x**3 - x + c - 1/18*x**4. Factor k(r).
-2*r*(r - 1)/3
Factor -15*s + 2 - 5*s**2 - 8 - 7*s**2 - 3*s**3.
-3*(s + 1)**2*(s + 2)
Find j, given that 20*j + 5/2*j**2 + 40 = 0.
-4
Let s(z) be the second derivative of -z**5/70 + z**3/7 + 2*z**2/7 + z. Determine y, given that s(y) = 0.
-1, 2
Let t(v) be the third derivative of 2*v**7/105 - v**6/10 + 2*v**5/15 + 6*v**2. Determine g so that t(g) = 0.
0, 1, 2
Let c(z) be the second derivative of 0*z**2 - 1/12*z**3 - 1/84*z**7 - 1/15*z**6 + 0 - 1/6*z**4 - 6*z - 3/20*z**5. Let c(n) = 0. What is n?
-1, 0
Let h(j) = j**2 - 2*j + 2. Let s be h(2). Let u(q) be the first derivative of 0*q**3 + 1 + 0*q + 1/6*q**4 + 0*q**s. Let u(l) = 0. What is l?
0
Determine y, given that -15*y**3 - 9*y**4 + 2*y**4 - 6*y**2 - 3*y**4 + y**4 = 0.
-1, -2/3, 0
Let f(g) be the second derivative of g**5/110 - g**4/33 + g**3/33 - 7*g. Suppose f(m) = 0. What is m?
0, 1
Factor -686/15 - 14/5*p**2 + 98/5*p + 2/15*p**3.
2*(p - 7)**3/15
Let j(l) be the first derivative of l**6/120 - l**5/20 + l**4/8 - 2*l**3/3 - 8. Let g(c) be the third derivative of j(c). Suppose g(o) = 0. Calculate o.
1
Let x(b) be the third derivative of b**7/350 - b**6/75 + b**5/300 + b**4/15 - 2*b**3/15 + 21*b**2. Solve x(t) = 0.
-1, 2/3, 1, 2
Suppose 30 = 2*b + b. Suppose -6*o = -o - b. Suppose -5/2*h**4 - h - 1/2*h**5 - 9/2*h**3 + 0 - 7/2*h**o = 0. Calculate h.
-2, -1, 0
Let f(r) = 3*r**3 - r. Let h be f(1). Factor -y**2 + 9 - 3*y + 2*y**h - 10 + 3*y**3.
(y - 1)*(y + 1)*(3*y + 1)
Let u(m) be the first derivative of 3*m**5/10 + 37*m**4/72 - m**3/36 - m**2/6 + 9*m - 3. Let n(k) be the first derivative of u(k). Find s such that n(s) = 0.
-1, -1/4, 2/9
Let p(s) be the first derivative of -1/18*s**3 + 0*s**4 + s**2 + 1/180*s**5 + 1 + 0*s. Let l(h) be the second derivative of p(h). Factor l(q).
(q - 1)*(q + 1)/3
Let t(q) = 2*q**4 - 13*q**3 - 8*q**2 + 7*q + 9. Let o(f) = f**4 - 6*f**3 - 4*f**2 + 4*f + 4. Let w(z) = -9*o(z) + 4*t(z). Find g, given that w(g) = 0.
-2, 0, 2
Let z(x) be the first derivative of x**4/16 + 5*x**3/12 + 3*x**2/4 + 5. Find r, given that z(r) = 0.
-3, -2, 0
Let y = -6 - -3. Let d be (y + (2 - 1))/(-1). Factor 4*w**2 - 4*w**2 - 2*w**5 + 2*w**3 - 2*w**d + 2*w**4.
-2*w**2*(w - 1)**2*(w + 1)
Let k(q) be the second derivative of -14/3*q**4 + 0 - 4*q + 4*q**2 - 2*q**3 + 2/3*q**7 - 4/5*q**5 + 8/5*q**6. Solve k(g) = 0 for g.
-1, 2/7, 1
Let b(g) be the first derivative of g**4/8 + g**3/3 + 7. Factor b(p).
p**2*(p + 2)/2
Determine t so that -t - 4 + 8*t + 2*t**2 - 9*t = 0.
-1, 2
Let b(f) be the first derivative of -2*f**7/105 - f**6/15 - f**5/15 + 7*f**2/2 + 3. Let x(i) be the second derivative of b(i). Factor x(w).
-4*w**2*(w + 1)**2
Let z = -183 + 735/4. Find p such that z + 5/4*p**2 + 1/4*p**3 + 7/4*p = 0.
-3, -1
Determine t, given that 7*t + 9*t - 2*t**3 - 2*t**3 = 0.
