tor 2/3*p**2 + 32/3 - 16/3*p.
2*(p - 4)**2/3
Let b(a) be the first derivative of -9/2*a**2 - a**3 - 6*a + 5. Determine i, given that b(i) = 0.
-2, -1
Suppose -2*z + 4*m + 0*m + 8 = 0, 0 = -4*z - 2*m - 4. Let q(t) be the first derivative of 1/8*t**4 + z*t + 1/12*t**3 + 2 + 0*t**2. Let q(h) = 0. What is h?
-1/2, 0
Let c(y) be the third derivative of -y**7/140 + y**6/80 + y**5/40 - y**4/16 - 10*y**2. Find v, given that c(v) = 0.
-1, 0, 1
Let s(o) be the third derivative of o**9/432 + o**8/840 - o**7/120 - o**6/180 - 5*o**3/3 - 2*o**2. Let j(p) be the first derivative of s(p). Factor j(u).
u**2*(u - 1)*(u + 1)*(7*u + 2)
Let t(s) be the third derivative of 0*s + 1/9*s**3 + 0*s**4 + 0 + s**2 - 1/90*s**5. Factor t(m).
-2*(m - 1)*(m + 1)/3
Factor -3*o**3 + 0*o**3 + o**5 + o**3 + o**3.
o**3*(o - 1)*(o + 1)
Let w be ((-2)/3)/((-8)/36). Suppose 5/3*r**4 - 5*r**2 + 0 - 2/3*r - 10*r**w + 14*r**5 = 0. What is r?
-1/2, -1/3, -2/7, 0, 1
Let u(f) = -2*f**3 + 11*f**2 + 2*f - 2. Let v(o) = -o**3 + 5*o**2 + o - 1. Let r(l) = 4*u(l) - 9*v(l). Factor r(q).
(q - 1)**2*(q + 1)
Let a(f) = f + 1. Let g be a(0). Suppose g = -4*q + 9. Solve -3*x**4 + 10*x**4 - 8*x**4 + x**q = 0 for x.
-1, 0, 1
Let f(r) = -11*r**2 - 5*r. Let t(w) = w**2 + 3*w - 5. Let c(j) = j**2 + 2*j - 3. Let h(n) = 5*c(n) - 3*t(n). Let i(o) = 6*f(o) + 34*h(o). Solve i(l) = 0 for l.
-2, 0
Let r(d) be the third derivative of -d**5/20 + 3*d**4/8 - 7*d**2. Suppose r(s) = 0. What is s?
0, 3
Let o be -1 + 0/4 - 0. Let v(k) = k**2 - k + 1. Let w(s) = -s**2 + s + 1. Let n(h) = o*v(h) + w(h). Factor n(m).
-2*m*(m - 1)
Let b be 0*(4 - 5)/1. Let n(m) be the first derivative of -2 - 6/5*m**5 - 2/3*m**3 - 2*m**4 + 0*m + b*m**2. Let n(r) = 0. Calculate r.
-1, -1/3, 0
Let d be 3 - (-51)/(-36)*2. Let f(c) be the first derivative of -2 + d*c**2 - 1/9*c**3 + 0*c. Solve f(j) = 0 for j.
0, 1
Let h(v) = -8*v**2 + 4*v. Let u(k) = -k**4 - k**2 + k. Let z(o) = h(o) - 4*u(o). Factor z(w).
4*w**2*(w - 1)*(w + 1)
Suppose -5*n + 2*d + 6 = -4, 0 = 3*n - d - 7. Find b such that -6*b**3 - 14*b**4 - n*b**2 - 4*b + 21*b**2 - 3*b**2 + 10*b**5 = 0.
-1, 0, 2/5, 1
Let j = -515/12 + 43. Let s(w) be the third derivative of 1/48*w**5 + 1/120*w**6 + 0 - 3*w**2 - j*w**3 - 7/96*w**4 + 0*w. Find c such that s(c) = 0.
-2, -1/4, 1
Let g be (-260)/(-16)*(-4)/(-90). Let p = g + -2/9. Solve -v**3 + 3/2*v - v**2 - p + 3/2*v**4 - 1/2*v**5 = 0 for v.
-1, 1
Let f be (-2)/8 + 110/8. Let z = f - 13. Factor -1/4*y**3 - z*y**2 + 0 + 0*y.
-y**2*(y + 2)/4
Factor -3*b**5 - 12*b**4 + 6*b**2 - 27*b**3 - 18*b**2 - 6*b - 9*b**2 - 3*b**4.
-3*b*(b + 1)**3*(b + 2)
Let k(j) be the first derivative of -j**5/210 + j**4/21 - 4*j**3/21 - j**2 - 8. Let b(i) be the second derivative of k(i). Determine c so that b(c) = 0.
