second derivative of v**8/6720 + v**7/1260 + v**6/720 + v**4/4 - v. Let d(r) be the third derivative of j(r). Factor d(x).
x*(x + 1)**2
Let f be (-22)/4 + 27/(-18). Let q = -7 - f. What is k in -1/3*k**2 + q*k + 0 = 0?
0
Let n = -4/7 - -23/28. Factor b**3 + 1/2*b - n*b**4 + 0 - 5/4*b**2.
-b*(b - 2)*(b - 1)**2/4
Let k(p) be the third derivative of -p**5/210 + p**4/14 + 45*p**2. Solve k(l) = 0 for l.
0, 6
Factor 8*k**5 - 10*k**3 - 25*k**4 + 20*k**4 - 3*k**5.
5*k**3*(k - 2)*(k + 1)
Suppose 3 - 6 = -s - 4*j, -3*s + 9 = -3*j. Let n(t) be the second derivative of 1/6*t**4 - 3*t + 1/2*t**s + 0 + 1/2*t**2. What is o in n(o) = 0?
-1, -1/2
Let m(b) = b - 9. Let p be m(9). Suppose p = t - 3*t. Factor -3*a**3 - a + t*a**2 + 2*a**3 + 2*a**2.
-a*(a - 1)**2
Let g(y) be the first derivative of 15*y**4/2 - 34*y**3/3 + 2*y**2 - 48. Factor g(v).
2*v*(v - 1)*(15*v - 2)
Let b(f) = f**2 + 22*f + 24. Let q be b(-21). Let r(h) be the second derivative of -1/48*h**4 + 0*h**q + 0 + 1/8*h**2 - h. Solve r(k) = 0.
-1, 1
Let j(p) = -p**4 + p + 1. Let a(y) = -21*y**4 - 40*y**3 - 30*y**2 + 6*y + 11. Let t(w) = a(w) - 6*j(w). Factor t(f).
-5*(f + 1)**3*(3*f - 1)
Let p be 63/49 + 2/(-7). Let z be (-2)/(-2*1/p). Factor 3 + 2*g - 2*g**2 - z + 0*g**2 - 2*g**3.
-2*(g - 1)*(g + 1)**2
Let t(h) be the first derivative of -h**6/420 + h**5/70 - h**4/42 + 5*h**2/2 + 3. Let s(p) be the second derivative of t(p). Factor s(n).
-2*n*(n - 2)*(n - 1)/7
Let s(f) be the first derivative of f**5/5 - f**4/4 - f**3/3 + f**2/2 - 18. Factor s(u).
u*(u - 1)**2*(u + 1)
Suppose 0 = -5*d - 0 - 25. Let u = d - -11. Find s such that 11*s**4 + u*s**3 - s**5 + s**5 + 3*s**5 - 2*s**4 = 0.
-2, -1, 0
Factor 3*s**2 - 2*s - 3*s**3 - 3*s**2 - s + 6*s**2.
-3*s*(s - 1)**2
Let d be ((-3)/2)/(15/(-80)). Let x(t) be the first derivative of -1/3*t**6 + 0*t**2 + 6/5*t**5 + 3 + d*t - 14/3*t**3 + 1/2*t**4. Suppose x(c) = 0. What is c?
-1, 1, 2
Let t be (-17)/(-7) - (-24)/(-56). Let p be 3/(5/2 - 1). Solve -y - 2*y**t - 5*y + p*y = 0 for y.
-2, 0
Let r(n) be the third derivative of n**7/105 - n**6/30 + 3*n**2. Factor r(z).
2*z**3*(z - 2)
Let u(z) = 3*z**3 + z**2 - 2*z + 1. Let j be u(1). Factor -n**5 + n**3 - 5*n**3 + 5*n**j.
-n**3*(n - 1)*(n + 1)
Let q be (2 + -2 + 1)/(1 - -4). Solve -1/5*j**4 - 1/5 + 1/5*j**5 + q*j + 2/5*j**2 - 2/5*j**3 = 0.
-1, 1
Suppose 0 = 28*c - 54*c + 30*c. Factor 3/2*s**2 + 3/2*s**4 + 3*s**3 + c*s + 0.
3*s**2*(s + 1)**2/2
Suppose 5*l - 2 = 8. Factor 0*d**3 - l*d**2 + d**2 + 1 - d**3 + 0*d**2 + d.
-(d - 1)*(d + 1)**2
Let y = 2651/850 + -52/17. Let q(o) be the second derivative of -y*o**5 + 1/10*o**3 + 0*o**4 - o + 0 + 0*o**6 + 0*o**2 + 1/70*o**7. Factor q(n).
3*n*(n - 1)**2*(n + 1)**2/5
Let f(h) be the third derivative of h**6/60 + 2*h**5/15 + 5*h**4/12 + 2*h**3/3 + 12*h**2. Factor f(z).
