*(x + 1)/3
Let s(d) be the third derivative of -d**5/630 + d**4/126 - d**3/63 + d**2. Find g, given that s(g) = 0.
1
Factor 1801*r**3 + 16*r**2 - 1837*r**3 + 24*r**4 + 2*r**5 - 6*r**5.
-4*r**2*(r - 4)*(r - 1)**2
Let h = 2076 + -435959/210. Let o(u) be the third derivative of 0*u**6 + 0 + 0*u**3 + 0*u - 1/60*u**5 + 0*u**4 + h*u**7 + 2*u**2. Let o(x) = 0. Calculate x.
-1, 0, 1
Let q(r) = 7*r**2 - 6*r + 5. Let o(c) = c**2 - c + 1. Let g(a) = -6*o(a) + q(a). Determine m so that g(m) = 0.
-1, 1
Let x(l) be the first derivative of -2*l**3/9 - 4*l**2/3 - 8*l/3 + 10. Solve x(v) = 0.
-2
Let n be ((25/15)/(-5))/(-5). Let y(f) be the first derivative of -2 + 1/10*f**2 - n*f**3 + 1/25*f**5 + 0*f - 1/20*f**4. Find l, given that y(l) = 0.
-1, 0, 1
Suppose 2*v - 5*q - 4 = 0, q = 2*v - 3 - 1. Suppose 8/5*m**v + 4/5 + 2*m + 2/5*m**3 = 0. Calculate m.
-2, -1
Let p = 3/113 - -1549/1243. Factor 0 - p*l**2 - 4/11*l - 10/11*l**3.
-2*l*(l + 1)*(5*l + 2)/11
Let l(o) be the third derivative of 4*o**2 + 0*o + 1/1440*o**6 - 2/3*o**3 + 0 + 1/160*o**5 + 1/48*o**4. Let m(x) be the first derivative of l(x). Factor m(g).
(g + 1)*(g + 2)/4
Let s(g) = 5*g**2 + 8*g - 1. Let o(c) be the first derivative of -3*c**3 - 15*c**2/2 + 2*c + 2. Let k(w) = -6*o(w) - 11*s(w). Suppose k(n) = 0. What is n?
1
Let m = -12 + 15. Factor -9*n**3 + 6*n**m + 5*n**2 - 2*n**2.
-3*n**2*(n - 1)
Suppose -2*u**2 - 4*u - 1 + 5 + 0*u + 2 = 0. What is u?
-3, 1
Let c(f) be the third derivative of -f**5/30 - f**4/6 + f**3 - 26*f**2. Factor c(j).
-2*(j - 1)*(j + 3)
Let h(r) be the first derivative of r**4/14 + 8*r**3/21 + 5*r**2/7 + 4*r/7 + 68. Let h(k) = 0. Calculate k.
-2, -1
Let a(v) be the third derivative of v**2 + 0*v + 1/112*v**8 + 2*v**3 + 5/4*v**5 + 0 + 1/10*v**7 + 19/40*v**6 + 2*v**4. Let a(w) = 0. Calculate w.
-2, -1
Suppose 5*p = 4*g + 4 - 17, -10 = 2*p. Let z = g + 5. Factor -o + 3*o**2 + 3*o - 1 - 4*o**z.
-(o - 1)**2
Let i(h) be the first derivative of 0*h**2 - 1/30*h**4 + 0*h**3 - h - 2 + 1/50*h**5. Let g(z) be the first derivative of i(z). Solve g(j) = 0.
0, 1
Let y(c) be the third derivative of -c**5/12 - c**4/2 - 2*c**3/3 + 21*c**2. Determine i, given that y(i) = 0.
-2, -2/5
Let t = 2521/20 + -126. Let d(f) be the third derivative of 1/15*f**5 - 1/24*f**4 - t*f**6 + 0*f - 1/336*f**8 - 2*f**2 + 0*f**3 + 2/105*f**7 + 0. Factor d(m).
-m*(m - 1)**4
Let p(v) = v**2 - 4*v. Let y be p(4). Factor y*m**2 + 7 - 3*m**3 - 3 + 6*m - m**3 - 6*m**2.
-2*(m - 1)*(m + 2)*(2*m + 1)
Let f(g) = -8 - 4 + 0 - g. Let u be f(-14). Solve -4/3*l - 10/3*l**u + 14/3*l**3 + 0 = 0 for l.
-2/7, 0, 1
Factor d + 4/3 - 1/3*d**2.
-(d - 4)*(d + 1)/3
Suppose 6*a - 9*a - 2835 = 0. Let k be (-15)/((a/10)/9). Find s such that 0 + 4/7*s**5 + 2/7*s**2 - k*s**4 + 6/7*s**3 - 2/7*s = 0.
-1/2, 0, 1
Factor 25*b**2 - 5*b**3 - 5*b**2 + 0*b**2.