2
Let j(z) be the first derivative of 21*z**4/4 - 5*z**3 - 3*z**2 - 7. Determine c, given that j(c) = 0.
-2/7, 0, 1
Let x(u) = -2*u - 10. Let r be x(-5). Let a(t) be the second derivative of 1/12*t**3 + 0*t**2 + 1/12*t**4 + r + 1/40*t**5 - t. Determine n, given that a(n) = 0.
-1, 0
Let r(j) = -j**4 - j**3 + j**2 + j - 1. Let c(z) = 7*z**4 + 6*z**3 - 9*z**2 - 8*z + 8. Let o(u) = 5*c(u) + 40*r(u). Let o(f) = 0. Calculate f.
-1, 0
Let h(k) be the third derivative of -k**7/70 - k**6/20 - k**5/20 + 6*k**2. Factor h(m).
-3*m**2*(m + 1)**2
Let p(h) be the second derivative of 0*h**3 + 1/12*h**4 + 1/15*h**5 + 1/60*h**6 + 0 - h + h**2. Let o(b) be the first derivative of p(b). What is a in o(a) = 0?
-1, 0
Let z(j) = -j**2 - j + 1. Let b be z(-1). Let n(r) be the first derivative of -b + 2*r - 2/3*r**3 + 1/2*r**4 - r**2. Solve n(x) = 0.
-1, 1
Let m(g) be the first derivative of 2*g**3/3 - 14. Find j such that m(j) = 0.
0
Let u(n) be the second derivative of -3*n**5/80 - n**4/8 + n**3/8 + 3*n**2/4 - n. Factor u(o).
-3*(o - 1)*(o + 1)*(o + 2)/4
Let h = 1108/1653 + -2/551. Let s = -4 - -6. Suppose s*f - 2/3 - 2*f**2 + h*f**3 = 0. Calculate f.
1
Let s be (0 + -2)/((-12)/30). Suppose 10*b**3 + b**s + 0*b**5 - 9*b**3 + 2*b**4 = 0. Calculate b.
-1, 0
Let u be 2/18*(-6)/21*-14. Suppose 2*n + 0 - 4 = 0. Suppose -u + 14/9*m - 2/3*m**n = 0. What is m?
1/3, 2
Let h(n) = 56*n**2 + 64*n + 12. Let b(c) = 55*c**2 + 63*c + 13. Let p(j) = 4*b(j) - 5*h(j). Let p(s) = 0. Calculate s.
-1, -2/15
Let p(z) be the first derivative of -2*z**5/75 - z**4/30 + 2*z**3/5 - 11*z**2/15 + 8*z/15 + 3. Solve p(b) = 0.
-4, 1
Let d(b) be the first derivative of b**6/9 + 2*b**5/15 - b**4/3 - 4*b**3/9 + b**2/3 + 2*b/3 + 33. Factor d(m).
2*(m - 1)**2*(m + 1)**3/3
Let k be (2/6)/((-5)/(-15)). Let b be 3*(3 - (k - -1)). Factor 1/4 + 3/4*u**2 - 3/4*u - 1/4*u**b.
-(u - 1)**3/4
Suppose -5*r - 2*j + 36 = -6*j, 0 = 5*j + 20. Let s(c) be the third derivative of 31/30*c**5 + 2*c**2 - 5/3*c**r + 4/3*c**3 + 0 - 1/4*c**6 + 0*c. Factor s(d).
-2*(d - 1)*(3*d - 2)*(5*d - 2)
Let i(p) be the third derivative of -p**8/1008 + 2*p**7/315 - p**6/90 + 3*p**2. Find q, given that i(q) = 0.
0, 2
Let a(u) = -11*u**5 + 26*u**4 - 27*u**3 + 11*u**2 - 2*u. Let k(c) = 32*c**5 - 78*c**4 + 82*c**3 - 34*c**2 + 6*c. Let p(b) = -8*a(b) - 3*k(b). Factor p(f).
-2*f*(f - 1)**3*(4*f - 1)
Let t = -8/3 - -3. Let p(g) be the second derivative of 0 - 1/30*g**5 + t*g**2 + 1/9*g**3 - 1/18*g**4 + 2*g. Factor p(q).
-2*(q - 1)*(q + 1)**2/3
Let p be 1 + (-3)/(-3 + 6). Factor 4/5*m**2 - 6/5*m**3 + 0 + p*m.
-2*m**2*(3*m - 2)/5
Let r(v) = 4*v**3 - 3*v**2 - 5*v - 5. Let g(b) = 2*b**3 - 2*b**2 - 2*b - 2. Let a(y) = 5*g(y) - 2*r(y). Factor a(w).
