c. Find y such that -t*y**2 + 2*y**3 + 2*y - 3 + 3 = 0.
0, 1
Let c be 2/(-6)*18/(-27). Let t(w) be the first derivative of 1 + c*w**2 + 2/27*w**3 + 2/9*w. Factor t(k).
2*(k + 1)**2/9
Let c(y) be the third derivative of -y**10/120960 + y**9/60480 - y**4/12 + 2*y**2. Let n(o) be the second derivative of c(o). Determine z, given that n(z) = 0.
0, 1
Factor 3/4 + 3/8*z**3 - 15/8*z + 9/8*z**2 - 3/8*z**4.
-3*(z - 1)**3*(z + 2)/8
Let p(w) be the third derivative of -w**5/15 + 11*w**4/6 - 20*w**3/3 - 2*w**2 + 30*w. Suppose p(a) = 0. What is a?
1, 10
Let g(k) be the second derivative of k**7/21 + 11*k**6/45 + k**5/2 + k**4/2 + 2*k**3/9 + k. Determine h, given that g(h) = 0.
-1, -2/3, 0
Suppose 35*y + 8 = 37*y. Let d be y/7*(-42)/(-12). Factor 0 - 2/7*r**d + 4/7*r.
-2*r*(r - 2)/7
Suppose 16/5*n**2 + 2*n**3 + 2/5*n**4 + 8/5*n + 0 = 0. Calculate n.
-2, -1, 0
Let f(l) be the first derivative of -l**6/24 + 9*l**5/20 - 23*l**4/16 + 7*l**3/12 + 3*l**2 - 4*l - 7. Solve f(y) = 0.
-1, 1, 4
Let u(p) be the third derivative of 0 + 0*p + 0*p**3 + 3*p**2 + 1/80*p**5 - 1/16*p**4. Factor u(f).
3*f*(f - 2)/4
Suppose 3*u + 30 = 2*u - 5*c, -39 = 2*u + 3*c. Let h be (-20)/36*6/u. Solve -2/9*o - h*o**2 + 0 = 0.
-1, 0
Factor 8 - 5*g**4 - 10*g - 37*g**3 - 3 + 47*g**3.
-5*(g - 1)**3*(g + 1)
Let y be (9/(-12))/(6/2). Let n = 21/20 + y. Solve -2/5 - 2/5*c**4 + 0*c + n*c**2 + 0*c**3 = 0 for c.
-1, 1
Suppose 4*n + 0 = 28. Factor 8*y**3 - 6*y**5 - 2*y**4 + y**4 - n*y**4.
-2*y**3*(y + 2)*(3*y - 2)
Let f(y) = -y - 3. Let z be f(-6). Let w be z*(-5)/(15/(-2)). Factor 10*p**w + 0 + 2*p - 3/2*p**3 - 35*p**4 + 49/2*p**5.
p*(p - 1)**2*(7*p + 2)**2/2
Let y(h) be the third derivative of -h**8/1680 + h**7/315 - h**6/180 + h**4/6 - 4*h**2. Let b(i) be the second derivative of y(i). Find k, given that b(k) = 0.
0, 1
Let p(n) = n**3 + 5*n**2 - 6*n. Let r be p(-6). Factor 0*a - 1/3*a**3 + 1/3*a**2 + r.
-a**2*(a - 1)/3
Suppose 3/2*x**2 + 0 - 9/2*x = 0. Calculate x.
0, 3
Let a be (2/7)/((-10)/28 - -1). Suppose -2/9*j**3 + 0 + a*j**2 + 0*j - 2/9*j**4 = 0. What is j?
-2, 0, 1
Suppose z = 2*z - 6. Solve 22/3*t**2 - z*t**3 - 4/3*t + 0 = 0 for t.
0, 2/9, 1
Let z(y) be the first derivative of -y**7/1365 + y**6/390 - y**4/78 + y**3/39 + 7*y**2/2 - 7. Let a(j) be the second derivative of z(j). Factor a(v).
-2*(v - 1)**3*(v + 1)/13
Let q be 5/((-15)/(-8)) - (-1)/3. Determine u, given that 0*u**q + 2/7*u**5 - 4/7*u**2 + 0 + 4/7*u**4 - 2/7*u = 0.
-1, 0, 1
Suppose k = -5*l + 1, -l + 5 = -2*l + 5*k. Factor -2/15*y**2 + 2/15*y**3 + 0*y + l.
2*y**2*(y - 1)/15
Let i(w) be the first derivative of -2*w**5/55 + 5*w**4/22 - 16*w**3/33 + 4*w**2/11 + 25. Factor i(a).
-2*a*(a - 2)**2*(a - 1)/11
Let w(a) be the first derivative of -25/21*a**3 - 1/7*a + 1 + 5/7*a**2. Determine c so that w(c) = 0.
