ivative of r**8/560 - r**6/120 - r**3 + 2*r. Let q(d) be the second derivative of c(d). Factor q(s).
3*s**2*(s - 1)*(s + 1)
Let o be (-63)/105 - 13/(-5). Find n, given that -75/4*n**3 + 6 + 105/2*n**o - 33*n = 0.
2/5, 2
Let k(y) = -5*y**3 - 6*y**2 - 3*y + 2. Let q(i) = i**3 + i**2. Let b(g) = k(g) + 6*q(g). Let b(l) = 0. Calculate l.
-2, 1
Solve 0 - 4/3*n**3 + 2*n**4 - 2/3*n**5 + 0*n + 0*n**2 = 0.
0, 1, 2
Let h = 68091/5 - 13567. Let p be (-1)/((-2)/4) + 3. Find a, given that -336/5*a**3 + 0 + 686*a**p - 32/5*a + h*a**2 - 1568/5*a**4 = 0.
-2/5, 0, 2/7
Let a = -46 + 232/5. Let -1/5*k**2 - 1/5 + a*k = 0. Calculate k.
1
Let t(z) be the first derivative of z**6/180 - z**5/20 + 2*z**3/3 + 5. Let h(n) be the third derivative of t(n). Factor h(m).
2*m*(m - 3)
Let a(l) be the second derivative of -6*l - 20/27*l**3 + 1/6*l**4 + 0 + 4/9*l**2. Let a(f) = 0. What is f?
2/9, 2
Let l = 37 + -20. Determine h, given that -l - 2*h**2 + 12*h - h**2 + 12 - 7 = 0.
2
Let p be 3 - (2/(-1))/(60/(-87)). Let z(u) be the second derivative of -3*u + 0 - u**3 + 1/2*u**4 + u**2 - p*u**5. Factor z(l).
-2*(l - 1)**3
Factor -2/3*h**2 - 32/3 - 16/3*h.
-2*(h + 4)**2/3
Let x = 351/2 - 175. Factor 0 + 0*p - p**2 + x*p**3.
p**2*(p - 2)/2
Suppose 16/3 + 1/3*o**2 + 8/3*o = 0. What is o?
-4
Let r(o) be the first derivative of 2*o**5/25 - o**4/10 - 2*o**3/5 + o**2/5 + 4*o/5 - 7. Find f, given that r(f) = 0.
-1, 1, 2
Factor 0*u**2 - 4/3*u + 0 + 4/3*u**3.
4*u*(u - 1)*(u + 1)/3
Let m(p) be the first derivative of 0*p + 0*p**2 - 4 - 2/3*p**3 - 1/2*p**4 + 2/5*p**5 + 1/3*p**6. Factor m(i).
2*i**2*(i - 1)*(i + 1)**2
Let u(l) be the second derivative of -3/2*l**3 + 0 + 3*l**2 + 1/4*l**4 + 9*l. Let u(g) = 0. Calculate g.
1, 2
Let p(y) be the first derivative of 1 + 0*y**3 - 1/2*y**2 + y + 1/12*y**4. Let u(l) be the first derivative of p(l). Determine k, given that u(k) = 0.
-1, 1
Suppose 0 = -4*o + 7 + 1. Let v(f) be the second derivative of 0 - 2*f + 1/5*f**6 + 2/5*f**5 + 0*f**o - 2/3*f**3 - 1/6*f**4. Determine z, given that v(z) = 0.
-1, 0, 2/3
Let t(i) be the first derivative of 196/27*i**3 - 16/9*i + 1 + 49/18*i**4 - 4/9*i**2. Let t(w) = 0. What is w?
-2, -2/7, 2/7
Let t(p) be the third derivative of -p**7/840 - p**6/160 + p**4/24 - 17*p**2. Solve t(k) = 0.
-2, 0, 1
Suppose -3*w - 8 = -20. Let a(q) be the first derivative of 0*q**3 + 1/6*q + 3 - 1/30*q**5 + 1/12*q**w - 1/6*q**2. Let a(d) = 0. Calculate d.
-1, 1
Factor 0*f + 4/7*f**5 + 0*f**2 + 0 + 0*f**3 - 4/7*f**4.
4*f**4*(f - 1)/7
Let o(c) be the third derivative of -c**8/10080 - c**7/840 - c**6/180 - c**5/12 - 5*c**2. Let z(b) be the third derivative of o(b). Solve z(r) = 0 for r.
-2, -1
Find v, given that 14/15*v - 2/15*v**3 - 4/5 + 0*v**2 = 0.
-3, 1, 2
Let g(h) be the second derivative of -2*h**6/15 + 3*h**5/5 - h**4 + 2*h**3/3 - 5*h. Determine w so that g(w) = 0.
