et r*h - 1/3*h**2 - 1/3 = 0. Calculate h.
1
Let i be (-3)/2 + 1 - (-5)/2. Let s(r) be the second derivative of -1/3*r**i - 1/3*r**3 - 1/6*r**4 + 0 - 2*r - 1/30*r**5. Determine h so that s(h) = 0.
-1
Let c(q) be the second derivative of q**5/20 - 2*q**3/3 - 3*q. Find r, given that c(r) = 0.
-2, 0, 2
Let r(y) be the first derivative of -y**3/9 + 5*y**2/6 - 4*y/3 - 8. Factor r(p).
-(p - 4)*(p - 1)/3
Let a(o) be the first derivative of o**7/420 + o**6/90 - o**5/60 - o**4/6 - 2*o**3/3 - 1. Let r(m) be the third derivative of a(m). What is s in r(s) = 0?
-2, -1, 1
Let v(o) be the first derivative of o**3/7 - 6*o**2/7 + 9*o/7 - 13. Suppose v(h) = 0. What is h?
1, 3
Let r(m) be the third derivative of -m**5/210 - m**4/42 + 10*m**2. Find i such that r(i) = 0.
-2, 0
Let a(p) be the first derivative of 4/9*p**3 + 2/15*p**5 + 1/2*p**4 + 0*p**2 + 1 + 0*p. Factor a(v).
2*v**2*(v + 1)*(v + 2)/3
Let b(n) = 4*n**2 - 7*n - 4. Let p(t) = t**2 - 2*t - 1. Let o(v) = -2*b(v) + 7*p(v). Factor o(g).
-(g - 1)*(g + 1)
Let f(s) = 4*s - 14. Let q be f(4). Determine v, given that 1/4*v**q + 1/2 + 3/4*v = 0.
-2, -1
Suppose 2*z - 1 = 3*n + 3, n + 5*z + 7 = 0. Let g be (-15)/9 + n/(-1). Let -1/3*r**5 + 2/3*r**3 - 1/3*r + 1/3*r**4 + g - 2/3*r**2 = 0. Calculate r.
-1, 1
Let g(o) be the third derivative of 2*o**7/105 - o**6/10 + o**5/5 - o**4/6 - 2*o**2 - 11*o. Solve g(a) = 0 for a.
0, 1
Let m(i) = -i - 4. Let f be m(-4). Let v be (f + 8)*(-17)/(-36). Factor 22/9*u**2 + 10/9*u**5 + 0 + v*u**4 + 14/3*u**3 + 4/9*u.
2*u*(u + 1)**3*(5*u + 2)/9
Let q = 4 + -4. Let u be (7 + 0)/(1 - q). Factor 10*y + 2 + 2*y**2 - u*y + y.
2*(y + 1)**2
Let z(y) be the first derivative of -y**9/1512 - y**8/420 + y**6/90 + y**5/60 - 5*y**3/3 + 1. Let w(t) be the third derivative of z(t). What is j in w(j) = 0?
-1, 0, 1
Let j(k) = -k**3 + 10*k**2 - 18*k + 16. Let a be j(8). Factor a + 0*q**2 + 0*q + 0*q**4 - 1/5*q**3 + 1/5*q**5.
q**3*(q - 1)*(q + 1)/5
Let x(v) be the first derivative of -3*v**5/5 - 2*v**4 - v**3 + v**2 + 14. Find t such that x(t) = 0.
-2, -1, 0, 1/3
Let a(c) be the first derivative of c**4/20 + c**3/15 - c**2/2 + 3*c/5 + 22. Suppose a(t) = 0. Calculate t.
-3, 1
Factor 0 + 10/3*d**4 + 0*d + 2*d**5 + 1/3*d**2 + 11/6*d**3.
d**2*(2*d + 1)**2*(3*d + 2)/6
Let d(l) be the third derivative of -3*l**8/112 + l**7/14 - l**6/40 - l**5/20 - 14*l**2. Solve d(o) = 0.
-1/3, 0, 1
Let 48*u + 3*u**2 - 26*u - u**2 - 26*u = 0. What is u?
0, 2
Let u(i) = -i**2 + 11*i - 13. Let d(o) = -5*o + 7. Let g(n) = -5*d(n) - 3*u(n). What is w in g(w) = 0?
2/3, 2
Let w(c) be the second derivative of -2/3*c**4 + 1/21*c**7 - c - 4/15*c**6 + 3/5*c**5 + 0*c**2 + 1/3*c**3 + 0. Factor w(r).
2*r*(r - 1)**4
Let t = 230 + -6899/30. Let r(a) be the third derivative of -t*a**5 + 0*a - a**2 - 1/12*a**4 + 0*a**3 + 0. Suppose r(j) = 0. What is j?