2*w**2*(w - 2)
Let d(t) be the second derivative of 0 - 3/2*t**2 + 1/3*t**4 - 11/6*t**3 + t. Factor d(q).
(q - 3)*(4*q + 1)
Factor -3/4*f**4 + 3/4*f**2 + 0 + 3/2*f - 3/2*f**3.
-3*f*(f - 1)*(f + 1)*(f + 2)/4
Let z be ((-95)/57)/((-10)/36). Factor -36*y**2 + 63/2*y**3 + 0 + z*y + 147/2*y**4.
3*y*(y + 1)*(7*y - 2)**2/2
Let u(y) be the second derivative of 15*y**4/4 - 5*y**2/2 + 20*y. Solve u(z) = 0.
-1/3, 1/3
Let y(q) be the first derivative of q**5/20 + q**4/4 + q**3/2 + q**2/2 + q/4 - 1. Solve y(s) = 0.
-1
Let h(r) = r**3 + 5*r**2. Let x be h(-5). Let c(m) be the second derivative of 1/3*m**4 - m + m**2 + 1/20*m**5 + x + 5/6*m**3. Determine u, given that c(u) = 0.
-2, -1
Let b(w) be the first derivative of w**6/3 + 4*w**5/15 - w**4 - 8*w**3/9 + w**2 + 4*w/3 + 15. Solve b(p) = 0 for p.
-1, -2/3, 1
Let k(x) be the second derivative of -x**7/3360 + x**6/1440 + x**3/6 + 3*x. Let h(v) be the second derivative of k(v). Factor h(i).
-i**2*(i - 1)/4
Let f(h) be the third derivative of -h**8/1680 - h**7/1050 + h**6/300 + h**5/150 - h**4/120 - h**3/30 - 12*h**2. Let f(j) = 0. Calculate j.
-1, 1
Factor 5*r**3 - 17*r**2 + 8 - 2*r**3 - 14*r + 4*r**3 - 2*r**3.
(r - 4)*(r + 1)*(5*r - 2)
Let l(y) = y + 11. Let g be l(-9). Let k be (-76)/(-18) + (-4 - 0). Find d such that 0*d - k + 2/9*d**g = 0.
-1, 1
Suppose 1 = 3*o - 8. Let f be (-15)/(-22)*36/27. Solve 10/11*j**o - 4/11 - f*j + 4/11*j**2 = 0 for j.
-1, -2/5, 1
Determine i so that 1/5*i**4 + 4/5*i**3 - 12/5*i + 9/5 - 2/5*i**2 = 0.
-3, 1
Let b(m) = 7*m**4 - 37*m**3 + 33*m**2 - 13*m. Let y(f) = 3*f**4 - 19*f**3 + 17*f**2 - 7*f. Let o(g) = -3*b(g) + 5*y(g). Factor o(j).
-2*j*(j - 1)**2*(3*j - 2)
Let z(g) be the first derivative of g**4/6 + 4*g**3/3 + 4*g**2 - g + 2. Let s(w) be the first derivative of z(w). Determine c so that s(c) = 0.
-2
Let n(m) be the first derivative of -m**3/9 - 8. Factor n(o).
-o**2/3
Let c(q) be the third derivative of q**8/1064 - 17*q**7/1995 + 37*q**6/1140 - 13*q**5/190 + 5*q**4/57 - 4*q**3/57 - 15*q**2. Find y, given that c(y) = 0.
2/3, 1, 2
Let a(q) be the third derivative of -q**6/48 + 17*q**5/120 - q**4/3 + q**3/3 - 57*q**2. Factor a(u).
-(u - 2)*(u - 1)*(5*u - 2)/2
Let a(x) be the first derivative of 21*x**4/4 - x**3 - 21*x**2/2 + 3*x - 5. Solve a(z) = 0 for z.
-1, 1/7, 1
Let k(f) = f**3 + 3*f**2 - 4*f - 5. Let b be k(-4). Let y = b + 7. Factor -3*h**3 - 2*h**2 - h - h**y - h**4 + 0*h**4.
-h*(h + 1)**3
Factor l**4 - l**4 - 5*l**5 + 30*l**3 + 120*l**2 - 80*l**2 + 15*l.
-5*l*(l - 3)*(l + 1)**3
Let q be (-4)/(-22) + (-2667)/(-33). Let c be (-144)/q*3/(-2). Suppose 70/3*d**5 + 8*d**2 + 46/3*d**3 + 0 - c*d - 44*d**4 = 0. What is d?
-2/5, 0, 2/7, 1
What is j in 1/2*j**2 + 1/2*j**3 - 1/4*j - 1/4 - 1/4*j**4 - 1/4*j**5 = 0?
-1, 1
Factor 5*c**2 + 5 - 10 + 5 - 10*c