of -6*k + 2/3*k**3 - 5 - 2*k**2. What is c in y(c) = 0?
-1, 3
Let z = -6 - -10. Let r(h) be the third derivative of 0*h - 1/105*h**7 - 1/12*h**z + 1/30*h**5 + h**2 + 0*h**3 + 0 + 1/60*h**6. Suppose r(b) = 0. What is b?
-1, 0, 1
Let l(q) be the first derivative of -q**6/240 - q**5/60 - q**4/48 - 3*q**2/2 + 3. Let j(h) be the second derivative of l(h). Factor j(c).
-c*(c + 1)**2/2
Let m(f) = f**2 + 2*f - 30. Let b be m(-7). Let g(s) be the third derivative of 0 + 4*s**2 + 1/420*s**6 - 1/105*s**b + 0*s**3 + 1/84*s**4 + 0*s. Solve g(j) = 0.
0, 1
Let q(x) be the second derivative of -x**4/48 - x**3/24 - 3*x. Factor q(a).
-a*(a + 1)/4
Suppose -3*o + 5*j + 9 + 12 = 0, -3*j - 9 = 0. Factor o*g**2 + g**4 - 5*g - 3*g**4 + 2*g**3 + 3*g.
-2*g*(g - 1)**2*(g + 1)
Let j = 30/19 + -3/38. Find w, given that 3/2*w**3 + j*w**4 + 0 + 1/2*w**2 + 1/2*w**5 + 0*w = 0.
-1, 0
Let u(f) be the first derivative of f**6/9 - 4*f**5/15 + 4*f**3/9 - f**2/3 - 2. Factor u(n).
2*n*(n - 1)**3*(n + 1)/3
Let y(b) = -b + 1. Let l be y(-1). Factor 3*r + 2 - 7*r**2 - 7*r**5 + 0*r**2 - 8*r**2 + 4*r**3 + r**l + 12*r**4.
-(r - 1)**3*(r + 1)*(7*r + 2)
Let i be 12/297 + 4/22 + 0. Let 2/9*o**3 + 0 + 4/9*o**2 + i*o = 0. Calculate o.
-1, 0
Let c(o) = -o**3 + 7*o**2 - 3*o - 14. Let i be c(6). Factor -2/5*n**i + 0 - 2/5*n**3 + 2/5*n**5 + 0*n + 2/5*n**2.
2*n**2*(n - 1)**2*(n + 1)/5
Factor 3*j**2 + 4*j + 8 + 0*j**2 - 7*j**2.
-4*(j - 2)*(j + 1)
Let s(m) = 16*m**3 - 21*m**2 + 6*m - 1. Suppose 0 = 4*v + 47 - 3. Let k(q) = -3*q**3 + 4*q**2 - q. Let z(j) = v*k(j) - 2*s(j). Find u, given that z(u) = 0.
-1, 1, 2
Let z(p) be the first derivative of -p**2 - 8/3*p**3 + 0*p + 8/5*p**5 + 1/2*p**4 + 3. Suppose z(d) = 0. Calculate d.
-1, -1/4, 0, 1
Let f = 175676/27 + -6505. Let i = f + -5/27. Solve -2*y - i + 10/3*y**2 = 0 for y.
-2/5, 1
Let l(m) = m**2 + 14*m + 2. Let y be l(-14). Let v(i) be the second derivative of 0 + 0*i**2 - y*i + 1/10*i**5 + 2/3*i**3 - 1/2*i**4. Factor v(n).
2*n*(n - 2)*(n - 1)
Let h(g) be the third derivative of g**5/105 - 11*g**4/84 + 5*g**3/21 - 21*g**2. Factor h(w).
2*(w - 5)*(2*w - 1)/7
Factor 5/4*k**2 - 1 - 3/4*k - 1/4*k**4 + 3/4*k**3.
-(k - 4)*(k - 1)*(k + 1)**2/4
Let y(s) be the first derivative of -s**5/20 - s + 1. Let m(v) be the first derivative of y(v). Let m(l) = 0. What is l?
0
Let c = -6 - -8. Let -w**4 + 2*w**5 - w**4 + 12*w**3 - 8*w**c - 6*w**4 + 2*w = 0. Calculate w.
0, 1
Factor 1/4*i**3 - i**2 - 1/4*i + 1.
(i - 4)*(i - 1)*(i + 1)/4
Let b(f) be the second derivative of -f**6/120 + f**4/24 + 3*f**2/2 - 3*f. Let s(u) be the first derivative of b(u). Factor s(g).
-g*(g - 1)*(g + 1)
Let o(u) = 8*u**4 - 23*u**3 + 22*u**2 - 13*u - 3. Let x(z) = -15*z**4 + 45*z**3 - 45*z**2 + 25*z + 5. Let k(y) = -5*o(y) - 3*x(y). Find j such that k(j) = 0.
