derivative of -z**4/24 + z**2. Let d(m) = -3*m**5 - 6*m**4 + 6*m**2. Let u(k) = d(k) - 3*s(k). Suppose u(r) = 0. What is r?
-1, 0, 1
Let s(k) = k**2 - 5*k + 2. Let r be s(5). Let q(a) = 4*a - 1. Let p be q(1). What is i in 14*i**4 + 16*i**p + 4*i**r + 0*i**2 + 2*i**3 = 0?
-1, -2/7, 0
Factor 0 - 5/4*x**2 + 25/2*x.
-5*x*(x - 10)/4
Let j be (-4)/10 - 278/30. Let n = j - -10. Find b such that 0 - 1/3*b + n*b**3 + 0*b**2 = 0.
-1, 0, 1
Suppose 3*g - 70 = -61. Let c be (-8)/5*(-3)/12. Find q such that c + 4/5*q - 14/5*q**2 + 8/5*q**g = 0.
-1/4, 1
Let f be (-2)/8 + (-105)/12. Let k be 2/f + (-60)/(-27). Factor -k*j**4 + 0*j**2 - 3*j**2 + 3*j - 3*j**3 + 5*j**4.
3*j*(j - 1)**2*(j + 1)
Let k = -453 - -455. Factor -3*j + j**4 - 11/3*j**3 + 2/3 + 5*j**k.
(j - 1)**3*(3*j - 2)/3
Let g(m) be the first derivative of 0*m**2 + 0*m - 3/5*m**5 + 0*m**3 + 0*m**4 - 4. Suppose g(l) = 0. Calculate l.
0
Let m(n) = -4*n**5 + 6*n**4 - 33*n**3 + 46*n**2 - 36*n + 12. Let f(d) = d**5 + d**4 + d**3 + d - 1. Let t(j) = -12*f(j) - 4*m(j). Factor t(p).
4*(p - 3)**2*(p - 1)**3
Suppose -h = 4*h + 4*n - 24, -2 = -2*n. Let -2/9*d**2 + 2/9*d**5 - 2/9*d**3 + 0*d + 0 + 2/9*d**h = 0. What is d?
-1, 0, 1
Let f = 12 + -7. Suppose -2*i + f*p = 3*i, -5*i - 4*p = -27. Factor 0*b**2 + 3*b**3 - 7*b**i - 2*b**4 - 2*b**2.
-2*b**2*(b + 1)**2
Let t(g) be the third derivative of -g**7/945 - g**6/540 + g**5/90 + g**4/108 - 2*g**3/27 - 8*g**2. Find b, given that t(b) = 0.
-2, -1, 1
Let d(s) = 2*s**4 - 4*s**3 + 2*s**2. Let v(q) = 9*q**4 - 20*q**3 + 11*q**2. Let h(n) = -11*d(n) + 2*v(n). Solve h(j) = 0 for j.
0, 1
Let g(n) = n**2. Let d(y) = 5*y**2 + 2*y. Let w(i) = d(i) - 6*g(i). Let o(t) = t**2 - t. Let a(z) = 3*o(z) + 2*w(z). Factor a(c).
c*(c + 1)
Let u(a) be the second derivative of 2*a**7/147 - 2*a**6/35 + a**5/35 + a**4/7 - 4*a**3/21 + 10*a. Solve u(x) = 0 for x.
-1, 0, 1, 2
Let z(x) be the second derivative of 1/15*x**3 - 6*x + 0*x**2 + 1/30*x**4 + 0. Determine f so that z(f) = 0.
-1, 0
Let q be 3 + -3 + (-6)/(-3). Let w(u) be the first derivative of 2/3*u**3 - u**q - 2*u - 2 + 1/2*u**4. Solve w(f) = 0 for f.
-1, 1
Factor 0 - 3/4*r**2 + 0*r - 9/4*r**4 - 3*r**3.
-3*r**2*(r + 1)*(3*r + 1)/4
Let k(n) be the second derivative of 5*n**8/112 - 4*n**7/35 + n**6/40 + n**5/10 + 7*n**2/2 + 7*n. Let u(r) be the first derivative of k(r). Factor u(b).
3*b**2*(b - 1)**2*(5*b + 2)
Let k be (-12)/(-2*(-3)/(-21)). Let s = k + -209/5. Factor 0*q + s*q**2 + 0 + 1/5*q**4 - 2/5*q**3.
q**2*(q - 1)**2/5
Let c(o) be the first derivative of -6*o**5/5 - 4*o**4 + 2*o**3 + 19. Factor c(r).
-2*r**2*(r + 3)*(3*r - 1)
Let c(l) be the second derivative of l**6/15 + l**5/10 - l**4/6 - l**3/3 - 2*l. Factor c(h).
