 + 1)/3
Let x(v) be the third derivative of -v**10/75600 - v**9/40320 + v**8/40320 + v**5/30 + v**2. Let b(l) be the third derivative of x(l). Solve b(a) = 0 for a.
-1, 0, 1/4
Let o = -2 + 2. Let f(x) be the first derivative of 0*x**2 + o*x**3 - 1 + 0*x - 1/3*x**6 + 4/5*x**5 - 1/2*x**4. Factor f(i).
-2*i**3*(i - 1)**2
Let a(f) = -f**2 + f. Suppose 4*i + 3*d - 67 = 4*d, -d - 13 = -i. Let s(m) = 8*m**2 - 7*m. Let c(l) = i*a(l) + 2*s(l). Factor c(r).
-2*r*(r - 2)
Suppose -2*h + i = 0, i = h + 3 - 1. Factor -12 - 4*f**h + 9*f - 3*f + 6*f + f**2.
-3*(f - 2)**2
Suppose -3/5*c**3 - 12/5*c**2 - 3*c - 6/5 = 0. Calculate c.
-2, -1
Let b(i) be the second derivative of -i**4/6 - i**3 + 2*i**2 - 6*i. Let t(v) = 1. Suppose 36 = 4*k + 4. Let l(a) = k*t(a) - b(a). Solve l(h) = 0.
-2, -1
Let u(j) = 6*j**3 - 6*j + 3. Let h(r) = -r**4 + 11*r**3 + r**2 - 11*r + 5. Let l(c) = 3*h(c) - 5*u(c). Factor l(g).
-3*g*(g - 1)**2*(g + 1)
Let m(j) be the third derivative of 2/15*j**4 + 0*j + 0*j**3 - 46/75*j**5 + 63/50*j**6 + 0 + 6*j**2 + 49/120*j**8 - 91/75*j**7. Factor m(x).
2*x*(x - 1)*(7*x - 2)**3/5
Let s(c) = -5*c**3 + 2*c**2 + 2*c + 1. Let l be s(-1). Let o be (-15)/l*12/(-45). Let 0*i + 4/3*i**5 + 2/3*i**2 - o*i**4 - 4/3*i**3 + 0 = 0. Calculate i.
-1, 0, 1/2, 1
Let m(b) = -b**2 + 3*b + 3. Let f be m(3). Suppose 4*l = f*t - 17, -2*t - 4*l - 4 = l. Determine w, given that 4*w**t + 3*w**4 + 2*w**5 - 2*w**3 + w**4 = 0.
-1, 0
Let d(k) = k + 13. Suppose -3*y - 23 - 10 = 0. Let s be d(y). Suppose -2*g**3 - 3*g**2 + 2*g - 5*g**s + g**4 + 4*g**2 + 3*g**2 = 0. Calculate g.
-1, 0, 1, 2
Let r(n) be the first derivative of -n**6/990 + n**5/660 + n**4/132 + 2*n**3/3 + 3. Let b(m) be the third derivative of r(m). Find d, given that b(d) = 0.
-1/2, 1
Let m(d) be the first derivative of -d**5 - 5*d**4/4 + 5*d**3 + 25*d**2/2 + 10*d + 39. Suppose m(v) = 0. What is v?
-1, 2
Let b(d) be the first derivative of -2 + 2/9*d**6 - 2/3*d**4 + 2/3*d**2 - 4/15*d**5 + 8/9*d**3 - 4/3*d. Suppose b(l) = 0. Calculate l.
-1, 1
Let f = 21 - 13. Let s = -6 + f. Factor 8*t + 4*t**2 + 8 + 0*t**2 - 2*t**s + 0.
2*(t + 2)**2
Let l(u) be the third derivative of -u**6/2340 - u**5/390 - u**3 - 7*u**2. Let o(z) be the first derivative of l(z). Suppose o(n) = 0. Calculate n.
-2, 0
Suppose -2*x = 2, 4*o + 6*x + 215 = 3*x. Let z = o - -161/3. Let -z*c**3 + 0 + 2/3*c**2 + 2/3*c - 2/3*c**4 = 0. What is c?
-1, 0, 1
Let w = -8 - -14. Solve -w*m + m - 3*m**2 + 2*m = 0.
-1, 0
Let o be 2 + (-2 - -3) + 7. Suppose 2*n + 1 = 3*a + 10, -2*a = 4*n - o. Factor 9*u - n*u**2 + 0*u + 0*u**2 - 6.
-3*(u - 2)*(u - 1)
Let g = 6/5657 + 1216231/22628. Let x = 54 - g. Factor 0*j + x*j**4 + 0 - 1/2*j**3 + 0*j**2.
j**3*(j - 2)/4
Let q(m) be the second derivative of -m**10/15120 - m**9/15120 - 7*m**4/12 - 9*m. Let s(h) be the third derivative of q(h). Factor s(j).