-5*b**2*(b - 4)
Let v(o) be the first derivative of 1/25*o**5 + 1/20*o**4 - 1/10*o**2 + 2/5*o - 1/5*o**3 + 6. Factor v(i).
(i - 1)**2*(i + 1)*(i + 2)/5
Let p(i) be the first derivative of -2*i**5/5 - 3*i**4/2 - 4*i**3/3 + 15. Let p(j) = 0. What is j?
-2, -1, 0
Suppose 0 = 3*q - 3 - 3. Determine r, given that 2*r**3 - 2*r**2 - 1 + 3 - 2 - 2*r + q = 0.
-1, 1
Let s be 31/10 - (11 - 8). Let o(q) be the third derivative of 0 + 0*q + q**2 + 1/12*q**4 + 1/168*q**8 + 2/15*q**5 + 4/105*q**7 + s*q**6 + 0*q**3. Factor o(c).
2*c*(c + 1)**4
Let k be -2*(-3)/2*1. Suppose f - k = -0*f. Solve -f*m**5 + 2*m**2 + 7*m**3 - 2*m**3 - 3*m**4 - m**4 + 0*m**2 = 0 for m.
-2, -1/3, 0, 1
Let z(r) = -2*r - 16. Let t be z(-12). Let v be (2/t)/((-6)/(-4)). Factor 0 + 2/3*o**4 - v*o**3 + 0*o**2 + 0*o - 1/2*o**5.
-o**3*(o - 1)*(3*o - 1)/6
Let y(p) = p**2 + 9*p + 7. Let s be y(-9). Let t(l) = -l**3 + 2*l**2 + l + 2. Let k(d) = -4*d**3 + 6*d**2 + 3*d + 7. Let b(z) = s*t(z) - 2*k(z). Factor b(r).
r*(r + 1)**2
Let f(c) be the second derivative of 10*c**5/7 - 10*c**4/7 + 3*c**3/7 + 20*c + 2. Factor f(n).
2*n*(10*n - 3)**2/7
Let h(i) = i - 2. Let n be h(2). Factor 1/3*r**3 + n + 0*r + 0*r**4 - 1/3*r**5 + 0*r**2.
-r**3*(r - 1)*(r + 1)/3
Let y(n) be the third derivative of 1/6*n**3 - 1/24*n**4 + 1/240*n**5 + 3*n**2 + 0 + 0*n. Factor y(x).
(x - 2)**2/4
Let l(q) be the first derivative of -2*q**2 + q**3 + 1 - 1/5*q**5 - 4*q + 1/2*q**4. What is v in l(v) = 0?
-1, 2
Let r(k) be the third derivative of k**6/600 + k**5/300 - 22*k**2. Factor r(h).
h**2*(h + 1)/5
Let l(o) be the first derivative of 2/3*o**3 - o**2 - 2*o + 1/2*o**4 - 3. Let l(n) = 0. Calculate n.
-1, 1
Let f(j) = 2*j**4 - 2*j**3 - 3*j + 3. Let q = -11 - -26. Let k(d) = -12*d**3 - 3*d**4 + 5*d - 5 + q*d**3 + 0*d**4. Let y(m) = -5*f(m) - 3*k(m). Factor y(w).
-w**3*(w - 1)
Let y(f) be the third derivative of 1/1980*f**6 + 0 + 1/132*f**4 - f**2 + 0*f + 1/6*f**3 - 1/330*f**5. Let g(o) be the first derivative of y(o). Factor g(k).
2*(k - 1)**2/11
Let d(y) be the third derivative of -1/21*y**5 - 1/147*y**7 + 0 - 5/84*y**4 - 11*y**2 - 1/42*y**6 + 0*y - 1/1176*y**8 - 1/21*y**3. Factor d(t).
-2*(t + 1)**5/7
Let s be 72/729*6/8. Let a(n) be the second derivative of s*n**3 - 1/30*n**5 + 1/18*n**4 + 0*n**2 - 2*n - 7/135*n**6 + 0 - 1/63*n**7. Factor a(t).
-2*t*(t + 1)**3*(3*t - 2)/9
Let u = 1/154 - -71/924. Let y(r) be the second derivative of u*r**4 + 0 + 1/2*r**2 - 1/3*r**3 + 2*r. Factor y(m).
(m - 1)**2
Let c(d) be the first derivative of 4*d**6/225 + 2*d**5/75 + d**4/60 - 2*d**3 - 1. Let k(v) be the third derivative of c(v). Determine x, given that k(x) = 0.
-1/4
Factor 8*b**4 + 2*b**4 + 4*b**4 - 6*b**3 - 3*b**5 - 5*b**4.