0, 1, 2
Let p(l) be the first derivative of -l**6/33 + 2*l**5/55 + 3*l**4/11 - 28*l**3/33 + l**2 - 6*l/11 + 12. Solve p(d) = 0 for d.
-3, 1
Let t be 4*(21/(-12) - -3). Let p(d) be the first derivative of -1/2*d**4 - 3 - 2/3*d**3 + 2/5*d**t + 0*d + d**2. Determine f, given that p(f) = 0.
-1, 0, 1
Factor 6 + f**2 + 21*f + 4*f**2 + 4*f**2.
3*(f + 2)*(3*f + 1)
Let t(d) be the first derivative of d**8/1050 + d**7/300 + d**6/450 - d**5/300 - d**3 + 1. Let f(b) be the third derivative of t(b). Factor f(h).
2*h*(h + 1)**2*(4*h - 1)/5
Suppose -4*v + 28 = 4*i, v - 34 = -4*i - 0*v. Suppose 3*p - 2*r + i = 3*r, 0 = -2*r + 6. Factor -2*j**2 - 3*j**p - 6*j - 2*j**3 - j**2 - 2.
-2*(j + 1)**3
Let l(j) be the second derivative of j**6/150 + 3*j**5/50 - 2*j**4/15 - j**3/5 + 7*j**2/10 - 62*j. Suppose l(s) = 0. Calculate s.
-7, -1, 1
Let f(a) be the first derivative of a**4/24 - a**3/9 + a**2/12 + 1. Let f(j) = 0. Calculate j.
0, 1
Let p = -6 - -8. Find s, given that -p*s**2 - 3*s**2 - 6 + 8*s + 3*s**2 = 0.
1, 3
Let j = 10 + -6. Let s be -3 - (2 - j - 1). Factor 0*p + 16*p**3 - 15*p**3 + s*p + p**2.
p**2*(p + 1)
Let r be 3/7 - 243/(-21). Let b = r + -9. Let 9*t**2 - 3*t - 7*t**2 - b*t**2 - 2 = 0. What is t?
-2, -1
Suppose -2*h + 2 = 2*l, 3*h - 2*l - 10 = -2. Solve 2*s**2 - 3*s**3 + s**3 + 0*s**2 + 2*s**5 - h*s**4 = 0.
-1, 0, 1
Let u = -7/9 + 1. Let j be 6/(-8)*(-24)/9. Determine h, given that 2/9 + 2/9*h**3 - u*h**j - 2/9*h = 0.
-1, 1
Suppose -35*f = -43*f + 16. Factor 0*o + 0 + o**f - 1/2*o**3.
-o**2*(o - 2)/2
Factor -37*m**2 + 5*m**3 - 8*m**5 + 42*m**2 + 3*m**5 - 5*m**4 + 0*m**3.
-5*m**2*(m - 1)*(m + 1)**2
Let n be (-24)/(-12 + 6) - (-1 + 4). Let s(v) be the first derivative of n + 0*v**2 + 0*v**4 - 2/7*v - 2/35*v**5 + 4/21*v**3. Suppose s(b) = 0. What is b?
-1, 1
Let x(m) be the second derivative of 0*m**2 - 7*m + 3/20*m**5 - 1/4*m**4 + 0*m**3 + 0. What is z in x(z) = 0?
0, 1
Let z = 16 - 9. Factor 83*y**2 - 56*y**2 - 6*y - 14*y**3 - z*y**3.
-3*y*(y - 1)*(7*y - 2)
Let x = -113/3 - -38. Determine u so that 4/3*u + 1 + x*u**2 = 0.
-3, -1
Suppose 2*x = 190 - 48. Determine k so that -61*k**4 - 31*k**4 + 5*k**2 + x*k**2 + 2*k**3 - 34*k + 12*k**4 + 4 + 32*k**5 = 0.
-1, 1/4, 1, 2
Suppose -11 + 2*f**3 + 21 - f**3 - 6 - 3*f**2 = 0. What is f?
-1, 2
Suppose 2*c = 4*c - 8. Suppose -c*k + 6 = -k. Factor 2*q**2 - q**k - 3*q + 2 + 0*q.
(q - 2)*(q - 1)
Let u be -82*(-2)/180 + 1/(-9). Suppose -u + 6/5*n - 2/5*n**2 = 0. What is n?
1, 2
Let y(g) be the first derivative of 1/3*g**6 + g**2 + 0*g + 3*g**4 - 8/5*g**5 + 1 - 8/3*g**3. Factor y(d).
2*d*(d - 1)**4
Let w(v) = v**3 + 4*v**2 - 3*v - 2. Let l(c) = -c**3 - 3*c**2 + 3*c + 2. Let h(o) = -4*l(o) - 3*w(o). Find f, given that h(f) = 0.