1/5
Suppose 5*c + 5*u = -5, -5*c - 2*u - 1 + 8 = 0. Factor -3*f**c + 3/5 + 3*f - 3/5*f**2.
-3*(f - 1)*(f + 1)*(5*f + 1)/5
Let s(h) = 19*h**2 - 19*h - 13. Let b(p) = -9*p**2 + 10*p + 6. Let t(m) = -5*m + 3. Let n be t(1). Let y(w) = n*s(w) - 5*b(w). Factor y(z).
(z - 2)*(7*z + 2)
Let f(s) = 7*s**3 + 10*s**2 + 4*s - 4. Let l(n) = 27*n**3 + 39*n**2 - 15 + 8*n + 10*n - 3*n. Let t(d) = -15*f(d) + 4*l(d). Factor t(v).
3*v**2*(v + 2)
Let q(p) = -p**2 - 12*p + 12. Let s be q(-12). Let v be (-2)/4 + 30/s. Factor 0*u**3 + 4/7*u**4 - 2/7*u**5 + 0 - 4/7*u**v + 2/7*u.
-2*u*(u - 1)**3*(u + 1)/7
Let s(r) = 7*r**3 - 13*r**2 + 7*r. Let i(q) = 3*q**3 - 6*q**2 + 3*q. Let j(v) = -9*i(v) + 4*s(v). Factor j(g).
g*(g + 1)**2
Solve 2/11 + 0*u**2 + 4/11*u**3 - 2/11*u**4 - 4/11*u = 0 for u.
-1, 1
Let j = -2 + 4. Factor -6/5*s + 3/5 + 3/5*s**j.
3*(s - 1)**2/5
Let o(k) be the second derivative of -2*k + 0 - 9/14*k**2 - 1/7*k**3 - 1/84*k**4. Factor o(j).
-(j + 3)**2/7
Let n be 0 + 3 + (-8 - 1). Let j(a) = -a**3 - 6*a**2 - a - 6. Let g be j(n). Find m such that m**3 + g*m**2 - m + 1/2 - 1/2*m**4 = 0.
-1, 1
Let d(h) be the second derivative of -h**4/3 + 2*h**3/3 + h. Solve d(k) = 0.
0, 1
Let s = -79 - -81. Factor 2/3*o - 4/3 + 2/3*o**s.
2*(o - 1)*(o + 2)/3
Let z(i) = i**2 - 6*i. Suppose -3*n + n + 3*m + 21 = 0, 0 = -5*n + 2*m + 36. Let p be z(n). Suppose -6*y**2 - y**3 + p*y**3 + 4*y**3 = 0. What is y?
0, 2
Let h = 107 - 102. Find y such that -16/5*y**2 - 4/5 - 2/5*y**h + 4/5*y**4 + 14/5*y + 4/5*y**3 = 0.
-2, 1
Suppose 4*k = 35 + 61. Let u be 10/12 + (-8)/k. Find b such that 0 - 1/2*b**2 - 1/2*b**3 + 1/2*b + u*b**4 = 0.
-1, 0, 1
Determine h so that -1/2 - 11/4*h - h**3 - 13/4*h**2 = 0.
-2, -1, -1/4
Let k(v) be the third derivative of v**6/60 + v**5/10 + v**4/4 + v**3/3 - 12*v**2. Solve k(h) = 0.
-1
Factor 48/11*d**2 + 32/11 + 64/11*d + 2/11*d**4 + 16/11*d**3.
2*(d + 2)**4/11
Let m(a) be the third derivative of -a**8/112 + 2*a**7/35 - a**6/8 + a**5/10 + 11*a**2. Suppose m(j) = 0. What is j?
0, 1, 2
Suppose 5*h + 2*a - 43 - 77 = 0, -2*a = 4*h - 96. Let t be h/28*1/3. Let 0 - t*f**2 + 0*f = 0. What is f?
0
Let f(z) be the second derivative of -z**7/840 - z**6/120 - z**5/40 - z**4/24 - z**3/2 - 3*z. Let h(l) be the second derivative of f(l). Factor h(g).
-(g + 1)**3
Let l(z) be the third derivative of z**8/70560 + z**7/8820 - z**6/840 + z**5/60 + 5*z**2. Let b(t) be the third derivative of l(t). Factor b(u).
2*(u - 1)*(u + 3)/7
Let a = 9 - 6. Suppose 2*u - 5*v = -5, 5*u + a = -0*u + 3*v. Factor -1/3*f**3 + f + u*f**2 - 2/3.
-(f - 1)**2*(f + 2)/3
Let m(l) be the second derivative of l + 0 - 1/50*l**5 + 2/15*l**3 - 1/105*l**7 - 1/25*l**6 + 0*l**2 + 1/10*l**4. Suppose m(q) = 0. What is q?