0, 1
Factor -2/5*m**2 + 2/5*m**3 + 0 + 2/5*m**4 + 0*m - 2/5*m**5.
-2*m**2*(m - 1)**2*(m + 1)/5
Suppose -3*l + 4*a - 7*a = 0, 0 = -4*l - 5*a. Let k(v) be the third derivative of -2*v**2 + 1/60*v**5 + 1/6*v**3 + 0*v + l - 1/12*v**4. Factor k(c).
(c - 1)**2
Let g(v) = -v - 13. Let o be g(-10). Let a be (-2)/o*6/14. Let a*b + 2/7*b**5 + 2/7 - 4/7*b**3 + 2/7*b**4 - 4/7*b**2 = 0. Calculate b.
-1, 1
Suppose 3*q - 10 = -2*q. Suppose 0 = -2*j - 5*r + 16, 3*j + 22 = 7*j + 5*r. Find i such that 4 + 0*i**2 - j*i**2 - q*i - 2*i**2 + 3*i**2 = 0.
-2, 1
Solve 4/13*t**2 + 0*t + 6/13*t**3 - 2/13*t**5 + 0*t**4 + 0 = 0 for t.
-1, 0, 2
Let j(q) be the first derivative of q**4/6 - 8*q**3/9 - 5*q**2/3 + 16. Factor j(y).
2*y*(y - 5)*(y + 1)/3
Let d(g) be the first derivative of 0*g**2 - 2/45*g**3 + 2/15*g - 5. Determine c, given that d(c) = 0.
-1, 1
Let k(b) be the second derivative of b**6/10 + 4*b**5/15 - 2*b**4/3 - b**2/2 - 7*b. Let s(u) be the first derivative of k(u). Factor s(m).
4*m*(m + 2)*(3*m - 2)
Let r(q) be the second derivative of -3*q**5/5 - 8*q**4/3 - 2*q**3 + 4*q**2 + 7*q. Find w, given that r(w) = 0.
-2, -1, 1/3
Let f(m) be the second derivative of -m**5/180 - m**4/36 - 5*m**2/2 + 3*m. Let t(u) be the first derivative of f(u). Solve t(j) = 0.
-2, 0
Let r(h) be the third derivative of -5*h**8/336 - 2*h**7/21 - h**6/4 - h**5/3 - 5*h**4/24 + 23*h**2. Factor r(i).
-5*i*(i + 1)**4
Suppose -8 = -4*v + i, 0 = 7*v - 3*v - 2*i - 8. Let m = 31 + -92/3. Find y, given that -1/3*y**4 + 1/3*y**5 - m*y**3 + 1/3*y**v + 0*y + 0 = 0.
-1, 0, 1
Let s(k) be the first derivative of k**6/33 + 4*k**5/55 + k**4/22 - 4. Suppose s(h) = 0. What is h?
-1, 0
Let d(v) = -v**3 - 7*v**2 + 17*v + 23. Let y(s) = -4*s**2 + 8*s + 12. Let g(a) = 4*d(a) - 7*y(a). Determine h, given that g(h) = 0.
-1, 2
Suppose 4*v - 13 - 13 = 2*s, 0 = -v + 2*s - 1. Factor 2*j**3 + j**4 + 3*j**2 - 14*j**3 + v*j**3 - j.
j*(j - 1)**3
Suppose -s + 4*f + 6 = 0, 3*f = 4*s - 2 - 9. Factor -3*x**3 - x**3 + 3*x**s + x**4 + x + 7*x**3 + 0*x**3.
x*(x + 1)**3
Suppose -l + 5 = 5*q, 5*l + 13 = -2*q - 8. Suppose 5*b - b**2 - 7*b - q*b - 2 - b**2 = 0. What is b?
-1
Let q(m) = m**3 + m**2 - m. Let x(s) = -s**5 + 2*s**4 - 6*s**3 - 5*s**2 + 5*s. Let k(a) = 20*q(a) + 4*x(a). Factor k(h).
-4*h**3*(h - 1)**2
Let i(q) = 2*q - 48. Let m be i(26). Factor 3*h + 9/2*h**m + 1/2 + 8*h**3 + 7*h**2 + h**5.
(h + 1)**4*(2*h + 1)/2
Let z(u) = -u**4 - 16*u**3 - 21*u**2 - 6*u - 4. Let q(t) = 5*t**4 + 65*t**3 + 85*t**2 + 25*t + 15. Let s(f) = -4*q(f) - 15*z(f). Solve s(x) = 0.
-2, -1, 0
Let n(f) = f**2 + 17*f - 38. Let i be n(-19). Determine k so that 0 + i*k - 1/4*k**3 - 3/4*k**2 = 0.
