Determine t, given that -22*t**3 - 5 - 2*t + 1 - 14*t**2 + 36*t**n + 0 + 6*t**4 = 0.
-1/3, 1, 2
Let c(a) be the second derivative of 1/12*a**4 + 0*a**2 - 3*a + 1/6*a**3 + 0. Suppose c(z) = 0. What is z?
-1, 0
Let o(k) be the second derivative of k**8/13440 - k**6/1440 + 5*k**4/12 - 2*k. Let y(m) be the third derivative of o(m). Suppose y(a) = 0. What is a?
-1, 0, 1
Let c(h) be the first derivative of -h**7/420 - h**6/120 - h**5/120 + h**2 + 1. Let z(x) be the second derivative of c(x). Let z(y) = 0. What is y?
-1, 0
Let b be 176/3 + 4/(-6). Let a = b - 20. Factor 3 + 2*p - 133*p**3 - a*p - 75*p**3 + 144*p**2 + 16*p**3.
-3*(4*p - 1)**3
Suppose -b = -2*b - 4*b. Let m(t) be the second derivative of b*t**3 + 1/15*t**5 + t - 1/45*t**6 + 0 + 0*t**2 - 1/18*t**4. Factor m(l).
-2*l**2*(l - 1)**2/3
Let b(o) = 4*o - 5. Let j be b(8). Let d = 29 - j. Solve 2/7*p + 0 + 1/7*p**d = 0.
-2, 0
Let w(i) = i**4 - i**2. Let n(j) = -5*j**4 + 11*j**3 - 8*j**2 + j + 1. Let x(o) = -n(o) - w(o). Factor x(b).
(b - 1)**3*(4*b + 1)
Let h(s) be the first derivative of s**6/50 - 3*s**5/50 + s**4/20 - s + 1. Let k(x) be the first derivative of h(x). Determine o so that k(o) = 0.
0, 1
Let h = -67 - -70. Factor 4/7*m + 0 - 2/7*m**h + 2/7*m**2.
-2*m*(m - 2)*(m + 1)/7
Let w(u) be the third derivative of u**8/2184 + u**7/1365 - u**6/780 - u**5/390 + 17*u**2. Let w(x) = 0. Calculate x.
-1, 0, 1
Let r(w) be the first derivative of -1/90*w**5 + 0*w - w**2 - 1/18*w**4 + 3 + 0*w**3. Let p(f) be the second derivative of r(f). Factor p(m).
-2*m*(m + 2)/3
Let v be 2/10*455/468. Let f(n) be the second derivative of -2*n + v*n**3 + 0 - 1/18*n**4 + 1/6*n**2. Factor f(c).
-(c - 2)*(4*c + 1)/6
Let k(o) = -4*o**2 - 17*o. Let v(x) be the second derivative of x**4/6 + 4*x**3/3 + 7*x. Let d(z) = -6*k(z) - 13*v(z). Determine a so that d(a) = 0.
-1, 0
Let k(x) be the second derivative of -1/9*x**3 + 0 + 2/3*x**2 - 1/18*x**4 + x. Factor k(y).
-2*(y - 1)*(y + 2)/3
Let t(j) = -4*j**2 - j. Let g be t(-1). Let x = 6 + g. Solve 0*m**2 + 9*m**5 + 39*m**4 - 9*m**2 + 42*m**3 - x*m**2 - 24*m = 0.
-2, -1, 0, 2/3
Let t(x) = -2*x**4 + 2*x**3 - 2*x**2 + 6. Let l(j) = 4*j**4 - 5*j**3 + 4*j**2 - 13. Let z(b) = -6*l(b) - 13*t(b). Factor z(c).
2*c**2*(c + 1)**2
Let m(v) be the second derivative of -v**4/4 - 10*v**3 - 150*v**2 - 37*v. Factor m(s).
-3*(s + 10)**2
Solve 16/3 + 4/3*h**2 - 16/3*h = 0.
2
Let q(t) = 8*t**2 - 8*t - 8. Let p(y) = 9*y**2 - 9*y - 8. Let i(a) = 4*p(a) - 5*q(a). Factor i(s).
-4*(s - 2)*(s + 1)
Let q(h) be the second derivative of h**4/18 + h**3/9 - 2*h**2 + 67*h. Factor q(n).
2*(n - 2)*(n + 3)/3
Determine r so that -r + 56*r**4 + 10*r**3 - 5*r**2 - 9*r - 51*r**4 = 0.
-2, -1, 0, 1
Suppose -9 = -5*k + 6. Suppose -d + 0*d**4 - k*d**3 + 17*d**2 - 20*d**2 - d**4 = 0. Calculate d.
-1, 0
Let i be (-3*(-1)/9)/(9 - 8). Let 1/3*o**2 + 2/3*o + i = 0. Calculate o.