2*h*(h - 1)*(h + 1)**2
Factor 11*s**3 - 5*s**3 - 9*s**3 - 3*s**2 + 2*s**4 + s**4 + 3*s.
3*s*(s - 1)**2*(s + 1)
Let z(l) be the second derivative of l**4/36 - 8*l**2/3 - 3*l + 7. Factor z(g).
(g - 4)*(g + 4)/3
Factor -8/15*d - 2/15*d**2 - 8/15.
-2*(d + 2)**2/15
Let l = -62/35 - -1291/630. Let z(h) be the second derivative of 7/45*h**6 - 2/63*h**7 + 0*h**2 - 3/10*h**5 - 1/9*h**3 + h + 0 + l*h**4. Factor z(k).
-2*k*(k - 1)**3*(2*k - 1)/3
Let o(c) be the first derivative of c**6/2 - 9*c**5/5 + 9*c**4/4 - c**3 + 29. Factor o(n).
3*n**2*(n - 1)**3
Let u = 1153/2 - 576. Factor -1/2 + g**2 - u*g.
(g - 1)*(2*g + 1)/2
Let g(h) be the second derivative of 5*h**7/42 - h**6/6 - h**5 + 5*h**4/3 + 2*h. What is p in g(p) = 0?
-2, 0, 1, 2
Let u(j) be the second derivative of -3*j + 8/21*j**4 + 9/70*j**5 - 2/7*j**2 + 5/21*j**3 + 0. Factor u(g).
2*(g + 1)**2*(9*g - 2)/7
Let l(d) = -5*d + 145. Let p be l(29). Determine b, given that b + p + b**2 + 1/4*b**3 = 0.
-2, 0
Let i(w) be the third derivative of 0*w**3 + 0 + 0*w + 2*w**2 + 1/84*w**4 - 1/210*w**5. Suppose i(t) = 0. Calculate t.
0, 1
Let r = -18 - -22. Factor b**5 + 4*b**r - b**2 - 5*b**4 + 2*b**4 - b**3.
b**2*(b - 1)*(b + 1)**2
Let g be -8 - (-6)/((-108)/(-150)). Solve 1/3*v + 2/3 - g*v**2 = 0.
-1, 2
Let y = -5 - -11. Let a(k) = -9*k**2 + 12*k - 12. Let l(s) = -8*s**2 + 12*s - 12. Let x(n) = y*l(n) - 5*a(n). Factor x(p).
-3*(p - 2)**2
Let g(n) be the third derivative of -n**6/80 + n**5/8 - 7*n**4/16 + 3*n**3/4 + 7*n**2. Factor g(c).
-3*(c - 3)*(c - 1)**2/2
Let p(r) be the third derivative of r**7/280 - r**6/240 + 5*r**4/24 - 5*r**2. Let b(k) be the second derivative of p(k). Factor b(g).
3*g*(3*g - 1)
Suppose -v + 5 - 1 = 0. Find k such that k**4 - k**3 + 0*k + k + 0*k**v - k**2 + 0*k = 0.
-1, 0, 1
Let h(f) = -4*f**4 + 20*f**3 - 2*f**2 - 14. Let b(a) = a**3 - 1. Let s(t) = 28*b(t) - 2*h(t). Let s(j) = 0. What is j?
0, 1/2, 1
Let o = -1 - -4. Determine v so that 14*v**2 - 4 - 8*v**o + 2*v**3 - 10*v**4 + 6*v + 0*v**4 = 0.
-1, 2/5, 1
Let t = 57/10 - 11/2. Let -t*r**2 + 2/5*r + 0 = 0. What is r?
0, 2
Let u = 4 + 0. Let c(v) be the second derivative of v + 0*v**2 + 0 + 1/6*v**u - 1/3*v**3. Factor c(y).
2*y*(y - 1)
Let c(z) be the second derivative of 0 + 0*z**2 + 0*z**3 + 1/60*z**5 + 0*z**4 - 1/90*z**6 + 4*z. Factor c(u).
-u**3*(u - 1)/3
Find r, given that -2/7*r**2 - 2/7 - 10/7*r - 16/7*r**5 + 4/7*r**4 + 26/7*r**3 = 0.
-1, -1/2, -1/4, 1
Let r(a) be the first derivative of a**5/60 - a**4/9 + 2*a**3/9 - 2*a + 1. Let t(n) be the first derivative of r(n). Let t(o) = 0. What is o?
0, 2
Let t(y) be the third derivative of 0*y - 1/204*y**6 + 1/204*y**4 + 1/714*y**8 + 0 - y**2 + 0*y**3 + 1/595*y**7 - 1/170*y**5. Determine g so that t(g) = 0.
-1, 0, 1/4, 1
Let c(t) = t**3 - 2*t**2 + 7*t. Let a(y) = -y. Suppose 10 = -4*j + 6. Let v(x) = j*c(x) - 6*a(x). Let v(d) = 0. Calculate d.