-j**4*(2*j + 1)
Let y(f) be the third derivative of -f**7/1260 - f**6/360 + f**5/30 + 7*f**4/24 + 8*f**2. Let g(u) be the second derivative of y(u). Let g(k) = 0. Calculate k.
-2, 1
Let m(n) be the first derivative of -n**5/15 - 5*n**4/12 - n**3 - 7*n**2/6 - 2*n/3 - 34. Find b, given that m(b) = 0.
-2, -1
Let q(j) be the second derivative of 3*j**5/100 + 3*j**4/20 + j**3/5 + 14*j. Factor q(d).
3*d*(d + 1)*(d + 2)/5
Suppose 5/2*m**4 + 20*m**2 + 8 + 1/4*m**5 + 20*m + 10*m**3 = 0. Calculate m.
-2
Let j(g) be the second derivative of -7*g**4/66 + 4*g**3/11 + 4*g**2/11 - 21*g. Factor j(l).
-2*(l - 2)*(7*l + 2)/11
Let p be (-4)/6 + 43/63. Let r = p - -59/252. Find z, given that -1/4*z**4 + 1/4*z**2 - r*z + 1/4*z**3 + 0 = 0.
-1, 0, 1
Suppose 6*y**5 - 6*y + 6*y**3 + 3*y - 9*y**5 = 0. Calculate y.
-1, 0, 1
What is r in -r**3 + 13*r**2 - 10*r**2 - 2*r**3 = 0?
0, 1
Let h(b) be the second derivative of -b**5/20 - b**4/4 + 2*b**3/3 + 33*b. What is k in h(k) = 0?
-4, 0, 1
Let q(c) be the first derivative of -4 + 1/4*c**2 + 0*c + 1/10*c**5 - 1/6*c**3 - 1/8*c**4. Factor q(k).
k*(k - 1)**2*(k + 1)/2
Let c(s) be the first derivative of s**5/180 + s**4/72 + s**2/2 + 2. Let t(n) be the second derivative of c(n). Factor t(i).
i*(i + 1)/3
Let h = -15 + 15. Let r(t) be the second derivative of -3*t - 1/6*t**4 + 0 + h*t**3 + 0*t**2. Factor r(g).
-2*g**2
Suppose 3 + 2 = -m. Let k = m + 8. Factor 2*r**2 - 4*r + k*r - 3*r + 2.
2*(r - 1)**2
Let x = 8 - 8. Let q(w) be the second derivative of -1/8*w**4 + w**2 + 1/3*w**3 + 2*w + x. Factor q(m).
-(m - 2)*(3*m + 2)/2
Let s(c) be the second derivative of 0*c**3 + 0*c**2 - 5*c - 1/40*c**5 + 0 + 0*c**4. Find x such that s(x) = 0.
0
Let l(f) be the first derivative of -f**7/210 - f**6/150 + f**5/100 + f**4/60 - 4*f + 2. Let d(o) be the first derivative of l(o). Factor d(k).
-k**2*(k - 1)*(k + 1)**2/5
Let s(u) be the first derivative of 2*u**3/57 + 9*u**2/19 - 20*u/19 + 46. Factor s(i).
2*(i - 1)*(i + 10)/19
Suppose -5 = -5*u + f, -4*u + 0*f - 3*f = -4. Let o be u - (-2)/(-1 - -3). Suppose 2 - 3*g**2 + 3*g**2 - o*g**2 = 0. Calculate g.
-1, 1
Let h(j) = 3*j + 2. Suppose -2*d + 12 = 3*b, b - 4*d + 15 - 5 = 0. Let a be h(b). Factor a*l**5 - 10*l - 2*l**5 + 22*l**3 - 2*l**3 - 4 + 20*l**4.
2*(l + 1)**4*(3*l - 2)
Let q = 3 + 0. Factor x - 2*x**3 - 2*x**3 + 3*x**q.
-x*(x - 1)*(x + 1)
Let x(g) = g**3 + 6*g**2 + 6*g + 7. Let o = 2 + -7. Let s be x(o). Determine b, given that 3*b - 2*b + b + s*b**2 = 0.
-1, 0
Factor 0*r**3 - 3*r**3 + 5*r**2 - 3*r**3 + r**3.
-5*r**2*(r - 1)
Solve 5*l**2 - 6*l**2 + l - 9*l**2 + 3*l + 2*l**4 - 2*l**5 + 6*l**3 = 0 for l.
-2, 0, 1
Let k(h) be the third derivative of -h**7/1470 + h**6/140 - 13*h**5/420 + h**4/14 - 2*h**3/21 - 11*h**2. Determine m, given that k(m) = 0.