-2, -1, 0, 1
Determine p, given that 0 + 2/9*p**4 - 4/9*p**2 + 0*p - 2/9*p**3 = 0.
-1, 0, 2
Let b(h) be the first derivative of 7*h**6/4 - 3*h**5/2 - 3*h**4/4 - 7. Factor b(a).
3*a**3*(a - 1)*(7*a + 2)/2
Let n be 0*((-52)/136 + (-10)/85). Factor n*x + 0 - 3/7*x**2 - 6/7*x**3 - 3/7*x**4.
-3*x**2*(x + 1)**2/7
Let z(g) be the second derivative of 0*g**4 - 1/24*g**3 + 0 + g + 1/240*g**5 + 1/2*g**2. Let j(v) be the first derivative of z(v). Factor j(p).
(p - 1)*(p + 1)/4
Factor -h + 1/2*h**2 + 1/2.
(h - 1)**2/2
Suppose -4*m - 13 + 21 = 0. Solve -1/4*x**4 + 1/4*x**5 - 1/4 - 1/2*x**3 + 1/4*x + 1/2*x**m = 0 for x.
-1, 1
Determine o so that -2/7 + 2/7*o**2 - 2/7*o + 2/7*o**3 = 0.
-1, 1
Let f(x) be the third derivative of 0*x - 1/360*x**5 - 1/1080*x**6 - x**2 + 1/36*x**4 + 0 - 2/3*x**3. Let i(d) be the first derivative of f(d). Factor i(k).
-(k - 1)*(k + 2)/3
Let i be (-9)/(-4) + 3/4. Find k, given that -2*k**i + 3*k**3 - 2*k**4 - 2*k**2 - 5*k**3 = 0.
-1, 0
Factor 6/7*y + 9/7 - 3/7*y**2.
-3*(y - 3)*(y + 1)/7
Let b(d) = d**3 + 13*d**2. Let c be b(-13). Suppose c = 4*q - 4*h - 28, -2*q = -q + h + 3. What is i in 0*i + 2*i - 5*i**q + i - i = 0?
0, 2/5
Let p be (224/120 + -2)*-6. Suppose -14/5*i**3 - p*i**4 + 0 + 14/5*i**5 + 4/5*i**2 + 0*i = 0. What is i?
-1, 0, 2/7, 1
Let t be (10 - -1 - 13)/(-6). Find n such that 0*n + 0*n**2 + 0 + 2/3*n**4 - 1/3*n**5 - t*n**3 = 0.
0, 1
Let t(i) be the third derivative of -5*i**8/168 - 46*i**7/735 + 79*i**6/420 + 19*i**5/105 - 11*i**4/21 + 8*i**3/21 - 2*i**2. Let t(r) = 0. Calculate r.
-2, -1, 2/7, 2/5, 1
Let p be (-3)/((-18)/4)*15/20. Let o = 0 - 0. Determine h, given that -p*h - 1/2*h**2 + o = 0.
-1, 0
Let g(b) be the first derivative of -3 + 2/3*b**3 - 2*b**2 + 0*b. Factor g(x).
2*x*(x - 2)
Let b(j) = -3*j - 15. Let l be b(-6). Solve 4*n**3 + 28 - 9*n - 6*n**l + 9*n**2 - 25 - n**3 = 0 for n.
1
Suppose -4*h + 3*c = -33, 5*c = 6 + 19. Factor 10*n**4 + 16 + 30*n**3 - h*n**2 + 3*n - 43*n - 4*n**3.
2*(n - 1)*(n + 2)**2*(5*n - 2)
Let h(q) be the second derivative of 0 + 5/3*q**6 - 1/3*q**7 + 4/7*q**2 + 145/42*q**4 - 47/14*q**5 - 40/21*q**3 + 5*q. Factor h(f).
-2*(f - 1)**3*(7*f - 2)**2/7
Factor 0 + s + 1/2*s**3 - 3/2*s**2.
s*(s - 2)*(s - 1)/2
Let u(o) be the second derivative of -o**7/126 - 2*o**6/45 - o**5/10 - o**4/9 - o**3/18 + 6*o. Factor u(v).
-v*(v + 1)**4/3
Let o(c) = c**3 - c + 0 - c**4 - 6 + 1 + 4. Let q(r) = -r**5 - 5*r**4 + 6*r**3 - 5*r - 5. Let u(t) = -5*o(t) + q(t). Suppose u(n) = 0. What is n?
-1, 0, 1
Factor 0*s**2 + 0 + 0*s + 2/7*s**4 - 2/7*s**3.
2*s**3*(s - 1)/7
Let i(j) be the second derivative of -j**7/9 + 26*j**6/45 - 13*j**5/30 - 17*j**4/9 + 20*j**3/9 + 8*j**2/3 - j. What is c in i(c) = 0?
-1, -2/7, 1, 2
Let x(m) be the third derivative o