he first derivative of v**6/60 + v**5/40 - 3*v + 1. Let l(t) be the first derivative of h(t). Suppose l(x) = 0. What is x?
-1, 0
Let r(k) = k**3 - 4*k**2 - 3*k + 8. Let g(x) = 5*x**3 - 21*x**2 - 14*x + 41. Let z(p) = -6*g(p) + 33*r(p). Find t, given that z(t) = 0.
-2, 1, 3
Suppose 9*j = 4*j + 25. Let d(k) be the second derivative of 0 + 0*k**2 - 1/12*k**4 - 2*k + 1/84*k**7 - 1/12*k**3 + 1/30*k**6 + 0*k**j. Let d(y) = 0. What is y?
-1, 0, 1
Let v(q) = -2*q - 13. Let z be v(-9). Suppose 0 - 4 = d, z*a - d = 29. Factor -t**4 + 3*t**3 - 4*t**3 + t**a + 5*t**2 - 4*t**2.
t**2*(t - 1)**2*(t + 1)
Suppose 7*v = 2*v - 70. Let q = -12 - v. Factor -1/4*d + 0 - 1/4*d**4 + 1/4*d**3 + 1/4*d**q.
-d*(d - 1)**2*(d + 1)/4
Suppose -2*r = -5*q, 4*q - 6*q = 2*r. Let s(c) be the first derivative of -2/25*c**5 + 0*c**4 + q*c**3 + 0*c**2 + 0*c + 2. Suppose s(b) = 0. Calculate b.
0
Let d = 4/83 + 229/415. Determine u, given that -3/5*u**3 - 1/5*u - 1/5*u**4 - d*u**2 + 0 = 0.
-1, 0
Let x(c) = -2*c - 4. Let y be x(-3). Suppose 7*v - 3*v = -2*m - 4, -2*m - v = -y. Factor 2*k**3 - 2*k**m - k**2 + 5*k**2.
2*k**2*(k + 1)
Let r(k) be the second derivative of -k**7/945 + k**6/270 - k**5/270 - 2*k**2 - 4*k. Let n(x) be the first derivative of r(x). Factor n(b).
-2*b**2*(b - 1)**2/9
Let 96*q - 2 - 95*q + 2 - q**3 = 0. Calculate q.
-1, 0, 1
Suppose 4*y = 16 - 0. Let 4*g**3 - 4*g - g**4 + g**y + 3 - 1 - 2*g**4 = 0. Calculate g.
-1, 1
Suppose -4*i + 14 = -6. Suppose -7*n + 20 = -3*n - j, i*j = -5*n. Let 2 - d + d + 2*d**2 - n*d**2 = 0. What is d?
-1, 1
Let h(p) be the first derivative of p**4 - 8*p**3 + 24*p**2 - 32*p + 0*p**4 - 155 + 166. Determine b, given that h(b) = 0.
2
Let z = 48 + -90. Let q be z/(-9) - (3 - 1). Suppose -q*h - 8/3*h**2 - 2/3 = 0. What is h?
-1/2
Factor -2/5*m**3 - 8/5*m**2 + 0 - 8/5*m.
-2*m*(m + 2)**2/5
Let v(s) = s + 1. Let w(d) = d - 7*d**2 + 2 + 8*d**2 - 7*d + d**3. Let a(j) = -v(j) - w(j). Solve a(b) = 0 for b.
-3, 1
Let d(k) be the first derivative of 3/4*k**2 + k + 1/6*k**3 - 2. Factor d(v).
(v + 1)*(v + 2)/2
Let r(x) be the second derivative of x**8/1120 + x**7/420 - x**5/135 - 5*x**4/12 - 4*x. Let f(s) be the third derivative of r(s). Factor f(t).
2*(3*t - 1)*(3*t + 2)**2/9
Let y(g) be the second derivative of g**6/90 + g**5/30 - 7*g**4/36 + 2*g**3/9 + 5*g. What is b in y(b) = 0?
-4, 0, 1
Let k be (-8)/(-15) + 4/6. Factor 0 - k*c**2 + 2/5*c + 6/5*c**3 - 2/5*c**4.
-2*c*(c - 1)**3/5
Let w(a) = a**3 + 5*a**2 - 5*a. Let b be w(-6). Let v = 8 + b. What is k in -1/2*k + 0 - 5/4*k**v = 0?
-2/5, 0
Let n = -7 + 11. Suppose -g - n*g = 15. Let q(r) = -10*r**4 + 10*r**2 - 14. Let d(y) = -2*y**4 + 2*y**2 - 3. Let h(f) = g*q(f) + 14*d(f). Factor h(s).
2*s**2*(s - 1)*(s + 1)
Suppose q - 19 = -5*j, -2*q - 1 = -9. Suppose 16 = 3*h - d, -2*h + 3*d + 8 = -3*h. Factor j - 1 + s - h*s**2 + 3*s**2.