-1, 2
Let i(q) = 2*q + 5*q + 3 - 8*q. Let h be i(3). Solve 0*t**4 + 3/5*t**5 + 0*t - 3/5*t**3 + h*t**2 + 0 = 0 for t.
-1, 0, 1
Suppose -6 - 2 = 4*l. Let h be 4*l/(-1*4). Suppose -h*p**4 + p**4 - 2*p - 6*p**3 - 6*p**2 - p**4 = 0. What is p?
-1, 0
Let m(n) be the second derivative of 0 + 6*n + 1/21*n**3 - 1/84*n**4 - 1/14*n**2. Find p, given that m(p) = 0.
1
Let t(k) be the first derivative of -27*k**5/25 - 33*k**4/20 + 7*k**3/5 + 33*k**2/10 + 6*k/5 + 21. Determine u, given that t(u) = 0.
-1, -2/9, 1
Let d(q) be the third derivative of q**8/1848 - q**7/231 + q**6/66 - q**5/33 + 5*q**4/132 - q**3/33 + 8*q**2. Determine j so that d(j) = 0.
1
Let f(r) be the first derivative of -r**4 - 8*r**3/3 - 2*r**2 + 2. Solve f(a) = 0.
-1, 0
Let r(j) be the second derivative of j**8/336 + j**7/70 - j**6/120 - 7*j**5/60 + 2*j**3/3 - j**2 - 3*j. Let y(u) be the first derivative of r(u). Factor y(m).
(m - 1)**2*(m + 1)*(m + 2)**2
Let f(r) be the third derivative of r**8/56 - r**7/70 - 9*r**6/20 + r**5/20 + 7*r**4/2 - 6*r**3 + 5*r**2. Let f(t) = 0. Calculate t.
-2, 1/2, 1, 3
Let p(j) be the third derivative of -2*j**7/35 + 7*j**6/40 - j**5/10 - j**4/8 + 25*j**2. Factor p(u).
-3*u*(u - 1)**2*(4*u + 1)
What is c in 4*c**4 - c**3 - c**5 - 2*c**3 + 4*c**3 + 0*c**5 - 4*c**2 = 0?
-1, 0, 1, 4
Let u = 233/18 - 77/6. Let b(l) be the second derivative of 1/18*l**4 + 0 + u*l**3 - l + 0*l**2. Factor b(i).
2*i*(i + 1)/3
Let k = 445 + -7563/17. Let x = k + 13/34. Suppose 0 + 1/2*r**4 + 0*r - x*r**3 + 0*r**2 = 0. Calculate r.
0, 1
Factor 3/7*f**5 - 3*f**4 + 6/7*f**2 + 30/7*f**3 + 15/7 - 33/7*f.
3*(f - 5)*(f - 1)**3*(f + 1)/7
Let h be 14/(-49) + (-834)/(-28). Let r = 30 - h. Let 0 - r*z**2 - z = 0. Calculate z.
-2, 0
Suppose -11*c + 6*c + 15 = 0. Let h(o) be the first derivative of -1 - 2*o**2 - 4/3*o + 13/9*o**c + 7/4*o**4. Determine q so that h(q) = 0.
-1, -2/7, 2/3
Let x(h) be the second derivative of h**5/10 - 7*h**4/12 - h**3/3 + h**2 - 3*h. Let u(m) = -m**3 + 3*m**2 + m - 1. Let k(r) = 5*u(r) + 2*x(r). Factor k(i).
-(i - 1)**2*(i + 1)
Solve -6*m**2 + 6*m + m**3 - 2 - 7*m**3 + 8*m**3 = 0.
1
Let z(n) be the second derivative of -2*n**7/21 - 2*n**6/15 + 2*n**5/5 + 2*n**4/3 - 2*n**3/3 - 2*n**2 + 4*n. Determine l, given that z(l) = 0.
-1, 1
Let y(d) = -d**2 - 13*d + 6. Let a be y(-13). Let c(p) = 5*p**2 + p + 1. Let v be c(-1). Factor 3*z**4 + 3*z**4 - z**v - z - a*z**4 + 2*z**3.
-z*(z - 1)**2*(z + 1)**2
Let g(s) be the first derivative of 2*s**3/3 - 8*s**2 + 32*s - 16. Factor g(m).
2*(m - 4)**2
Let s = -3 + 3. Let q(u) be the second derivative of u - 2/3*u**3 + u**2 + s - 1/2*u**4. Find o, given that q(o) = 0.
-1, 1/3
Let n(g) be the third derivative of -g**7/6300 - g**6/900 - g**5/300 - g**4/12 + g**2. Let o(d) be the se