 + j*c + 8*c**2 + c**4 - 1 - 14*c**2 = 0. Calculate c.
1
Let k(l) be the second derivative of -l**6/30 - l**5/10 - l**4/12 + l. Factor k(u).
-u**2*(u + 1)**2
Suppose -3*t - 3 = -15, 0 = x - t + 6. Let s = x + 4. Suppose -2 + 3 - 1 + 2*i**s + 2*i**3 = 0. What is i?
-1, 0
Let q(w) be the third derivative of -w**7/2520 - w**6/360 - w**5/120 - w**4/12 - 2*w**2. Let o(b) be the second derivative of q(b). Factor o(i).
-(i + 1)**2
Let q(c) be the first derivative of -1/6*c**3 + 1/2*c - 1/8*c**4 - 3 + 1/4*c**2. Let q(g) = 0. Calculate g.
-1, 1
Let u(d) be the second derivative of 2*d + 0 + 1/3*d**3 + 1/30*d**5 - 1/6*d**4 - d**2. Let j(x) be the first derivative of u(x). Determine m so that j(m) = 0.
1
Suppose 4*x + 1 = 9. Suppose 8*j - 3*j**x + 4*j**2 + 3*j**4 + 3*j**5 - 2*j - 4*j**2 - 9*j**3 = 0. Calculate j.
-2, -1, 0, 1
Let w(q) = 6*q**2 - 6*q + 18. Suppose -2*f = -4*a - 20 - 8, 16 = -4*f. Let n(c) = -c**2 - 1. Let i(u) = a*n(u) - w(u). Factor i(o).
3*(o - 1)*(o + 3)
Let h(r) be the third derivative of r**8/10080 - r**7/1800 + r**6/900 - r**5/12 - 5*r**2. Let m(p) be the third derivative of h(p). Find u, given that m(u) = 0.
2/5, 1
Let p(r) be the third derivative of 2*r**7/105 - r**6/6 + 7*r**5/15 - r**4/2 + 9*r**2. Factor p(v).
4*v*(v - 3)*(v - 1)**2
Suppose 0 = 5*j + 5, -17*o = -21*o - 4*j + 4. Find i such that 4*i + 6 + 2/3*i**o = 0.
-3
Factor 8/3*r**3 + 0*r + 9 - 6*r**2 - 1/3*r**4.
-(r - 3)**3*(r + 1)/3
Factor 2/23*z**5 + 2/23*z - 8/23*z**4 - 8/23*z**2 + 0 + 12/23*z**3.
2*z*(z - 1)**4/23
Let c(x) be the first derivative of x**5/5 - x**4/2 - x**3 + 2*x**2 + 4*x - 10. Solve c(k) = 0 for k.
-1, 2
Let z(t) be the second derivative of 0 - 5*t - 8/3*t**2 + 4/9*t**3 - 1/36*t**4. Solve z(p) = 0.
4
Let b(m) be the second derivative of 0*m**4 - 3*m - 3/2*m**2 + 0 - 1/90*m**5 + 1/9*m**3. Let l(t) be the first derivative of b(t). Determine g so that l(g) = 0.
-1, 1
Let z = 3 + -1. Let c be (-7 + 6)/((-1)/2). Factor -c*w**3 - 7/2*w**z + 1/2 - w.
-(w + 1)**2*(4*w - 1)/2
Let h(x) = -2*x**2 - 3*x**2 - 7*x + 0*x**2 + x**3 + 9. Let u be h(6). Factor 2/3*n**u + 0 + 2/3*n**5 + 0*n - 4/3*n**4 + 0*n**2.
2*n**3*(n - 1)**2/3
Suppose -4*z = -13 + 1. Let -4*a**3 + 2*a + 3*a**z + a - 2*a**2 - 4*a = 0. What is a?
-1, 0
Let o = 110/21 + -1168/231. Let 4/11*w**2 + 0*w**3 - o*w**4 - 2/11 + 0*w = 0. What is w?
-1, 1
Let s(l) = -l**3 + 2*l**2 + 3*l. Let o be s(3). Suppose o = b - 2. Factor 4/5*y + 2/5*y**b + 2/5.
2*(y + 1)**2/5
Let k(i) = -3*i**2 + 4*i - 2*i - 5 + 7 - i**3 + 2*i**3. Let s be k(2). Solve 0 + 0*a - 2/7*a**3 - 2/7*a**4 + 2/7*a**s + 2/7*a**5 = 0.
-1, 0, 1
Suppose 0 = 2*c - 3 - 1. Let y = c + 2. Factor -11*t**2 - 6*t**y - 12*t**3 - 2*t**3 - 2*t + t**2.
-2*t*(t + 1)**2*(3*t + 1)
Let p(g) be the first derivative of 4*g + 3*g**2 - 1/2*g**4 + 1 + 0*g**3. Factor p(y).