-2, 0, 2
Let i(d) be the second derivative of d**4/18 - 2*d**3/9 + d**2/3 - 3*d. Let i(j) = 0. What is j?
1
Solve 2/3*l**3 - 4*l**2 + 1/3*l**4 + 14/3*l - 5/3 = 0 for l.
-5, 1
Let x(o) be the second derivative of o**5/130 - o**4/26 + 2*o**3/39 + 5*o. Factor x(n).
2*n*(n - 2)*(n - 1)/13
Let w = 67/660 - 3/44. Let k(c) be the second derivative of 1/6*c**2 + 3*c + 0*c**4 + 0 - w*c**5 + 1/9*c**3 - 1/90*c**6. Find j such that k(j) = 0.
-1, 1
Let m(h) = -4*h**3 + 3*h**2 - 2*h + 6. Let f(k) = -3*k**3 + 3*k**2 - k + 5. Let x(y) = -5*f(y) + 4*m(y). Find j, given that x(j) = 0.
-1
Let u(t) be the first derivative of -3*t**2 - 3 - 9*t - 1/3*t**3. Factor u(k).
-(k + 3)**2
Let k(h) be the first derivative of 2*h**3/9 + h**2 + 4*h/3 - 8. Let k(o) = 0. What is o?
-2, -1
Let s(l) be the first derivative of 4/3*l**3 - 4*l - l**2 + 3 + 1/2*l**4. Solve s(p) = 0 for p.
-2, -1, 1
Let t(r) = r**5 + 5*r**4 - 5*r**3 + 3*r**2 + 4*r + 4. Suppose -2*f = -4*f - 2. Let x(j) = j**5 - j**4 + j**3 + j + 1. Let k(p) = f*t(p) + 4*x(p). Factor k(d).
3*d**2*(d - 1)**3
Let z(h) be the second derivative of -h**6/900 + h**5/300 + h**3/3 + 3*h. Let q(g) be the second derivative of z(g). Factor q(p).
-2*p*(p - 1)/5
Suppose 0 = -4*y + 2*y - 8. Let i(d) = d**3 - d**2 + d. Let z(h) = -h**3 - h. Let u(o) = y*i(o) - 6*z(o). Factor u(s).
2*s*(s + 1)**2
Let m(r) be the first derivative of -4*r**3/9 + 8*r**2/3 - 23. Suppose m(z) = 0. What is z?
0, 4
Let s = 11 + -8. Suppose -5*l - s*b - 3 - 6 = 0, 6 = -3*l - 2*b. Factor r**2 + 2 + r - 4*r + l*r.
(r - 2)*(r - 1)
Let 0 - 16/3*j + 112/3*j**2 - 140/3*j**3 + 44/3*j**4 = 0. Calculate j.
0, 2/11, 1, 2
Suppose -2*a + 17 - 13 = 0. Solve 4/3*v**a + 4/9 - 2/3*v**5 + 14/9*v - 16/9*v**4 - 8/9*v**3 = 0 for v.
-1, -2/3, 1
Let c(i) = 2 + 6 - 7*i**2 + 4 - 6 + 4*i. Let x(y) = y**2 - y - 1. Suppose -4*v = 19 + 5. Let o(h) = v*x(h) - c(h). Suppose o(m) = 0. Calculate m.
-2, 0
Let x(d) be the second derivative of -1/80*d**6 - 1/2*d**2 + 0*d**3 + 1/8*d**4 + 1/40*d**5 - 4*d + 0. Let w(c) be the first derivative of x(c). Factor w(b).
-3*b*(b - 2)*(b + 1)/2
Let w(j) be the second derivative of -j**7/126 - j**6/90 + j**5/20 + 5*j**4/36 + j**3/9 - 25*j. Factor w(y).
-y*(y - 2)*(y + 1)**3/3
Let x(l) be the third derivative of 16*l**7/525 + 2*l**6/75 + l**5/150 + 10*l**2. What is b in x(b) = 0?
-1/4, 0
Let -16/9 + 1/9*s**3 + 8/3*s - s**2 = 0. Calculate s.
1, 4
Let n(x) be the third derivative of 1/48*x**8 + 3/20*x**5 + 0*x - 1/12*x**4 + 0 - 1/24*x**6 + 5*x**2 - 3/70*x**7 + 0*x**3. Find h, given that n(h) = 0.
-1, 0, 2/7, 1
Let b = -11296/21 + 538. Let o(m) be the first derivative of 2/7*m**2 + 2/7*m + b*m**3 - 1. Let o(f) = 0. Calculate f.
-1
Let s(o) be the third derivative of -o**6/540 - o**5/30 - 2*o**4/9 - 16*o**3/27 - 16*o**2. Suppose s(c) = 0. What is c?