-3, 0
Let d(o) be the second derivative of o**8/3360 - o**7/1260 - o**6/180 - o**4/4 + o. Let j(y) be the third derivative of d(y). Factor j(t).
2*t*(t - 2)*(t + 1)
Let g(c) = -c**2 - 6*c - 5. Let l be g(-4). Let h be (-5)/15*(2 - l). Suppose -2*x**2 + 4/3*x**3 - h + 4/3*x - 1/3*x**4 = 0. Calculate x.
1
Let y be 4/(-1*4)*-3. Suppose 3*z**3 + 2*z**4 + 0*z**5 + 6*z**5 - 3*z**2 + y*z**5 + 13*z**4 = 0. What is z?
-1, 0, 1/3
Suppose -3*a + w + 18 = -w, 3*a = 5*w + 27. Factor -16*j**2 - 3*j + 4*j**4 + 17*j + j**4 + 4*j**3 - 2*j**5 - j**4 - a.
-2*(j - 1)**4*(j + 2)
Let r(c) be the third derivative of -7*c**6/160 - 41*c**5/240 - c**4/4 - c**3/6 - 4*c**2. Factor r(l).
-(l + 1)*(3*l + 2)*(7*l + 2)/4
Let g(n) be the first derivative of -1/6*n**3 + 1 - 3/2*n**2 - 9/2*n. Determine w so that g(w) = 0.
-3
Factor 1/2*s**2 - 2*s + 3/2.
(s - 3)*(s - 1)/2
Let n(g) be the second derivative of -g**4/6 - g**3/3 - 19*g. Factor n(l).
-2*l*(l + 1)
Suppose 3*u = -4*s - 6, -s - 5*u = 11 - 1. Let j(l) be the second derivative of -3*l + 1/27*l**3 + s + 1/90*l**5 + 0*l**2 - 1/27*l**4. Factor j(x).
2*x*(x - 1)**2/9
Factor -2/7*q**3 - 6/7*q**2 + 0*q + 8/7.
-2*(q - 1)*(q + 2)**2/7
Let i = -784 + 2405/3. Let s = i + -17. Let 4/3 + s*a - 2/3*a**2 = 0. Calculate a.
-1, 2
Let s be 3 - 4/(-36)*-25. Let k(g) be the first derivative of -1 - 4/45*g**5 - 1/9*g**2 - s*g**3 + 5/18*g**4 + 2/9*g. Factor k(w).
-2*(w - 1)**3*(2*w + 1)/9
Let j(y) = y. Let s be j(-8). Let u be (12/(-14))/(12/s). Factor -u*p - 2/7*p**2 - 2/7.
-2*(p + 1)**2/7
Find h such that -5 - 4*h**4 - 2*h**3 + 6*h**2 + 1 + 2 + 2*h = 0.
-1, 1/2, 1
Let b(f) be the second derivative of f**7/3780 - f**6/540 - f**4/4 - 3*f. Let u(d) be the third derivative of b(d). Factor u(i).
2*i*(i - 2)/3
Let y(l) = -2*l + 24*l**3 + 0*l - 18*l**4 + 2*l - 8*l**2. Let o(u) = 18*u**4 - 24*u**3 + 8*u**2. Let s(q) = -3*o(q) - 2*y(q). Find d, given that s(d) = 0.
0, 2/3
Let n be (20/42)/5*1*3. Find v such that 0 - 4/7*v**2 - n*v = 0.
-1/2, 0
Let f = 5 - 3. Suppose 2 - 6 = -f*n. Solve -4*v + 2*v**n + 0 + 1 + 1 = 0.
1
Let a(y) = y - 3. Let h be a(8). Factor -15*g**2 + h + 7 - 15*g - 10*g + g.
-3*(g + 2)*(5*g - 2)
Let u be (4/(-6))/(1/(-6)). Let k(n) be the second derivative of 2*n + 1/9*n**3 - 1/6*n**2 - 1/36*n**u + 0. Solve k(w) = 0.
1
Let o be (2/165)/(4 - 2). Let c(r) be the second derivative of -o*r**6 + 1/110*r**5 + 0 + 0*r**3 + 0*r**4 + 0*r**2 - r. Factor c(a).
-2*a**3*(a - 1)/11
Suppose -v - 2 = -8. Suppose 0 = -6*g + 3*g + v. Factor 2/3*n**3 + 0 + 4/3*n**4 + 0*n + 0*n**g + 2/3*n**5.
2*n**3*(n + 1)**2/3
Let g = 230 + -658/3. Find i such that 22/3*i + g*i**2 + 4/3 + 14/3*i**3 = 0.
-1, -2/7
Let h(n) be the second derivative of -n**4/12 + n**2/2 + 11*n. Determine y, given that h(y) = 0.
