(3*k + 1)
Find v, given that 4/5*v**3 - 4/5*v**4 + 4/5*v**2 - 4/5*v**5 + 0*v + 0 = 0.
-1, 0, 1
Let r = 1321/188 + 21/94. Let w = -7 + r. Determine i, given that w*i**3 - 1/4*i**2 + 0 + 0*i = 0.
0, 1
Let u(a) be the first derivative of 2*a**5/65 - a**4/26 - 2*a**3/39 + a**2/13 + 5. Determine d, given that u(d) = 0.
-1, 0, 1
Let n(b) be the third derivative of 29*b**5/36 - 5*b**4/36 - b**2 + 3. Factor n(z).
5*z*(29*z - 2)/3
Let z(w) be the third derivative of -1/9*w**3 + 5/72*w**4 + 1/360*w**6 + 0 - 2*w**2 - 1/45*w**5 + 0*w. Factor z(k).
(k - 2)*(k - 1)**2/3
Let x(p) be the third derivative of p**9/30240 - p**8/10080 - p**7/1260 - 2*p**5/15 + 2*p**2. Let f(w) be the third derivative of x(w). Factor f(n).
2*n*(n - 2)*(n + 1)
Suppose 30 = 2*w + 3*w. Let n be 0*(-1 - (-9)/w). Factor -14/3*c**4 + n + 4/3*c + 32/3*c**3 - 22/3*c**2.
-2*c*(c - 1)**2*(7*c - 2)/3
Let n(k) be the third derivative of k**8/504 - k**6/60 + k**5/45 - 12*k**2. Factor n(p).
2*p**2*(p - 1)**2*(p + 2)/3
Let a(k) be the third derivative of -k**7/1260 + k**6/360 + k**5/360 - k**4/72 + 3*k**2. Factor a(o).
-o*(o - 2)*(o - 1)*(o + 1)/6
Let o(z) be the second derivative of -1/2*z**2 + 2*z - 1/20*z**5 + 1/12*z**4 + 0 + 1/6*z**3. Solve o(x) = 0.
-1, 1
Let q = 9 + -7. Let t(g) be the second derivative of 0 - 1/3*g**2 + q*g + 7/18*g**3 - 5/36*g**4. Factor t(o).
-(o - 1)*(5*o - 2)/3
Solve 5/2*d**4 - 5/2*d**2 + 0*d**3 + 5/4*d - 5/4*d**5 + 0 = 0.
-1, 0, 1
Factor -2/13*n**2 + 22/13*n - 20/13.
-2*(n - 10)*(n - 1)/13
Let d(v) be the second derivative of 4*v**7/147 + v**6/15 + v**5/35 - v**4/42 - 5*v. Factor d(a).
2*a**2*(a + 1)**2*(4*a - 1)/7
Let z(r) be the second derivative of 2*r**2 - 3*r**3 + 6*r - 11/6*r**4 + 0. Suppose z(j) = 0. What is j?
-1, 2/11
Factor -2*b**2 - 2*b**2 + 10*b + 4 - 2*b**2 + 0*b**2.
-2*(b - 2)*(3*b + 1)
Suppose 0*m - 4*m - 2*r + 30 = 0, 4*m - 15 = 3*r. Let d be 4 + m/(1*-3). Factor 4 + 4 + p**3 - 3*p**3 - 6*p**d.
-2*(p - 1)*(p + 2)**2
Let k(s) be the third derivative of -s**5/180 - s**4/72 + 14*s**2. Factor k(c).
-c*(c + 1)/3
Let y(o) = 2*o - 84. Let i be y(43). What is x in 1/6*x**i + 2/3 + 2/3*x = 0?
-2
Let q(x) be the first derivative of 0*x - 1 - 1/2*x**2 + 1/4*x**4 + 0*x**3. Factor q(s).
s*(s - 1)*(s + 1)
Suppose 2*u = -2*k, 3 = 3*k - 3*u - 15. Let 0*l - 1/2*l**2 + 0 + 1/4*l**k = 0. What is l?
0, 2
Let k = 62 + -58. Let w(d) be the second derivative of -1/10*d**k + 3/10*d**2 + 3*d + 0*d**5 + 0 + 1/50*d**6 + 0*d**3. Factor w(q).
3*(q - 1)**2*(q + 1)**2/5
Factor -4*r**2 + 1169*r**3 - 1164*r**3 + 13*r**4 + 2*r**5 - 2*r**2.
r**2*(r + 1)*(r + 6)*(2*r - 1)
Suppose -s + 6 - 4 = 0. Let -2 + 6*t + 5 + 21*t**4 - 12*t**5 - 24*t**s + 3*t**3 + 3*t**3 = 0. What is t?
