 v(l) be the first derivative of l**4/21 - l**3/7 + l**2/7 - l + 4. Let y(u) be the first derivative of v(u). Determine d so that y(d) = 0.
1/2, 1
Let g(j) = -j + 4. Let x be g(3). Let r be (-1)/1 + x + 2. Solve -2/7*h**3 - 2/7*h + 4/7*h**r + 0 = 0 for h.
0, 1
Let q = 20 + -18. Let a(o) be the third derivative of -1/210*o**7 + 1/30*o**5 + 0*o**6 + 0 - 1/6*o**3 + 0*o + 3*o**q + 0*o**4. Suppose a(d) = 0. What is d?
-1, 1
Let w = -27 - -63. What is v in 12*v**2 + 6 + v**3 + 21*v - w*v - 4*v**3 = 0?
1, 2
Let t be 5*4/(-10) + 5. Factor -3/2*m**5 - 3*m**2 - t*m**3 - 3/2 + 9/2*m**4 + 9/2*m.
-3*(m - 1)**4*(m + 1)/2
Let c(i) = 7*i**2 + 9*i - 10. Let n(x) = -15*x**2 - 19*x + 21. Let w(o) = 13*c(o) + 6*n(o). Determine a so that w(a) = 0.
-4, 1
Let q = -332 + 8966/27. Let n(s) be the first derivative of 4/9*s + 1/9*s**2 - 2 - q*s**3. Solve n(i) = 0.
-1, 2
Find k, given that 0 + 0*k**2 + 2/3*k - 2*k**5 + 16/3*k**4 - 4*k**3 = 0.
-1/3, 0, 1
Let r(p) be the first derivative of -2*p**5/7 + p**4/14 + 10*p**3/21 - p**2/7 + 46. Suppose r(q) = 0. Calculate q.
-1, 0, 1/5, 1
Let s = -1280 - -8962/7. Solve 2/7 + 2/7*i - s*i**2 - 2/7*i**3 = 0.
-1, 1
Let o(z) be the first derivative of z**6/30 + 7*z**5/25 + 9*z**4/10 + 4*z**3/3 + 4*z**2/5 + 16. Factor o(h).
h*(h + 1)*(h + 2)**3/5
Solve -13*s**4 + 7*s**4 - 1 - 4*s**3 + 5*s**4 - 6*s**2 - 4*s = 0.
-1
Let g(o) be the first derivative of o**6/2 + 9*o**5/5 - 3*o**4/4 - 11*o**3 - 18*o**2 - 12*o + 29. Factor g(r).
3*(r - 2)*(r + 1)**3*(r + 2)
Let q be (1/(-20))/(20/(-648)). Let y = q - 3/25. Let -y*d**2 + 0 - 1/2*d = 0. What is d?
-1/3, 0
Factor -31*o**3 + 33*o**3 + 4*o**2 - 2*o**4 - 4*o + 4*o.
-2*o**2*(o - 2)*(o + 1)
Let q(d) be the second derivative of d**5/20 + 5*d**4/12 + 4*d**3/3 + 2*d**2 + 2*d. Suppose q(g) = 0. What is g?
-2, -1
Let k(d) be the third derivative of -d**7/1260 - d**6/360 + d**5/360 + d**4/72 - 13*d**2. Factor k(v).
-v*(v - 1)*(v + 1)*(v + 2)/6
Let b(h) = -4*h**2 + 2 - 2*h + 5*h**2 - h. Let o be b(3). Find g such that -2*g**4 + g**o + 2*g**3 + 0*g**4 - 3*g**3 = 0.
-1, 0, 1/2
Suppose -h + 2*s - 21 = 0, -4*h - 20 = 5*s + 64. Let k be -3 + (-66)/h + 1. Factor -2/7*b**5 + 0 + k*b**4 - 2/7*b - 12/7*b**3 + 8/7*b**2.
-2*b*(b - 1)**4/7
Let o = -3/17 + 43/51. Let -o + 1/3*h**2 - 1/3*h = 0. Calculate h.
-1, 2
Let u be (42/(-245))/((-3)/2). Let b(i) be the third derivative of -3/35*i**6 + 0 + u*i**5 + 11/84*i**4 + 1/21*i**3 - i**2 + 0*i. Solve b(n) = 0 for n.
-1/6, 1
Let y(r) be the first derivative of -3*r**4/16 + 3*r**3/4 - 9*r**2/8 + 3*r/4 - 8. Find f such that y(f) = 0.
1
Let o(w) be the second derivative of -w**7/840 + w**5/40 - w**4/6 - 3*w. Let c(v) be the third derivative of o(v). Factor c(b).