2*(z + 1)**2*(z + 2)
Suppose 0 = -4*q - 5*q + 18. Let n(z) be the second derivative of -1/3*z**3 + 1/6*z**4 - 2*z**q - 3*z + 0. Suppose n(m) = 0. Calculate m.
-1, 2
Let a(t) be the second derivative of -t**7/56 - t**6/24 + t**5/16 + 5*t**4/48 - t**3/12 + 6*t. Find q, given that a(q) = 0.
-2, -1, 0, 1/3, 1
Let o(n) be the first derivative of 0*n**4 - 1/7*n**3 + 1/70*n**5 + 2*n - 2/7*n**2 - 2. Let u(a) be the first derivative of o(a). Factor u(p).
2*(p - 2)*(p + 1)**2/7
Let f(j) = j**2 - 1. Let i = 10 + -4. Let c(n) = -9*n**2. Let m(b) = i*f(b) + c(b). Let a(s) = -7*s**2 - 13. Let r(k) = 6*a(k) - 13*m(k). Factor r(g).
-3*g**2
What is g in 0 + 4/3*g**3 - 16/3*g**2 + 0*g = 0?
0, 4
Let q(p) be the second derivative of -p**8/6720 - p**7/420 - p**6/80 - p**5/30 + p**4/2 - 9*p. Let o(j) be the third derivative of q(j). Factor o(h).
-(h + 1)**2*(h + 4)
Let o be 6/3*-1 + 9. Let l = 7 - o. Solve -2*x**2 + l*x - 5*x + 3*x = 0.
-1, 0
Let i(d) be the second derivative of -4*d**5/5 - 11*d**4 - 48*d**3 - 32*d**2 + 8*d. Suppose i(p) = 0. What is p?
-4, -1/4
Let b be (1 - 20/15)*-1. Let k(d) be the first derivative of b*d**6 + d**2 - 1 - 2*d - d**4 + 4/3*d**3 - 2/5*d**5. Factor k(y).
2*(y - 1)**3*(y + 1)**2
Let i(n) be the second derivative of 7*n**5/24 - 37*n**4/36 + n**3/9 + 2*n**2/3 + n. Factor i(f).
(f - 2)*(5*f - 2)*(7*f + 2)/6
Let c(q) be the second derivative of -361*q**4/16 + 19*q**3/2 - 3*q**2/2 + 28*q. Find u, given that c(u) = 0.
2/19
Factor 0 + 0*x - 4/5*x**2 - 2/5*x**3.
-2*x**2*(x + 2)/5
Let i(w) be the first derivative of -w**7/105 - w**6/20 - w**5/10 - w**4/12 + 7*w**2/2 - 9. Let p(z) be the second derivative of i(z). Factor p(f).
-2*f*(f + 1)**3
Let 9*d - 2*d - 5*d**2 + 14*d - d = 0. What is d?
0, 4
Let p(w) be the third derivative of -2/9*w**3 + 0*w - w**2 + 1/90*w**5 + 1/36*w**4 + 0. Suppose p(j) = 0. What is j?
-2, 1
Let u(h) be the first derivative of -2*h + 1/3*h**6 + 5*h**4 - 20/3*h**3 + 1 - 2*h**5 + 5*h**2. Factor u(o).
2*(o - 1)**5
Let q(t) be the third derivative of -t**5/12 - 5*t**4/6 - 5*t**3/2 - 10*t**2. Factor q(x).
-5*(x + 1)*(x + 3)
Let r(l) be the first derivative of l**6/120 - l**5/120 + 2*l**3/3 + 4. Let y(z) be the third derivative of r(z). Find s such that y(s) = 0.
0, 1/3
Let h(c) = -c**3 + 17*c**2 + 15*c + 56. Let i be h(18). What is v in 2/7*v**3 + 0 - 4/7*v**i + 0*v = 0?
0, 2
Let o(s) be the first derivative of -4 - 2/9*s**3 + 2/3*s**2 - 2/3*s. Find m such that o(m) = 0.
1
Let u(w) = -2*w**2 - 8*w - 8. Let s(n) = -2*n**2 - 8*n - 8. Let h = -16 + 11. Let z(q) = h*u(q) + 6*s(q). Factor z(d).
-2*(d + 2)**2
Solve -8/11*u + 4/11*u**3 - 2/11*u**4 - 8/11 + 6/11*u**2 = 0.
-1, 2
Let m be (-12)/(-66) - 3/1386*62. Let d(a) be the first derivative of -1/14*a**4 - m*a**6 + 0*a**3 + 0*a**2 - 3 + 0*a - 4/35*a**5. What is s in d(s) = 0?