-1, 0
Let i(h) = 3*h**4 + 10*h**3 + 6*h**2 + 3*h. Let b(o) = 3*o**4 + 10*o**3 + 5*o**2 + 2*o. Let y(g) = 6*b(g) - 4*i(g). Factor y(d).
2*d**2*(d + 3)*(3*d + 1)
Factor -6*f - 2 + 2*f**2 + 6 + 0*f**2.
2*(f - 2)*(f - 1)
Suppose 0 = 3*r - 3*v + v, -5*r - 5 = -5*v. Let h = -4 + 6. Factor k - h*k**2 + r - 4*k + 2*k**3 + k.
2*(k - 1)**2*(k + 1)
Determine c so that -33/5*c**3 - 27/5*c - 9*c**2 - 9/5*c**4 - 6/5 = 0.
-1, -2/3
Let x(v) be the second derivative of v**4/6 + 2*v**3/3 - 3*v**2 - 26*v. Factor x(k).
2*(k - 1)*(k + 3)
Factor 11*m + 16 - 30*m + 84*m**2 - 77*m - 20*m**3.
-4*(m - 2)**2*(5*m - 1)
Solve 0 - 23*q**2 - 8*q + 0 + 19*q**2 = 0 for q.
-2, 0
Let j(q) be the first derivative of -q**4/14 - 2*q**3/21 + q**2/7 + 2*q/7 - 3. Factor j(s).
-2*(s - 1)*(s + 1)**2/7
Let u(z) be the second derivative of 1/15*z**6 + 0 + 0*z**3 + 0*z**4 - z + 1/5*z**5 + 0*z**2. Factor u(w).
2*w**3*(w + 2)
Let o be ((-6)/27)/(5/(-10)). Solve o - 2/3*i + 2/9*i**2 = 0.
1, 2
Suppose 6*x - 2*x - 140 = 0. Let n be (-7)/x - (-2)/5. Factor 0 - 1/5*k**4 + 3/5*k**3 - 3/5*k**2 + n*k.
-k*(k - 1)**3/5
Let l be 4*(-3)/(-90)*90/54. Suppose 0 + 2/9*u**5 + 4/9*u**4 - 4/9*u**2 + 0*u**3 - l*u = 0. Calculate u.
-1, 0, 1
Let t(m) be the first derivative of 1 + 2/3*m**2 - 2/15*m**5 + 2/3*m**3 + 0*m + 0*m**4. Suppose t(r) = 0. Calculate r.
-1, 0, 2
Suppose -2*u = -0*u - 5*c - 37, -3*u + 62 = -c. Suppose 4*h = h + u. Factor -h - t - t**3 + 7 + 2*t**2.
-t*(t - 1)**2
Let m(a) be the first derivative of 2 + 0*a**2 - 4/25*a**5 + 4/15*a**3 - 7/10*a**4 + 7/15*a**6 + 0*a. Find d such that m(d) = 0.
-1, 0, 2/7, 1
Factor 47*y**2 + 5*y - 7*y**2 + 47*y**3 - 59*y**3 + 47*y**3.
5*y*(y + 1)*(7*y + 1)
Let w(g) be the second derivative of -1/15*g**6 + 0*g**2 + 0 - 1/3*g**3 + 1/10*g**5 + 1/6*g**4 - 6*g. Let w(o) = 0. Calculate o.
-1, 0, 1
Let n = 471/268 - 1/134. Solve n*b + 9/4*b**2 - 1/2 = 0 for b.
-1, 2/9
Suppose -6*a + 2 = -5*a. Let b(l) = 4*l - 5. Let j be b(a). Find c, given that 0 - 3/2*c**2 - 1/2*c**4 - 1/2*c - 3/2*c**j = 0.
-1, 0
Let i(a) = -a**2 + 8*a - 9. Suppose -v + 3*w - 9 = 0, -2*w = 2*v - w - 17. Let q be i(v). Let -4*o**2 + 0*o - 2 - q*o + 3*o**2 = 0. What is o?
-2, -1
Let w(c) be the second derivative of 5*c + 0*c**2 - c**4 - 4/5*c**5 + 0 + 2/3*c**3. Factor w(q).
-4*q*(q + 1)*(4*q - 1)
Let y(q) = 2*q + 15. Let o be y(-6). Let n(x) be the third derivative of 1/12*x**o - 1/80*x**6 + 2*x**2 - 5/48*x**4 + 7/120*x**5 + 0*x + 0. Factor n(l).
-(l - 1)**2*(3*l - 1)/2
Let y(c) be the third derivative of 1/525*c**7 + 0*c**3 - 7/600*c**6 - 1/150*c**5 + 0 - c**2 + 0*c + 0*c**4 + 1/240*c**8. Find t, given that y(t) = 0.
-1, -2/7, 0, 1
Let b(v) be the first derivative of v**3/9 - 2*v**2/3 + 4*v/3 + 5. Factor b(h).