-3*(b - 1)*(b + 1)
Let t(x) = 5*x**4 - x**3 + 3*x - 3. Let d(n) = -6*n**4 + 2*n**3 - 4*n + 4. Let l(c) = -3*d(c) - 4*t(c). Let l(i) = 0. What is i?
-1, 0
Let a(w) = w + 15. Let m be a(-12). Find j, given that -4*j**2 - 5 + 8*j + 2*j**2 - m = 0.
2
Let h = -25 + -35. Let q be 6/(-8) + (-85)/h. Determine x, given that -x + q + 1/3*x**2 = 0.
1, 2
Let g(k) = -k**4 - k**2. Let y(v) = 3*v**4 + 2*v**3 + 7*v**2 - 8*v + 4. Let h(r) = -4*g(r) - y(r). Determine i, given that h(i) = 0.
-2, 1, 2
Let a(i) be the first derivative of -6*i**5/35 - i**4/7 + 2*i**3/3 - 2*i**2/7 + 15. Let a(p) = 0. Calculate p.
-2, 0, 1/3, 1
Let f(r) be the second derivative of -r**10/20160 + r**9/5040 - r**8/4480 + r**4/12 + 4*r. Let a(s) be the third derivative of f(s). Factor a(c).
-3*c**3*(c - 1)**2/2
Let 2*m**3 + 0*m**3 + 286*m**2 - 294*m**2 + 6*m = 0. What is m?
0, 1, 3
Let o(y) be the second derivative of 2*y + 0 + 1/18*y**4 - 4/9*y**2 + 0*y**3 + 1/90*y**5. Factor o(x).
2*(x - 1)*(x + 2)**2/9
Let j(a) be the third derivative of -a**8/168 - a**7/105 + a**6/30 + a**5/15 - a**4/12 - a**3/3 - 5*a**2. Solve j(c) = 0.
-1, 1
Let w(j) be the first derivative of j**4/6 - 4*j**3/9 + j**2/3 + 7. Factor w(q).
2*q*(q - 1)**2/3
Let x(c) be the first derivative of 2*c**6/3 - 3*c**4 + 8*c**3/3 - 7. Find q such that x(q) = 0.
-2, 0, 1
Suppose -2*w - 3*w - 4 = -2*s, -32 = -4*s - 2*w. Let l be s/2 + 12/(-4). Solve 1/2 + l*c**2 + c = 0.
-1
Let i be ((-6)/(-15))/((-3)/(-30)). Let x = i - 2. Factor -2/5*z**x + 2/5*z + 0.
-2*z*(z - 1)/5
Let p = 3805/7 - 543. Determine y, given that p + 2/7*y**3 - 4/7*y**2 - 2/7*y = 0.
-1, 1, 2
Find m, given that -3/2*m - 1/2*m**2 - 1 = 0.
-2, -1
Let b(d) = -d**2. Let a(q) = -8*q**2 + 2. Let r(l) = -1. Let f(v) = a(v) + 4*r(v). Let s(n) = 10*b(n) - f(n). Find h such that s(h) = 0.
-1, 1
Let i(m) be the second derivative of m**5/50 + m**4/15 - m**3/15 - 2*m**2/5 - 19*m. Factor i(a).
2*(a - 1)*(a + 1)*(a + 2)/5
Let u be (42/(-4))/((-11)/(-22)). Let a = 23 + u. Find c such that 0*c + 0*c**a - 2/3*c**3 + 0 = 0.
0
Let i(s) be the third derivative of 0 + 1/4*s**4 + 1/3*s**3 + 1/10*s**5 + 1/60*s**6 + 6*s**2 + 0*s. What is m in i(m) = 0?
-1
Let t be 3 + 3 + 30/(-3). Let d be (-2)/2 - 6/t. What is q in -q**2 + d*q**3 + 0*q + 0 = 0?
0, 2
Let o be 42/(-15) - -1*3. Let w be (2/(-10))/(2 + -3). Factor -2/5 + w*i + o*i**2.
(i - 1)*(i + 2)/5
Let f(u) = u**2 - 11*u + 28. Let m be f(4). Let s(i) be the first derivative of 3/2*i**2 + 0*i**4 - 6/5*i**5 + m*i + 3 + 2*i**3 - 1/2*i**6. Factor s(h).
-3*h*(h - 1)*(h + 1)**3
Let t = 157 + -1409/9. Determine s, given that -t*s**3 - 2/9*s**2 + 0 + 4/9*s + 2/9*s**4 = 0.
-1, 0, 1, 2
Factor 12/7 + 2*n + 2/7*n**2.
2*(n + 1)*(n + 6)/7
Suppose 5*h + 18 - 43 = 0. Let g(m) = -4*m**2 - 13*m - 9. Let f(z) = 4*z**2 + 12*z + 8. Let t(v) = h*f(v) + 4*g(v). Determine s so that t(s) = 0.