-(s - 2)*(s + 1)
Let v(n) be the third derivative of n**5/210 + n**2. Factor v(r).
2*r**2/7
Let l be 2 + (8 - 2) + 0. Let a be 2/l + 54/8. Determine y, given that -a*y**3 - 6*y + 14*y**4 + 4*y + 8*y**5 + 2 + 3*y**3 - 2*y - 16*y**2 = 0.
-1, 1/4, 1
Let o(b) be the first derivative of 2*b**3/5 - 7*b**2/5 + 4*b/5 + 3. Factor o(h).
2*(h - 2)*(3*h - 1)/5
Let h be 4/(-12)*(-16 + 1). Let m be 1/h + (-576)/(-20). Determine x so that m*x**2 - 1 - 3 - 14*x**4 - 11*x**4 = 0.
-1, -2/5, 2/5, 1
Suppose -a + 3 = 1. Suppose -4 = -x - a. Factor 0 - x*z + 0*z + 2 + 3*z - z**2.
-(z - 2)*(z + 1)
Solve -8*a**4 + 8*a**2 - 804*a**3 + 804*a**3 - 4*a**5 + 4*a = 0 for a.
-1, 0, 1
Let h(u) be the third derivative of u**10/30240 - u**9/15120 - u**8/6720 + u**7/2520 + u**4/24 - 2*u**2. Let y(t) be the second derivative of h(t). Factor y(a).
a**2*(a - 1)**2*(a + 1)
Let m(h) be the second derivative of h**7/21 + h**6/45 - h**5/5 - h**4/9 + h**3/3 + h**2/3 + 3*h. Solve m(w) = 0 for w.
-1, -1/3, 1
Solve g**3 + 3*g**2 - 10 + 34 - 10 + 3*g - 13 = 0 for g.
-1
Suppose o = 8 - 2. Factor -16*d**2 - 8*d - o*d**3 - d + d.
-2*d*(d + 2)*(3*d + 2)
Let w = 21 - 21. Factor 2/11*y + w + 2/11*y**3 + 4/11*y**2.
2*y*(y + 1)**2/11
Let f(j) = -j**2 + j - 2. Let s(u) = -7*u**2 + 9*u - 2. Let n(t) = -30*f(t) + 5*s(t). Factor n(v).
-5*(v - 5)*(v + 2)
Let i(p) be the third derivative of p**5/20 + 13*p**4/8 - 3*p**2 - 13. Let i(s) = 0. Calculate s.
-13, 0
Let k(h) be the first derivative of 9*h**5/20 - 21*h**4/8 + 4*h**3 - 3*h**2/4 - 9*h/4 + 20. Let k(f) = 0. Calculate f.
-1/3, 1, 3
Let f(g) = -g**5 + 8*g**4 + 2*g**3 - 2. Let x(n) = 9*n**4 + 3*n**3 - 3. Suppose l = -4 + 1. Let d(o) = l*f(o) + 2*x(o). Let d(u) = 0. What is u?
0, 2
Let v(u) be the first derivative of u**7/280 + u**6/240 - u**5/60 - u**4/48 + u**3/24 - 7*u**2/2 - 5. Let l(p) be the second derivative of v(p). Factor l(c).
(c - 1)*(c + 1)**2*(3*c - 1)/4
Determine v, given that -1/5*v**4 + 3/5*v**3 + 9/5*v**2 + 0 + v = 0.
-1, 0, 5
Let q be 10/8 + 3/4. Suppose 0*u + 5*u = 0. Factor -4*v - q*v**2 + v + u*v + v.
-2*v*(v + 1)
Let a(t) = -t**2 + 19*t - 12. Let m be a(18). Let u(x) be the first derivative of -x + 2 + 1/6*x**m - 3/2*x**2 + 3/5*x**5 - 2/3*x**3 + 1/2*x**4. Factor u(f).
(f - 1)*(f + 1)**4
Let h(x) be the second derivative of x**6/120 - x**5/40 - 7*x**4/48 - x**3/6 + 2*x - 2. Let h(f) = 0. Calculate f.
-1, 0, 4
Let h(s) = -s + 1. Let p be h(3). Let g be -2 + (-1 - 7)/p. Find m, given that 3 + g*m**2 - 3 = 0.
0
Let c(i) be the second derivative of i**7/70 + i**6/20 + i**2/2 - 3*i. Let p(m) be the first derivative of c(m). Let p(j) = 0. What is j?
-2, 0
Let x(w) = -w**2 - 4. Let c be x(4). Let p be 95/c*-1 + -4. Factor -3/4 - 9/4*g**2 - p*g**3 - 9/4*g.