-2*(y - 2)*(y + 1)**2
Let o(i) be the third derivative of i**6/840 + i**5/105 + i**4/42 - 7*i**2. Factor o(b).
b*(b + 2)**2/7
Suppose 3 + 3 = -3*n, -5*n = -2*h + 16. Find c, given that 19*c + 12*c**2 + 2*c**h + 5*c + 54 - 38 = 0.
-2
Let p(z) = z + 14. Let h be p(-8). Suppose 3*l - h = -0. Factor -2*u + 2*u**l + 2 - 3*u**2 + u.
-(u - 1)*(u + 2)
Let x(j) be the second derivative of j**5/18 + 7*j**4/36 + 2*j**3/9 - 2*j**2 + 6*j. Let f(h) be the first derivative of x(h). Let f(i) = 0. What is i?
-1, -2/5
Let g(i) = -2*i**4 - 8*i**3 + 6*i**2 - 4*i + 4. Let k(z) = 2*z**4 + 7*z**3 - 6*z**2 + 3*z - 3. Let h(r) = 3*g(r) + 4*k(r). Determine t, given that h(t) = 0.
-3, 0, 1
Suppose -4*u + 0*u + 3*q = 0, -4*u + q = 0. Let p(d) be the second derivative of 0*d**2 + 1/30*d**6 - 1/12*d**4 - d + 1/20*d**5 - 1/6*d**3 + u. Factor p(o).
o*(o - 1)*(o + 1)**2
Let v(r) be the second derivative of 0*r**2 + 0 + 1/12*r**7 + 1/30*r**6 + 0*r**3 - 7/40*r**5 - 1/12*r**4 + r. Solve v(o) = 0 for o.
-1, -2/7, 0, 1
Let c = -2/91167 - 1347211/1580228. Let y = -4/39 - c. Factor -1/4*b**4 + 1/4*b - 3/4*b**2 + 0 + y*b**3.
-b*(b - 1)**3/4
Suppose 6/17*i**2 + 0 - 2/17*i = 0. Calculate i.
0, 1/3
Let p(r) be the third derivative of 1/20*r**4 + 0 + 1/100*r**5 + 3*r**2 + 1/10*r**3 + 0*r. Factor p(a).
3*(a + 1)**2/5
Factor 12 + 7*a**2 - 2*a**2 - 8*a**2.
-3*(a - 2)*(a + 2)
Let k(t) be the second derivative of 5*t**4/12 - 5*t**2/2 + 23*t. Factor k(x).
5*(x - 1)*(x + 1)
Let x = -2133/5 - -429. Let -x*z + 18/5 + 2/5*z**2 = 0. Calculate z.
3
What is c in 0*c**4 + 2/9*c**2 - 8/9*c**5 + 14/9*c**3 - 2/3*c - 2/9 = 0?
-1, -1/2, 1
Factor -2*u**2 + 3*u - 25 + 25 - 28*u**3 + 27*u**3.
-u*(u - 1)*(u + 3)
Let o = 13 - 8. Let v be (3 - 0) + 3/o. Find w such that -2/5*w**2 - v*w**4 + 8/5*w**5 + 0*w + 12/5*w**3 + 0 = 0.
0, 1/4, 1
Let s(z) be the third derivative of -3/2*z**3 + 0 - 1/60*z**5 + 0*z + 1/4*z**4 + 6*z**2. Factor s(i).
-(i - 3)**2
Factor 10/3*o**3 + 14/3*o + 6*o**2 + 4/3 + 2/3*o**4.
2*(o + 1)**3*(o + 2)/3
Suppose -3*g + 3 = -3. Suppose 4*j - 6*j + 4*j**g - j**3 - j**2 = 0. What is j?
0, 1, 2
Solve -4*z**4 - 3*z**4 + 3*z**2 + 4*z**4 = 0.
-1, 0, 1
Let 1/4*l**2 - 1/4*l**4 + 0 + 1/4*l**5 - 1/4*l**3 + 0*l = 0. What is l?
-1, 0, 1
Let v(r) = -2*r**2 + 36*r - 162. Let s(h) = -4*h**2 + 72*h - 324. Let x(b) = -4*s(b) + 10*v(b). Factor x(c).
-4*(c - 9)**2
Factor 0 + 2/15*q**5 + 0*q - 2/15*q**4 - 2/15*q**3 + 2/15*q**2.
2*q**2*(q - 1)**2*(q + 1)/15
Let z(g) = g - 8. Let w be z(8). Find i, given that w*i**2 - 7*i**2 + 6*i**2 - 6*i + 4*i**2 = 0.
0, 2
Let q(m) be the first derivative of -1/20*m**5 + 0*m + 1/16*m**4 + 1/12*m**3 - 4 - 1/8*m**2. Determine p so that q(p) = 0.