-1
Let p = 80 + -80. Factor 2/3*h**3 + 8/3 + p*h - 2*h**2.
2*(h - 2)**2*(h + 1)/3
Let u(d) be the second derivative of -d**5/15 - d**4/3 + 5*d**2/2 + 2*d. Let l(b) be the first derivative of u(b). Let l(y) = 0. Calculate y.
-2, 0
Let s be (-20)/8*(-4)/5. What is y in 6*y**s + 21*y + 11*y - 20*y**2 - 8 = 0?
2/7, 2
Let j(d) be the first derivative of -d**8/840 - d**7/420 + d**6/90 + 7*d**3/3 + 5. Let k(c) be the third derivative of j(c). Let k(n) = 0. Calculate n.
-2, 0, 1
Let y(z) = 4 - 8*z**3 + 3*z**2 - 5 + 4*z - 7 + z**2. Let d(g) = g**3 - g**2 - g + 1. Let c(b) = 14*d(b) + 2*y(b). Determine i, given that c(i) = 0.
-1
Let c(h) = -h**2 - 19*h - 6. Let v(s) = 20*s + 5. Let j(n) = 5*c(n) + 4*v(n). Factor j(m).
-5*(m + 1)*(m + 2)
Suppose 0 = -5*o + 20, 2*j - 2*o + 12 = 4*j. Let w(s) be the second derivative of -1/15*s**6 + 0 - s**j + 0*s**5 + 0*s**3 + 1/3*s**4 + 2*s. Factor w(x).
-2*(x - 1)**2*(x + 1)**2
Suppose 0*m = -5*u - 3*m + 14, 3*m - 2 = -2*u. Determine w so that w**u - 3*w**3 + 2*w**4 - 8*w**4 - 3*w**5 - w**4 = 0.
-1, 0
Let k(b) be the first derivative of b**8/5880 - b**6/630 + b**4/84 + b**3/3 - 1. Let z(o) be the third derivative of k(o). Factor z(g).
2*(g - 1)**2*(g + 1)**2/7
Let p(h) be the second derivative of 3*h**5/20 - h**3/2 + 3*h. Determine t, given that p(t) = 0.
-1, 0, 1
Let y be 4 + (-4 + 3)*(3 - 2). Let n(f) be the first derivative of 1 + 5/6*f**y + 2*f - 3*f**2. Solve n(g) = 0 for g.
2/5, 2
Let z(x) = -8*x**5 + 11*x**4 - 11*x**2 + 3*x. Let q(a) = -44*a**5 + 60*a**4 - 60*a**2 + 16*a. Let s(o) = 5*q(o) - 28*z(o). Solve s(p) = 0.
-1, 0, 1
Solve -2/15*h**4 + 0 + 2/15*h**2 - 4/15*h**5 + 4/15*h**3 + 0*h = 0 for h.
-1, -1/2, 0, 1
Let v(x) be the third derivative of x**8/336 - 2*x**7/105 + x**6/40 + 36*x**2 + 2. What is t in v(t) = 0?
0, 1, 3
Suppose -2*w - w = -18. Suppose -z + w - 4 = 0. Determine p so that -3/2*p**3 + p**4 + 0 - 1/4*p + p**z - 1/4*p**5 = 0.
0, 1
Let y = -6 - -7. Suppose -x - f + 3 + y = 0, 0 = 5*f + 10. Factor -10*p**5 + 10*p + 2*p**3 + 4*p**5 - 4 - 16*p**3 - x*p**3 + 20*p**4.
-2*(p - 1)**4*(3*p + 2)
Suppose 0 = a, -4*b = 2*a - 34 + 14. Let d(p) be the first derivative of -4/15*p**3 + 1 + 1/15*p**6 + 2/5*p + 2/25*p**b - 1/5*p**4 + 1/5*p**2. Factor d(r).
2*(r - 1)**2*(r + 1)**3/5
Let z(y) = y**3 + 8*y**2 - 10*y - 9. Let u be z(-9). Let 16 + u*i**2 - 7 + 12*i + 3*i**2 = 0. What is i?
-3, -1
Suppose -3*j + 15 + 0 = 0. Suppose 0 = -3*d + 2*d + j. Determine z, given that 2*z**3 + 10/3*z**4 - 10/3*z**2 + 0 - 8/3*z**d + 2/3*z = 0.
-1, 0, 1/4, 1
Let x = -13 - -27/2. Let g = -250 + 253. Factor 0 + x*t + 11/4*t**2 + 9/4*t**g.
t*(t + 1)*(9*t + 2)/4
Let q = -10 + 6. Let s = q + 4. Factor 2*y**2 - 2 + 2*y**2 + s*y**4 - 2*y**