(h - 2)**2/3
Let t(v) be the third derivative of -v**2 - 1/30*v**6 - 1/105*v**7 + 1/168*v**8 + 1/15*v**5 + 1/12*v**4 + 0*v - 1/3*v**3 + 0. Factor t(p).
2*(p - 1)**3*(p + 1)**2
Let l be (3/(-2))/(27/(-144)). Let g(i) = i - 6. Let h be g(l). Find v such that 2/7*v + 0 - 2/7*v**h = 0.
0, 1
Let y = 222/1705 - -14/31. Let h = y - 2/5. Factor -h*s + 0 - 2/11*s**2.
-2*s*(s + 1)/11
Factor 0*o + 3/2*o**3 - 3/2*o**4 + 0 + 3*o**2.
-3*o**2*(o - 2)*(o + 1)/2
Let y be (-2)/4 + 246/4. Let v = -243/4 + y. Factor v*t - 1/4*t**2 + 0.
-t*(t - 1)/4
Let k be 5/25*0*(-3)/6. Find o such that -1/4*o**2 + 1/2*o**3 + k*o - 1/4*o**4 + 0 = 0.
0, 1
Let l = 1/10 + 2/5. Let s(y) be the second derivative of 1/3*y**4 + 2*y - 1/2*y**2 + 0 - l*y**3. Factor s(t).
(t - 1)*(4*t + 1)
Factor -2/9*l**4 + 0*l + 0 + 2/9*l**2 + 0*l**3.
-2*l**2*(l - 1)*(l + 1)/9
Suppose -2*x + 0*x = -5*w + 14, -4 = -4*x + 2*w. Let p be 1/((-305)/(-100) - 3). Find s such that -x*s**4 + 21*s**5 - p*s**5 + 4*s**2 + s + 7*s**4 + 6*s**3 = 0.
-1, 0
Let v(l) be the third derivative of l**8/1344 + l**7/420 - l**6/480 - l**5/120 + 3*l**2. Determine u, given that v(u) = 0.
-2, -1, 0, 1
Let j(f) be the third derivative of 0 - 1/6*f**3 + 0*f - 2*f**2 - 1/120*f**5 + 1/16*f**4. Suppose j(v) = 0. What is v?
1, 2
Let s(d) be the third derivative of d**5/15 - 2*d**3/3 + 15*d**2. Factor s(k).
4*(k - 1)*(k + 1)
Find g, given that -13*g - g**3 - 17*g - 4*g**3 - 25*g**2 = 0.
-3, -2, 0
Factor -4/7*i**3 + 16/7*i - 4/7*i**2 + 16/7.
-4*(i - 2)*(i + 1)*(i + 2)/7
Let f = -10 - -51/5. Factor 1/5*u**2 + 2/5*u + 0 - f*u**3.
-u*(u - 2)*(u + 1)/5
Let w(y) be the first derivative of -2*y**3/15 + y**2/5 + 4*y/5 + 3. Find r such that w(r) = 0.
-1, 2
Suppose 0*l + 0*l**3 - 8/7*l**2 + 2/7*l**4 + 0 = 0. Calculate l.
-2, 0, 2
Let n(f) = -13*f - 50. Let z be n(-4). Suppose -1/2*g**2 + 2*g - z = 0. Calculate g.
2
Let t be ((-10)/(-4) + -4)*-2. Let d(j) be the second derivative of 25/18*j**5 + 0 - 2*j + 25/9*j**4 + 8/9*j**2 + 20/9*j**t. Determine q, given that d(q) = 0.
-2/5
Factor 0*m + 6*m**2 + 4*m**3 + 0 + 2/3*m**4.
2*m**2*(m + 3)**2/3
Let d(w) be the second derivative of w**7/168 - w**6/60 + w**5/80 - 29*w. Factor d(f).
f**3*(f - 1)**2/4
Let t(x) = 7*x**5 - 88*x**4 - 38*x**3 - 6*x**2 - 9*x + 9. Let r(q) = q**5 - q**3 + q - 1. Let y(i) = -18*r(i) - 2*t(i). Factor y(z).
-2*z**2*(z - 6)*(4*z + 1)**2
Factor 0 + 5/3*w - 5/3*w**2.
-5*w*(w - 1)/3
Let u(c) be the first derivative of -9*c**6/40 + 3*c**5/5 - c**4/2 + 4*c**2 - 4. Let t(y) be the second derivative of u(y). Solve t(g) = 0 for g.
0, 2/3
Suppose 10*i - 13*i + 15 = 0. Solve 0*r + 1/3*r**3 + 1/3*r**4 + 0 - 1/3*r**i - 1/3*r**2 = 0 for r.
-1, 0, 1
Let i(g) be the first derivative of g**3 + 