-3*(g + 1)**3/4
Let o(q) be the second derivative of q**4/36 + 2*q**3/9 + q**2/2 + 2*q. Factor o(l).
(l + 1)*(l + 3)/3
Let i = 39 - 36. Find u, given that -2/3*u + 2/3*u**2 - 2/3 + 2/3*u**i = 0.
-1, 1
Suppose 4*c + 5 = 25. Factor 11*y**4 + 4*y**3 + 9*y**4 - c*y**4 - y**4.
2*y**3*(7*y + 2)
Let h(f) be the second derivative of f**9/15120 - f**8/6720 - f**4/6 + f. Let l(s) be the third derivative of h(s). Factor l(b).
b**3*(b - 1)
Let a be 9/60 + (-6)/(-24). Let w(x) be the first derivative of -4/5*x + a*x**5 + 1/5*x**2 - 13/10*x**4 + 6/5*x**3 + 1. Factor w(v).
2*(v - 1)**3*(5*v + 2)/5
Let n = -6 + 11. Let f(x) be the third derivative of -1/525*x**7 - 1/60*x**4 + 1/150*x**n + 1/300*x**6 + x**2 + 0*x + 0 + 0*x**3. Suppose f(y) = 0. Calculate y.
-1, 0, 1
Let p = -113 - -343/3. Suppose -2/3*q**2 + p - 2/3*q = 0. What is q?
-2, 1
Factor 9*m**3 + 13 - 6*m**2 - 9 - 2*m**4 - 5*m**2.
-(m - 2)**2*(m - 1)*(2*m + 1)
Let x be (0 + 1)/(2/(-10)). Let t = x - -7. Factor 2*v**2 + 2*v - 9*v**2 + 0*v**t.
-v*(7*v - 2)
Let t = 146 - 437/3. Factor 2/3*b - t*b**3 + 0 - 1/3*b**2.
-b*(b - 1)*(b + 2)/3
Let j(m) = m**2 + m + 1. Let d(k) = -5*k**3 + 13*k**2 + 3*k + 3. Let h(o) = -d(o) + 3*j(o). Factor h(c).
5*c**2*(c - 2)
Let y(j) = j + 4. Let w be y(-2). Factor 2*h - 10*h - 5*h**w + 9*h**2.
4*h*(h - 2)
Let x be 0/(-2) + 0 + 2. Suppose 4*u + 6 = -4*z + x*u, -2*u = 3*z + 6. Factor -2 + 4*w**3 + 2*w**5 - 4*w**2 + z*w**3 - 6*w + 6*w**4 + 0.
2*(w - 1)*(w + 1)**4
Let d = -1/23 - -672/115. Let v = -27/5 + d. Factor v*b + 0 + 0*b**4 - 4/5*b**3 + 0*b**2 + 2/5*b**5.
2*b*(b - 1)**2*(b + 1)**2/5
Let o(r) = -4*r**4 + r**3 + 2*r**2 + 3*r + 3. Let z(c) = -12*c**4 + 4*c**3 + 5*c**2 + 8*c + 8. Let h(f) = 8*o(f) - 3*z(f). Solve h(l) = 0.
0, 1/2
Let k(x) be the first derivative of -7*x**4/8 + x**3/3 + 7*x**2/4 - x - 7. What is d in k(d) = 0?
-1, 2/7, 1
Factor 1/4*f**2 + 1/8*f**3 + 0 + 1/8*f.
f*(f + 1)**2/8
Determine r so that 0*r + 0 + 2/5*r**4 + 2*r**2 + 12/5*r**3 = 0.
-5, -1, 0
Let o(h) be the first derivative of 5/3*h**3 - 1/4*h**4 - h + 1/2*h**2 - 4 - 8/5*h**5 - 2/3*h**6. Solve o(i) = 0.
-1, 1/2
Let c(d) be the first derivative of -44/3*d**3 + 0*d - 28/5*d**5 - 16*d**4 + 10 - 4*d**2. Suppose c(q) = 0. Calculate q.
-1, -2/7, 0
Factor -1/3*j**3 - 2/3*j - j**2 + 0.
-j*(j + 1)*(j + 2)/3
Let r(w) = 2*w**2 - 9*w - 11. Let m(v) = v**2 - 5*v - 6. Let c(b) = 5*m(b) - 3*r(b). Factor c(n).
-(n - 3)*(n + 1)
Let p(y) = -y + 1. Let j be p(-1). Suppose 10 = j*v, -5*v = -5*d - 4*v + 5. Factor -d*x**4 + 6*x**2 - x**4 - 3*x**2.
-3*x**2*(x - 1)*(x + 1)
Suppose 5*f - 12 + 2 = -b, -4*b = -5*f + 10. Let r = 2896 + -2896. Determine o, given that -3/4*o**f - 3/4*o + r = 0.
-1, 0
Supp