-1, 0
Suppose 3*c = p - 5, -2*p = -c + 1 + 14. Let l = -6 - p. Factor -24*h**l - 45*h**3 - h**4 - 8*h + 4*h - 24*h**2.
-h*(h + 1)*(5*h + 2)**2
Suppose -b + 18 = -0*b - 3*g, -5*g = -5*b + 70. Find y such that 18 - b*y**2 - 5 + 6*y**3 + 3*y**4 - 4 - 6*y = 0.
-3, -1, 1
Let j(c) be the first derivative of 21*c**3/4 - 3*c**2/4 + 9. Determine u, given that j(u) = 0.
0, 2/21
Suppose 0*r - 32 = -16*r. Solve -16/5*a - 4/5 + 11/5*a**3 - 4/5*a**4 + 3/5*a**r = 0.
-1, -1/4, 2
Factor -2 - 8*m**4 + 26*m + 46*m**3 + 14*m - 14 + 84*m**2 + 16*m**4.
2*(m + 2)**3*(4*m - 1)
Let g(d) be the third derivative of -d**8/1680 + d**7/420 - d**6/360 + 7*d**3/6 + 8*d**2. Let p(s) be the first derivative of g(s). Factor p(f).
-f**2*(f - 1)**2
Let j(d) = d**4 - 3*d**3 + 2*d. Let c(p) = p**3 - p. Let k(a) = 2*c(a) + j(a). Factor k(y).
y**3*(y - 1)
Let c = 3159/22 + -142. Let d = -12/11 + c. Let 3/2*y - d*y**3 + 1 + 0*y**2 = 0. Calculate y.
-1, 2
Suppose 4*y + 5*g - 7 - 12 = 0, -2*y - 2*g + 10 = 0. Suppose 2*x - y = -2*t, 2*t - 12 = -4*x + 7*t. Factor 0 + 0*c**2 + 0*c - 2/3*c**x.
-2*c**3/3
Suppose -t + 17 = -3. Suppose f = 3*n + 3 - 15, -5*n + t = 0. Factor 2/7*i**2 + 0*i + f + 2/7*i**3.
2*i**2*(i + 1)/7
Determine a so that -11/5*a**2 - 3/5*a**3 - 8/5*a + 4/5 = 0.
-2, 1/3
Find o such that -24*o - 4/3*o**2 + 6*o**3 + 16/3 = 0.
-2, 2/9, 2
Let x = 7 + -2. Factor 0*m**5 + m**5 + 2*m**2 - 2*m**3 - 2*m**4 + m**x.
2*m**2*(m - 1)**2*(m + 1)
Let g(c) be the first derivative of c**4/5 + 2*c**3/5 - 2*c**2/5 - 3. Factor g(p).
2*p*(p + 2)*(2*p - 1)/5
Suppose 2*y - 2*s = -1 - 7, 2 = 3*y + 4*s. Let p be ((-4)/(-12))/(y/(-12)). Factor 1/2 + f + 1/2*f**p.
(f + 1)**2/2
Let k(p) be the first derivative of -1 + 1/6*p**4 + 1/9*p**2 + 0*p - 2/45*p**5 - 2/9*p**3. Factor k(l).
-2*l*(l - 1)**3/9
Let g(o) = o**3 + 5*o**2 + 2*o + 1. Let b be g(-4). Let l be -1 + b/7 - 0. Factor 0*i - 8/7*i**3 + 0 + 6/7*i**4 + l*i**2.
2*i**2*(i - 1)*(3*i - 1)/7
Let k(o) = 33*o**3 + 3*o**2 + 21. Let w(v) = 8*v**3 + v**2 + 5. Let x(c) = -5*k(c) + 21*w(c). Find s such that x(s) = 0.
-2, 0
Suppose 7*c + 0 - 14 = 0. Let b(a) be the first derivative of 0*a - 2 + 2/9*a**3 + 1/3*a**c. Factor b(v).
2*v*(v + 1)/3
Let a be 3044/260 - 11 - 2/5. Factor a*k + 8/13*k**3 + 0 + 10/13*k**2 + 2/13*k**4.
2*k*(k + 1)**2*(k + 2)/13
Suppose 342*w = 338*w. Solve -3/4*k - 3/8*k**2 + w + 3/8*k**3 = 0.
-1, 0, 2
Suppose 3*q - 9*h + 5*h + 5 = 0, 3*q - 30 = -3*h. Let o be (q/75)/((-1)/(-5)). Factor 0*l**3 - 1/3*l + o*l**5 + 2/3*l**4 - 2/3*l**2 + 0.
l*(l - 1)*(l + 1)**3/3
Suppose -10 = -4*t + q + 3, -26 = -3*t + 4*q. Let m(h) be the third derivative of -h**t + 0*h**3 - 1/30*h**5 +