-1, -1/4, 1
Let f(n) be the second derivative of -2/15*n**6 + 4*n + 0 + 4*n**2 - 2*n**3 - 1/3*n**4 + 3/5*n**5. Determine m so that f(m) = 0.
-1, 1, 2
Let q(r) = -36*r**4 + 61*r**3 + 13*r**2 - 12*r. Let p(j) = 54*j**4 - 92*j**3 - 20*j**2 + 18*j. Let w(a) = 5*p(a) + 7*q(a). Suppose w(t) = 0. What is t?
-1/2, 0, 1/3, 2
Let h = 9 + -7. Suppose l = -n + 2, 3*l + 3*n - 6 = h*n. Solve l - m**2 + 4*m**2 - 5*m**2 = 0 for m.
-1, 1
Suppose -j = -n - 21, -3*n = 2*j + j - 51. Factor -22*r**2 - 12*r**3 + j*r**2 + 0 + 12*r + 3.
-3*(r - 1)*(r + 1)*(4*r + 1)
Let f be (-210)/30 - (-12)/1. Find u, given that 0*u - 3/5*u**f + 0 + 3/5*u**3 + 6/5*u**4 - 6/5*u**2 = 0.
-1, 0, 1, 2
Let a(m) be the second derivative of m**10/15120 + m**9/7560 - m**4/12 + m. Let v(r) be the third derivative of a(r). Suppose v(n) = 0. Calculate n.
-1, 0
Let n(h) be the second derivative of h**6/60 - 3*h**5/40 + h**4/24 + h**3/4 - h**2/2 + 4*h. Factor n(g).
(g - 2)*(g - 1)**2*(g + 1)/2
Let z(m) = 2*m**4 + 5*m**3 - 2*m**2 + m. Let r(f) = f**4 + f**3 - f**2 + f. Let b(u) = 3*r(u) - z(u). Let b(t) = 0. Calculate t.
-1, 0, 1, 2
Suppose g - 2 = 2. Factor -3*b**g + 7*b**3 - 5*b**2 - b**3 + 2*b**2.
-3*b**2*(b - 1)**2
Let l(a) = -a + 1. Let o(k) = 4*k - 34. Let m(r) = 6*l(r) + o(r). Let z be m(-15). Factor 2/5*c**z + 2/5*c**3 + 0*c + 0.
2*c**2*(c + 1)/5
Let f(o) be the first derivative of -4*o**3/3 - 18*o**2 - 32*o - 42. Let f(l) = 0. What is l?
-8, -1
Let a be 354/24 + -3 + -2 + -3. Factor 15/4*w**2 - 9/4*w - 3/4*w**3 - a.
-3*(w - 3)**2*(w + 1)/4
Let k = -1/745 - -1493/2235. What is c in 0*c + 0 - k*c**3 + 0*c**2 = 0?
0
Let x be 10*(-1)/2 - -2. Let i be (x/(-21))/(1/2). Determine r, given that -i + 8/7*r**2 - 6/7*r = 0.
-1/4, 1
Let g(c) be the second derivative of 1/12*c**3 + 1/12*c**2 + 1/36*c**4 + 2*c - 1/60*c**5 - 1/60*c**6 + 0 - 1/252*c**7. Factor g(q).
-(q - 1)*(q + 1)**4/6
Let a(g) be the third derivative of -g**7/42 + g**6/8 - g**5/12 - 5*g**4/8 + 5*g**3/3 - 3*g**2. Factor a(b).
-5*(b - 2)*(b - 1)**2*(b + 1)
Let y(p) be the first derivative of 4*p**3/3 - 8*p**2 - 20*p - 6. Determine q so that y(q) = 0.
-1, 5
Let k = -1303/9 - -145. Let l be ((-14)/(-198) - 4/22)*-2. Let -l - 4/9*m + 4/9*m**3 + 0*m**2 + k*m**4 = 0. What is m?
-1, 1
Let m(h) be the first derivative of h**4/16 + 7*h**3/12 + 11*h**2/8 + 5*h/4 - 18. Factor m(o).
(o + 1)**2*(o + 5)/4
Let h = 17 - 6. Suppose 4 = 5*t - h. Factor -4*a**3 + 5*a - 6*a**2 - a - 1 + 8*a**t - a**4.
-(a - 1)**4
Suppose -4*p - 8*u + 10*u + 24 = 0, -p - u = 0. Let t(m) be the second derivative of 2*m - 1/6*m**p + 0 + 1/6*m**3 + 6/5*m**6 + 0*m**2 - 3/4*m**5. Factor t(i).
i*(3*i - 1)**2*(4*i + 1)
Let n(b) be the first derivative of -b**4/48 - b**3/24 + 4*b + 4. Let v(k) be the first derivative of n(k). Factor v(r).
-r*(r + 1)/4
Factor -4/5*m - 2/5*m**2 - 2/5.