-1
Let n(k) be the second derivative of -k**5/80 - k**4/12 - k**3/6 + 14*k. Factor n(t).
-t*(t + 2)**2/4
What is m in 1/2*m**3 + 0*m + m**2 + 0 = 0?
-2, 0
Let y = -1/1460 + 11689/13140. Determine b, given that 0 - 2/9*b**4 - 8/9*b**2 + 0*b - y*b**3 = 0.
-2, 0
Let i be ((-72)/16)/((-9)/6). Let y(x) be the second derivative of -1/9*x**i + 0 + 0*x**2 + x + 1/18*x**4. Solve y(u) = 0.
0, 1
Suppose -2*p - 5*f = 21, -2*p + 3*f + 9 = -5*p. Solve 6/5*b**3 + 8/5*b**4 - 2*b**p - 6/5*b + 2/5 = 0.
-1, 1/4, 1
Let d(m) be the third derivative of -m**6/180 - m**5/30 + m**4/36 + m**3/3 - 12*m**2. Factor d(o).
-2*(o - 1)*(o + 1)*(o + 3)/3
Let h(i) be the third derivative of i**6/540 + i**5/54 + 2*i**4/27 + 4*i**3/27 - 9*i**2. Find p, given that h(p) = 0.
-2, -1
Let g = 227/175 + 39/25. What is c in g*c**3 + 108/7*c - 54/7 - 2/7*c**4 - 72/7*c**2 = 0?
1, 3
Let n(a) = -4*a**2 - 4*a. Let k(l) = l**3 + 5*l**2 + 4*l. Let d(p) = -4*k(p) - 5*n(p). Factor d(w).
-4*w*(w - 1)*(w + 1)
Let -1/8*w**3 + 0*w + 0 - 1/4*w**2 = 0. What is w?
-2, 0
Determine u so that 1/2*u**2 - u + 0 = 0.
0, 2
Let t(x) be the first derivative of x**6/240 - x**4/16 + x**3/6 - x**2 + 6. Let p(k) be the second derivative of t(k). Solve p(j) = 0.
-2, 1
Suppose -3*q = -4*q - 3. Let d = q - -4. Factor 0*a**2 - d - 1 + 2*a**2.
2*(a - 1)*(a + 1)
Let x be 3/10*((-8)/(-6) - 0). Factor 2*m**2 - x*m**5 - 2/5*m**4 + 6/5*m**3 + 4/5*m + 0.
-2*m*(m - 2)*(m + 1)**3/5
Let y(j) be the second derivative of 3*j**5/20 - j**4/4 - 4*j. Suppose y(v) = 0. What is v?
0, 1
Let j be 238/(-12)*36/(-56). Let a = 365/28 - j. Factor -a*c**4 + 0 + 2/7*c**3 + 2/7*c**2 - 2/7*c**5 + 0*c.
-2*c**2*(c - 1)*(c + 1)**2/7
Suppose 9/4*i**5 - 3*i**4 - 5/4*i**3 + 0 - i + 3*i**2 = 0. What is i?
-1, 0, 2/3, 1
Let d(u) = 9*u**2 + 6*u - 3. Let a(g) = 19*g**2 + 13*g - 6. Let o(w) = -6*a(w) + 13*d(w). Solve o(r) = 0.
-1, 1
Suppose 2*t = t + 2. Suppose -1 = c, 2*h - t = -c + 1. Suppose -2 + 4*r**2 - 2*r**2 + 0*r**h = 0. What is r?
-1, 1
Let s(y) = -8*y**3 - 20*y**2 + 48*y. Let c(t) = -t**3 - 3*t**2 + 7*t. Let f(a) = -20*c(a) + 3*s(a). Solve f(p) = 0 for p.
-1, 0, 1
Let o(n) = 3*n**3 + 11*n**2 - 4. Let q(a) = 2*a**3 + 9*a**2 - 3. Let l(r) = 3*o(r) - 4*q(r). Factor l(u).
u**2*(u - 3)
Let s(v) be the first derivative of -v**4/6 - v**3/3 + 2*v**2 + 3*v - 1. Let d(p) be the first derivative of s(p). Factor d(g).
-2*(g - 1)*(g + 2)
Factor -4*o**2 - 45 + 3*o**2 + 7*o - 36 + 11*o.
-(o - 9)**2
Let z be (-1064)/(-224) - (-3)/(-13 - -1). Factor -3 - z*u - 3/2*u**2.
-3*(u + 1)*(u + 2)/2
Let t(o) be the third derivative of -1/80*o**5 - 1/1440*o**6 + 0 - 3/32*o**4 + 0*o - 2/3*o**3 - 3*o**2. Let q(i) be the first derivative of t(i). Factor q(g).