-3*b**3*(b - 2)*(b - 1)
Let q(a) = -a**3 - 9*a**2 - 3*a + 11. Let d(s) = s**3 + 8*s**2 + 2*s - 10. Let m(o) = 5*d(o) + 4*q(o). Let y be m(-4). Solve -1/4*p**y + 0 + 1/4*p = 0 for p.
0, 1
Factor 0*t - 1/5*t**2 + 0 - 1/5*t**3.
-t**2*(t + 1)/5
Let c be ((-60)/(-8))/(3/4). Suppose -c + 0 = -5*z. Factor 2*u**2 - 2*u + 1 + 0*u**z - u**2.
(u - 1)**2
Let u(w) = -3*w - 1. Let i be u(-1). Let d be i/3*12/20. Factor d*n**4 + 2/5*n + 0 - 2/5*n**3 - 2/5*n**2.
2*n*(n - 1)**2*(n + 1)/5
Let b be (-2)/(-7) - (-8)/(-28). Find q such that b*q**2 - 3*q - 5*q**2 - 6*q**3 - 4*q**2 = 0.
-1, -1/2, 0
Let n = 4952/66123 + -2/2449. Let j(m) be the first derivative of 4/9*m - n*m**3 - 1/9*m**2 - 1. Factor j(p).
-2*(p - 1)*(p + 2)/9
Let f(m) = -m**2 + 18*m + 2. Let b be f(18). Suppose -2/7*h + 2/7*h**b - 4/7 = 0. Calculate h.
-1, 2
Let y = 68 - 68. Let b(c) be the first derivative of 2/15*c**3 + 0*c**2 - 1/5*c**4 + y*c + 2/25*c**5 + 1. Factor b(q).
2*q**2*(q - 1)**2/5
Let d(h) = h**4 + 7*h**3 + 11*h**2 + 10*h + 4. Let v(r) = r**3 - r**2 + 1. Let b(w) = 5*d(w) - 5*v(w). Solve b(o) = 0 for o.
-3, -1
Let n(u) = 6*u**2 + 17*u + 3. Let w(g) = -12*g**2 - 34*g - 7. Let i(o) = 13*n(o) + 6*w(o). Factor i(x).
(x + 3)*(6*x - 1)
Suppose -2/7*i - 2/7*i**3 - 4/7*i**2 + 0 = 0. What is i?
-1, 0
Let w(l) = l**4 + l**2 + 2*l. Let t(v) = -v - 5. Let f be t(0). Let o(a) = -a**4 - 2*a**2 - 3*a. Let u(y) = f*w(y) - 4*o(y). Factor u(b).
-b*(b - 2)*(b + 1)**2
Let z(h) be the second derivative of -2*h**6/15 - 7*h**5/5 - 5*h**4 - 6*h**3 - 8*h. Let z(r) = 0. Calculate r.
-3, -1, 0
Let h(o) be the first derivative of -3/2*o**2 + 1/4*o**4 - 8 + 0*o**3 - 2*o. Factor h(i).
(i - 2)*(i + 1)**2
Let x(j) be the second derivative of 1/3*j**4 + j - 4/15*j**6 - 2/5*j**5 - 1/21*j**7 + 0 + 5/3*j**3 + 2*j**2. Factor x(i).
-2*(i - 1)*(i + 1)**3*(i + 2)
Let k = 259 + -5179/20. Let p(l) be the first derivative of 0*l**2 - 1/4*l + 1/6*l**3 + 2 - k*l**5 + 0*l**4. Let p(d) = 0. Calculate d.
-1, 1
Let g(j) = -5*j**5 - 24*j**4 - 64*j**3 - 56*j**2 + 11. Let b(n) = n**5 + 5*n**4 + 13*n**3 + 11*n**2 - 2. Let t(m) = 33*b(m) + 6*g(m). Let t(o) = 0. What is o?
-3, -1, 0
Let l(a) be the first derivative of -1/4*a**4 + 1/2*a**3 - 1/10*a**5 - 3 - 2*a + a**2. Suppose l(y) = 0. What is y?
-2, 1
Suppose 0 = 6*f - 0*f + 48. Let j be f/36*(-4 + 1). Factor -j + 1/3*d**3 + d**2 - 1/3*d - 1/3*d**4.
-(d - 2)*(d - 1)*(d + 1)**2/3
Let t = -1/12 - -5/12. Suppose 0 = 3*w - 2*l + 2, -w - 2*l = 2*l - 4. Factor w + t*d - 1/3*d**2.
-d*(d - 1)/3
Let u be -2 + -2 + 6 - 21. Let h be u/95 + (-11)/(-5). What is q in -8/9*q**h + 0 + 8/9*q + 2/9*q**3 = 0?
0, 2
Factor 4/3*a**2 - 16/9 + 4/9*a**3 + 0*a.
4*(a - 1)*(a + 2)**2/9
Let t(l) be the third derivative of l**7/1680 + l**6/240