-2*(m + 1)**2/5
Let p(i) be the second derivative of -i**8/840 - i**7/315 - i**6/360 + 7*i**4/12 + 9*i. Let q(v) be the third derivative of p(v). Factor q(a).
-2*a*(2*a + 1)**2
Let t be 52 + -58 - 48/(-5). Factor -8/5*w - 32/5*w**2 + 0 - 42/5*w**3 - t*w**4.
-2*w*(w + 1)*(3*w + 2)**2/5
Let b(j) = -2*j**2 + 32*j - 158. Let t(a) = -2*a**2 + 33*a - 159. Let w(c) = 3*b(c) - 4*t(c). Factor w(r).
2*(r - 9)**2
Let d(z) be the second derivative of 0 + 6*z - 1/18*z**4 - 1/90*z**5 - 2/27*z**3 + 0*z**2. What is b in d(b) = 0?
-2, -1, 0
Let v(b) be the third derivative of -1/6*b**3 + 2*b**2 + 1/60*b**5 + 0*b + 1/120*b**6 + 0 - 1/24*b**4. Determine o so that v(o) = 0.
-1, 1
Let n(r) be the first derivative of -2 - 2/3*r**3 + 2*r**2 + r. Let z(y) = -7*y**2 + 15*y + 3. Let c(s) = -22*n(s) + 6*z(s). Solve c(k) = 0.
-2, 1
Let k(n) be the second derivative of n**6/10 - 6*n**5/5 + 21*n**4/4 - 9*n**3 - 10*n. Determine i, given that k(i) = 0.
0, 2, 3
Let z = 1111/3 + -370. Factor -z*m + 2/3*m**3 - 1/3*m**4 + 2/3*m**2 - 1/3 - 1/3*m**5.
-(m - 1)**2*(m + 1)**3/3
Let o(i) = 23*i**2 - 9*i + 5. Let l(k) = -5*k**2 - 3*k**2 + 4*k + 0 - 3*k**2 - 2. Let u(r) = 5*l(r) + 2*o(r). Determine p so that u(p) = 0.
0, 2/9
Let v(s) be the first derivative of 3 - 1/18*s**4 + 4/27*s**3 - 1/9*s**2 + 0*s. What is y in v(y) = 0?
0, 1
Let b(u) be the first derivative of u**5/5 - u**4/6 - u**3/3 - 3*u + 4. Let r(i) be the first derivative of b(i). Factor r(o).
2*o*(o - 1)*(2*o + 1)
Suppose 0 = -5*c + c - 5*d + 2, -3*c - d = -7. Let n**4 - 2*n**4 - 4*n - 2*n - 6*n**2 - 4*n**c - 1 + 2*n = 0. What is n?
-1
Let m(j) = 2*j**2 - 2*j - 1. Let p(c) = 3*c**2 - 4*c - 2. Let u(r) = 10*m(r) - 6*p(r). Factor u(z).
2*(z + 1)**2
Let m(r) = -r**2 + r - 1. Let x(n) = -3. Let z(l) = 3*m(l) - x(l). Solve z(i) = 0 for i.
0, 1
Factor -29*f - 3*f**5 + 2*f**2 - 12*f**4 - 14*f**2 - 18*f**3 + 26*f.
-3*f*(f + 1)**4
Suppose 0 = -5*l - 0*l - 15, -2*o = -5*l - 23. Determine v, given that -v + 0 + 5/2*v**5 - 7/2*v**o + 7/2*v**2 - 3/2*v**3 = 0.
-1, 0, 2/5, 1
Suppose 5*i - 21 = -3*a, 0*i = -4*i - 4*a + 20. Factor -v**3 + 3*v**3 - 2*v**3 - i*v**3 + 6*v**2.
-3*v**2*(v - 2)
Factor 2/11*l - 2/11*l**4 - 2/11*l**3 + 0 + 2/11*l**2.
-2*l*(l - 1)*(l + 1)**2/11
Let v(j) be the third derivative of -j**8/672 - 2*j**2. Factor v(t).
-t**5/2
Solve 4*r**5 + 40 - 8*r**3 + 4*r - 40 = 0.
-1, 0, 1
Let k(j) = j**2 + 2*j. Suppose -2*t + 3*h = -2, t = 4*h - 3*h. Let v(i) = 5*i**2 + 9*i - 3*i**2 + 3*i**2. Let l(f) = t*v(f) + 9*k(f). Factor l(a).
-a**2
Solve -2*u - 4*u + 0*u**2 + 10 - 3 - u**2 = 0 for u.
-7, 1
Let l = 17/2 - 67/8. Let y(a) be the first derivative of -1/16*a**4 + 1/6*a**3 - l*a**2 + 0*a + 3. Factor y(w).
-w*(w - 1)**2/4
Let a(h) be the third derivative of -h