-1, 0, 1
Let x(t) = -30*t**3 + 5*t**2 - 5*t + 30. Let s(g) = 5*g**3 - g**2 + g - 5. Let m(n) = 35*s(n) + 6*x(n). Find f, given that m(f) = 0.
-1, 1
Let z(g) be the second derivative of 1/60*g**5 - 1/45*g**6 + 0*g**3 + 1/126*g**7 + 0 + 0*g**2 + 2*g + 0*g**4. Suppose z(p) = 0. What is p?
0, 1
Let d(n) be the second derivative of n**5/20 + n**4/8 - 2*n**2 + n. Let q(r) be the first derivative of d(r). Let q(p) = 0. Calculate p.
-1, 0
Let z(c) be the first derivative of -7/2*c**4 + 0*c - 10/3*c**3 - 1 + 2*c**2. Solve z(b) = 0 for b.
-1, 0, 2/7
Let r(h) = -h**4 - 3*h**3 + 6*h**2 + h - 3. Let a(u) = -u**4 - 4*u**3 + 7*u**2 + 2*u - 4. Let p(o) = -3*a(o) + 4*r(o). Factor p(b).
-b*(b - 1)**2*(b + 2)
Solve 4*j**2 + 5*j**5 + 18*j**3 + 6*j**2 - 4*j - 10*j**4 - 19*j**5 = 0 for j.
-1, 0, 2/7, 1
Let s be (-24)/(-36)*30/4. Suppose -s*r = -r - 8. Factor -2/9*o - 2/9*o**3 + 4/9*o**r + 0.
-2*o*(o - 1)**2/9
Let f(q) be the third derivative of 3*q**6/140 - q**5/70 - 3*q**4/28 + q**3/7 + 33*q**2. Factor f(x).
6*(x - 1)*(x + 1)*(3*x - 1)/7
Let u(q) = -3*q + 7 - 4*q + 2*q + 4*q. Let b be u(5). Solve -o**b - 4*o**4 + 2*o**4 + 3*o**4 = 0 for o.
-1, 0, 1
Let t be 1/3 - 6/(-54). Let m be (-5)/(-3) - (-4)/(-4). Factor -m*o**2 + 0 - t*o.
-2*o*(3*o + 2)/9
Let g be 25/2*(-2)/(-5). Let j(u) be the third derivative of 0*u - 1/27*u**3 + 1/135*u**6 + 0 - 1/45*u**g + 2*u**2 - 1/945*u**7 + 1/27*u**4. Factor j(x).
-2*(x - 1)**4/9
Solve -2/17*g**3 + 0 + 0*g - 8/17*g**2 = 0 for g.
-4, 0
Let z(c) be the third derivative of -1/48*c**4 + 1/30*c**5 + 1/105*c**7 + 0*c**3 + c**2 - 1/40*c**6 - 1/672*c**8 + 0*c + 0. Factor z(k).
-k*(k - 1)**4/2
Suppose 113*t**2 - 97*t**2 + 2*t**4 - 6*t**4 = 0. Calculate t.
-2, 0, 2
Let t = -244 + 247. Suppose 9/4*c + 3/4*c**t - 9/4*c**2 - 3/4 = 0. Calculate c.
1
Suppose 3*j - 2*j = 1. Let o be j + 3 + -2 + 1. Factor -2*c + 6*c + 1 + 0 - 2*c**2 - o.
-2*(c - 1)**2
Let w(y) = y**3 + y. Let f(o) = -2*o**4 + 3*o**3 + 4*o**2 + 3*o - 2. Let g(c) = -2*f(c) + 6*w(c). Factor g(i).
4*(i - 1)**2*(i + 1)**2
Let w be 3/(-6) - (-279)/540. Let r(k) be the third derivative of w*k**5 - 3*k**2 + 0 - 1/24*k**3 + 0*k - 1/32*k**4. Factor r(j).
(j - 1)*(4*j + 1)/4
Let y(h) be the first derivative of -h**4/32 + 17*h**3/24 - 63*h**2/16 - 81*h/8 - 63. Factor y(z).
-(z - 9)**2*(z + 1)/8
Let y(d) be the second derivative of d**5/30 - 13*d**4/90 + 4*d**3/45 + 4*d**2/15 + 8*d. Factor y(t).
2*(t - 2)*(t - 1)*(5*t + 2)/15
Let z(u) be the third derivative of -1/21*u**4 + 4/21*u**3 + 9*u**2 + 0 + 0*u + 1/210*u**5. Factor z(x).
2*(x - 2)**2/7
Let d = 5/12 + -11/84. What is p in 4/7 - d*p**2 - 2/7*p = 0?
-2, 1
Let h = 2 - 2. Suppose -1 + 3 = 2*g + 2*w, h = 2*g + 5*w + 4. Factor -2*n - 3*n**g + n**2 + 2*n**3 + 5*n**3 - 1 - 2*n**3.
(n - 1)*(n + 1)*(2*