1, 2
Factor -1/3*z + 0*z**2 + 0 + 1/3*z**3.
z*(z - 1)*(z + 1)/3
Let j = -2/295 - -608/2655. Let i(y) = -y**2 - 12*y + 16. Let n be i(-13). Factor j*r**2 - 2/9 - 2/9*r + 2/9*r**n.
2*(r - 1)*(r + 1)**2/9
Let m be 272/44 - (-4)/(-22). Let r(x) be the first derivative of 0*x**2 + 0*x + 0*x**4 + 0*x**3 - 1/5*x**5 + 2 + 1/6*x**m. What is t in r(t) = 0?
0, 1
Let n(d) = 4*d**5 - 8*d**4 + 4*d**3 + 4*d**2 + 4*d. Let z(a) = 8*a**5 - 16*a**4 + 8*a**3 + 9*a**2 + 9*a. Let x(u) = -9*n(u) + 4*z(u). Factor x(g).
-4*g**3*(g - 1)**2
Determine u so that 2/7*u**3 - 2*u + 4/7*u**2 + 8/7 = 0.
-4, 1
Let k be 2*(-6)/(-4) - 1. Let v(y) = -y**3 - 5*y**2 + 7*y + 9. Let d be v(-6). Factor -k + d*q**3 + 3 - q**4 - q**3 - 2*q.
-(q - 1)**3*(q + 1)
Suppose 0 = b - 4 - 1. Factor -6*l**5 + 2*l**4 + 2*l**3 + 8*l**b - 2*l**3.
2*l**4*(l + 1)
Suppose 5*h - 2*h - 15 = 0. Let v(d) = -d**3 + d**2 + d. Let i(n) = 0*n**3 + 4*n**2 - 7*n - 6*n**3 + 12*n. Let q(o) = h*v(o) - i(o). Factor q(j).
j**2*(j + 1)
Suppose -4*g = -2*d - 2*g + 6, -d + 2*g = 0. Let i = 8 - d. Determine y, given that 2/5 + 4/5*y + 2/5*y**i = 0.
-1
Let q(o) be the first derivative of -o**3 + 12*o**2 - 48*o - 6. Solve q(g) = 0.
4
Factor 4/7 + 2/7*n**2 - 6/7*n.
2*(n - 2)*(n - 1)/7
Let p = -17797/25 - -712. Let y(n) be the first derivative of 0*n**3 + 3/10*n**4 - 4 - p*n**5 + 3/5*n - 3/5*n**2. Factor y(u).
-3*(u - 1)**3*(u + 1)/5
Suppose 0 = -p, 0 = 6*w - 2*w - 4*p. Factor 0*h**4 + w - 2/7*h**5 + 4/7*h**3 + 0*h**2 - 2/7*h.
-2*h*(h - 1)**2*(h + 1)**2/7
Let v be -1*70/25 - -3. Let w(z) be the first derivative of 1 - 1/4*z**4 - v*z**5 + 0*z**2 + 0*z + 0*z**3. What is f in w(f) = 0?
-1, 0
Let n(g) = -g**3 - 6*g**2 - 5*g + 4. Suppose -3*q - q = 20. Let a be n(q). Solve 4 - 7*t - 2*t**2 + a*t**2 + t = 0.
1, 2
Suppose 0 = 18*t - 16*t - 4. Factor -1/4*w**t - 9/4 + 3/2*w.
-(w - 3)**2/4
Let o(m) be the first derivative of 2*m**7/21 + 7*m**6/30 + m**5/10 - m**4/12 - 6*m + 7. Let x(b) be the first derivative of o(b). Factor x(t).
t**2*(t + 1)**2*(4*t - 1)
Let k = -3/386 + 907/17370. Let i(p) be the second derivative of 0 - 1/63*p**7 + 0*p**4 + 0*p**2 - p + k*p**6 - 1/30*p**5 + 0*p**3. Factor i(c).
-2*c**3*(c - 1)**2/3
Let s(y) be the first derivative of -y**6/3 + 2*y**5 - 5*y**4 + 20*y**3/3 - 5*y**2 + 2*y - 8. Let s(b) = 0. Calculate b.
1
Let z(b) be the second derivative of -1/2*b**4 + 0*b**2 - 1/2*b**3 - 3*b + 0 - 3/20*b**5. Factor z(d).
-3*d*(d + 1)**2
Let o(x) = -7*x**3 - 5*x + x**3 + 4*x**4 + 14 + 4*x**4. Let u(h) = -3*h**4 + 2*h**3 + 2*h - 5. Suppose -d - 12 = -4*d. Let p(w) = d*o(w) + 11*u(w). Factor p(r).
-(r - 1)*(r + 1)**3
Let q(x) be the second derivative of x