-4, -1
Determine a so that 3/2*a + 1 + 1/2*a**2 = 0.
-2, -1
Let r(l) be the second derivative of -l**6/360 + l**5/180 + 3*l**2/2 + 3*l. Let g(d) be the first derivative of r(d). Suppose g(j) = 0. Calculate j.
0, 1
What is o in 2/13*o**5 + 8/13*o**2 - 2/13*o**3 + 0 - 8/13*o**4 + 0*o = 0?
-1, 0, 1, 4
Let o(q) = 2*q**3 + 40*q**2 + 3*q + 60. Let g be o(-20). Find t such that -16/3*t**2 - t**3 + 4/3*t + g - 4/3*t**5 + 13/3*t**4 = 0.
-1, 0, 1/4, 2
Let s(a) be the first derivative of -4 + 8/3*a - 8*a**2 - 1/6*a**4 + 25/9*a**6 + 82/9*a**3 - 6*a**5. Suppose s(h) = 0. What is h?
-1, 2/5, 1
Let c(k) = -k**3 - 2*k**2 + k + 4. Let v be c(-2). Let v - 16*b**4 + 20*b - 16*b**3 - 4*b**5 - 8 + 8*b**2 + 14 = 0. What is b?
-2, -1, 1
Suppose -4 + 2 = l, -5*l - 4 = 3*f. Suppose 0 + 2/5*h**f + 4/5*h = 0. What is h?
-2, 0
Factor -7*r**3 + 10*r**2 - 10*r**3 + 5*r**5 - 6*r**3 + 8*r**3.
5*r**2*(r - 1)**2*(r + 2)
Let z = -20 - -35. Let b be ((-9)/z)/(1/(-5)). Factor -8*c**3 + c**b + 0*c - 6*c**4 + c.
-c*(c + 1)*(2*c + 1)*(3*c - 1)
Suppose 3*i + s - 2 = 0, -4*i + s = 3*s. Factor -i*q**3 + 1/2 - q - 7/2*q**2.
-(q + 1)**2*(4*q - 1)/2
Suppose 11 = -13*u + 63. Let i(l) be the second derivative of 3*l - 1/36*l**u + 1/9*l**3 + 0 + 0*l**2. Factor i(b).
-b*(b - 2)/3
Suppose 2*l - i + 3*i = -4, 5*l - 20 = 5*i. Let x(k) be the first derivative of -k + 7/8*k**4 - 1/2*k**3 - 7/4*k**2 - l + 1/2*k**5. Factor x(a).
(a - 1)*(a + 1)**2*(5*a + 2)/2
Let f = 467 - 933/2. Factor f*v - 1/4 + 0*v**2 - 1/2*v**3 + 1/4*v**4.
(v - 1)**3*(v + 1)/4
Let h(s) be the third derivative of s**6/600 - s**5/300 - s**4/120 + s**3/30 + 3*s**2. Factor h(v).
(v - 1)**2*(v + 1)/5
Let r be (-2 + 4)*(-27)/(-18). Let s(j) = -j**2 - 8*j + 13. Let t be s(-9). Factor -6*w**r - 6*w + 3/2*w**t + 9*w**2 + 3/2.
3*(w - 1)**4/2
Let y(j) be the first derivative of 13*j**4/4 + 7*j**3/3 + 8. Let r(v) = -6*v**3 - 3*v**2. Let c(h) = -5*r(h) - 2*y(h). Factor c(p).
p**2*(4*p + 1)
Find c such that 4 - 5 - c**2 - c + 3 = 0.
-2, 1
Suppose 20*t**3 - 15*t**3 + 6*t**4 - t**4 = 0. What is t?
-1, 0
Suppose -5*n + 2*n + 6 = 0. Let r be (36/21)/(44/28). Factor 2/11*i**5 + r*i**3 + 0 + 8/11*i**4 + 2/11*i + 8/11*i**n.
2*i*(i + 1)**4/11
Let l(z) = z - 2. Let w be l(5). Let h be (-2)/(-6) + (-60)/(-9). Let -q**w - q + 8 + 3*q**2 - 2*q - h = 0. What is q?
1
Let s(d) be the second derivative of -d**7/1050 + d**5/300 + d**2 - 3*d. Let o(q) be the first derivative of s(q). Suppose o(l) = 0. Calculate l.
-1, 0, 1
Suppose 2 = 3*c - 10. Let v be (-8)/(-5) + (-4)/(-10). Find w, given that -9*w**2 + 12*w + 8*w**c - 2 + 10*w**4 - 7*w**v - 12*w**3 = 0.
-1, 1/3, 1
Let g(n) 