4 - w**3 + w - 1. Let z(a) = -a**5 - 4*a**3 + 4*a**2 + 3*a - 4. Let x(b) = -2*y(b) + z(b). Suppose x(m) = 0. What is m?
-1, 1, 2
Suppose -3*k + 20 = 14. Let u(r) be the third derivative of -4/3*r**3 - 2*r**k + 0*r + 0 - 1/3*r**4 - 1/30*r**5. Find c such that u(c) = 0.
-2
Factor -2/15*h - 2/5*h**2 + 2/15*h**3 + 2/5.
2*(h - 3)*(h - 1)*(h + 1)/15
Let m be ((-50)/(-2975))/(1/7). Factor m*u**4 + 2/17 - 2/17*u**5 - 4/17*u**2 - 2/17*u + 4/17*u**3.
-2*(u - 1)**3*(u + 1)**2/17
Let o(z) be the second derivative of 2*z + 1/24*z**4 + 1/4*z**2 + 0 - 1/6*z**3. Determine g, given that o(g) = 0.
1
Let m = -8 - -11. Suppose 3*t + 9 = -m*c, 4*t - c = 8 - 5. Factor 0*g**2 - 1/2*g + 1/2*g**3 + t.
g*(g - 1)*(g + 1)/2
Let v(u) = u**2 + 9*u + 7. Let c be v(-8). Let a be (c/(-5))/(12/20). Factor h**2 + 1/3*h**3 + h + a.
(h + 1)**3/3
Suppose -b 