0, 1
What is h in 4/9*h**4 + 32/9*h + 20/3*h**2 - 64/9 - 32/9*h**3 = 0?
-1, 1, 4
Factor -4*n + 11*n**4 + 2*n - 10*n**4 - 3*n**2.
n*(n - 2)*(n + 1)**2
Determine r, given that -16*r**3 - r**4 + 14*r - 219 - 270*r - 37 + 24*r**2 - 120*r**2 = 0.
-4
Let w be (-49)/3 - (-1)/3. Let y = w - -16. Factor y - 3/2*i**2 - 3*i.
-3*i*(i + 2)/2
Let f(i) = i**3 - 1. Let y(k) = -25*k**3 - 50*k**2 - 85*k - 20. Let o(d) = -20*f(d) - y(d). Let o(j) = 0. Calculate j.
-8, -1
Let p be ((-24)/(-5 - -1))/2. Factor -1 + 7 - p - l**2 + 4*l**2 + 6*l.
3*(l + 1)**2
Let k(z) = z**2 - 19*z + 4. Let u(c) = -10*c**2 + 170*c - 35. Let f(w) = -35*k(w) - 4*u(w). Factor f(l).
5*l*(l - 3)
Suppose 0 = 6*p - 8*p + 4. Determine w, given that -2*w**2 + 4 + 0*w**p - 2 + 0*w**2 = 0.
-1, 1
Let n = -29 - -32. Factor 0*o**n - 1/2*o - o**2 + 0 + o**4 + 1/2*o**5.
o*(o - 1)*(o + 1)**3/2
Suppose -m**4 + 12*m**3 - 36*m - 3*m**2 + 6*m**2 - 2*m**4 - 27 + 3*m**2 = 0. What is m?
-1, 3
Let t(p) be the second derivative of 9*p**5/20 + 5*p**4/2 + 2*p**3 - 12*p**2 - 36*p - 2. Factor t(s).
3*(s + 2)**2*(3*s - 2)
Let c(u) be the second derivative of -u**6/10 + 9*u**5/20 - 2*u**3 - 35*u. Find v, given that c(v) = 0.
-1, 0, 2
Let c(g) be the first derivative of -2*g**3/45 - 4*g**2/15 - 8*g/15 + 2. Factor c(q).
-2*(q + 2)**2/15
Let i(x) be the first derivative of -10*x**3/21 + 2*x**2/7 + 9. Factor i(z).
-2*z*(5*z - 2)/7
Suppose 1 = -2*c + 5. Let w be ((-7)/(-28))/(2/(-4) + 1). Factor 0*n**c + 3/2*n + w - 2*n**3.
-(n - 1)*(2*n + 1)**2/2
Let p(c) = -3*c**2 - 4*c - 11. Let q(r) = 5*r**2 + 6*r + 17. Let w(z) = 8*p(z) + 5*q(z). Factor w(a).
(a - 3)*(a + 1)
Determine j so that 2/13*j + 0 + 2/13*j**2 - 10/13*j**4 - 6/13*j**3 - 4/13*j**5 = 0.
-1, 0, 1/2
Let n be 28/(-7) - 32/(-7). What is i in -n - 8/7*i**2 - 2/7*i**3 - 10/7*i = 0?
-2, -1
Find v, given that 2/15*v + 0 + 2/15*v**2 = 0.
-1, 0
Let z(y) be the first derivative of -y**3/4 - y**2/8 + y/2 + 10. Suppose z(b) = 0. What is b?
-1, 2/3
Let v(a) = -4*a**2 - 6*a - 2. Let k(s) = -4*s**2 - 7*s - 3. Let c(g) = -2*k(g) + 3*v(g). Find p such that c(p) = 0.
-1, 0
Let z(s) be the first derivative of -s**3/3 - s**2 - s - 15. Determine h so that z(h) = 0.
-1
Let t be (-1)/4 + 43/(-4). Let k = 13 + t. Suppose 0 + 1/3*c**4 + 2/3*c**k + c**3 + 0*c = 0. What is c?
-2, -1, 0
Let u(x) be the second derivative of 0*x**2 + 0 - 1/40*x**6 + 8*x - 9/80*x**5 - 1/8*x**3 - 3/16*x**4. Determine i so that u(i) = 0.
-1, 0
Let t = -19 - -23. Suppose 2*r = 2*w + t, -1 = -3*r + 11. Solve -1/3*z**w - 2/3*z - 1/3 = 0.
-1
Let h be (2/(-4))/(30/(-940)). Let b = -15 + h. Factor 2/3 - 2*v + 2*v**2 - b*v**3.
-2*(v - 1)**3/3
Let f(r) = 14*r - 52. Let j be f(4). Let w(a) be