-(g + 3)**2/4
Factor -1/7*i**3 + 1/7 - 3/7*i + 3/7*i**2.
-(i - 1)**3/7
Let c(y) be the first derivative of 3*y**5/5 + 21*y**4/4 + 15*y**3 + 39*y**2/2 + 12*y + 4. Factor c(d).
3*(d + 1)**3*(d + 4)
Suppose -5*m = 4*w - 23, 2*w + 2*m - 4*m = -2. Suppose 0 = -3*k + w*b - 6, -k - 12 = 2*k - 4*b. What is p in k + 0*p - 2/7*p**3 + 2/7*p**2 = 0?
0, 1
Let d(b) = -3*b**2 + 15*b. Let t(v) = -v. Let y(z) = d(z) + 9*t(z). Determine p so that y(p) = 0.
0, 2
Let h(j) be the third derivative of j**8/312 + 19*j**7/1365 + 2*j**6/195 - 2*j**5/195 - 5*j**2. Find q, given that h(q) = 0.
-2, -1, 0, 2/7
Let u = -37 + 42. Let s(b) = b**2 - b - 2. Let o be s(3). Factor -2*i**o + 7/4*i + u*i**3 - 1/4 - 9/2*i**2.
-(i - 1)*(2*i - 1)**3/4
Let s = -880064 - -714612585/812. Let i = s - 2/203. Factor -1/4 - 3/4*q**2 - i*q - 1/4*q**3.
-(q + 1)**3/4
Let y(h) be the second derivative of -h + 0 - 4/3*h**2 - 1/18*h**4 + 4/9*h**3. Factor y(b).
-2*(b - 2)**2/3
Let r(f) = -f**5 + 7*f**4 + 2*f**3 - 4*f**2 - 4*f. Let z(y) = -y**5 + 8*y**4 + 3*y**3 - 5*y**2 - 5*y. Let o(l) = 5*r(l) - 4*z(l). Suppose o(w) = 0. What is w?
0, 1, 2
Let v(s) be the second derivative of 2*s + 0*s**3 + 0 + 1/12*s**4 + 0*s**2. Factor v(f).
f**2
Factor 16*a**2 - a**4 - 8*a**5 + 9*a**2 - 9*a**2 - 16*a**3 - 27*a**4.
-4*a**2*(a + 2)**2*(2*a - 1)
Let x(f) = -f**4 + f**3 - f**2 + 1. Let j(b) = 4*b**4 - 11*b**3 + 26*b**2 - 28*b + 9. Let i(w) = -j(w) - 3*x(w). Suppose i(l) = 0. What is l?
1, 2, 3
Let 125*z**3 + 5*z**5 + 108*z - 108*z + 50*z**4 = 0. What is z?
-5, 0
Let b(j) be the second derivative of j**7/7560 - j**6/2160 - j**4/4 + 2*j. Let t(q) be the third derivative of b(q). Determine w, given that t(w) = 0.
0, 1
Let l(q) be the first derivative of 2/5*q**5 + 1/3*q**3 + 7/8*q**4 + 1 + 0*q - 1/4*q**2. Factor l(k).
k*(k + 1)**2*(4*k - 1)/2
Let d(g) be the third derivative of -g**7/420 + g**6/20 - 9*g**5/20 + 9*g**4/4 - 27*g**3/4 + 5*g**2. Let d(z) = 0. What is z?
3
Let h = -3196/143 + 300/13. Find x such that -6/11*x**2 - 2/11*x**4 + 8/11*x - h*x**3 + 8/11 = 0.
-2, -1, 1
Let f be -1 - -1 - 21/(189/(-6)). Factor f*o - 1/6*o**2 - 2/3.
-(o - 2)**2/6
Suppose -5*d + 2*d - 4*b = 148, -d - 4*b = 36. Let l = d - -84. Factor -25*y - 6 + 4 - y**2 + l*y.
-(y - 2)*(y - 1)
Let p(d) be the first derivative of 2*d**3/7 - 2*d**2/7 - 2*d/7 + 7. Find o, given that p(o) = 0.
-1/3, 1
Let q = -5/77 + 7/11. Determine k, given that -q*k**3 + 2/7 + 2/7*k**4 - 4/7*k**2 + 2/7*k**5 + 2/7*k = 0.
-1, 1
Let j(y) be the second derivative of y**4/18 + 8*y**3/9 + 16*y**2/3 + 13*y. Factor j(l).
2*(l + 4)**2/3
Suppose 0 = -3*k - k. Suppose k = -5*j - 0*j - 2*m + 34, m - 8 = -j. Solve 3*r**2 - r**2 + 2*r**4 - 1 - j*r**3 + 6*r -