*f**2 - w*f = 0.
-1, 1
Let x(w) be the first derivative of 1/5*w**4 + 4/5*w**2 - 4/5*w**3 + 0*w + 12. What is s in x(s) = 0?
0, 1, 2
Factor 54 - 39*s**2 + 4*s**4 - 7*s**4 - 9*s + 301*s**3 - 280*s**3.
-3*(s - 3)**2*(s - 2)*(s + 1)
Let z(u) = u**2 - u. Let t(s) = -2*s**2 + 5*s - 3. Let b(n) = t(n) + 3*z(n). Let c(r) = r - 1. Let g(l) = -2*b(l) + 2*c(l). Factor g(q).
-2*(q - 1)*(q + 2)
Suppose -3*b + 34 - 31 = -5*z, -z + 5*b = 5. Let k(u) = u**2 + 5*u + 4. Let t be k(-4). Determine c so that 8*c + z - 2*c**2 + t*c**2 - 2 - 12*c = 0.
-1
Let m(u) be the first derivative of u**8/420 - u**6/90 - 22*u**3/3 - 17. Let k(h) be the third derivative of m(h). Suppose k(i) = 0. What is i?
-1, 0, 1
Let x(z) be the first derivative of -z**5/5 + 22*z**4 - 674*z**3 + 1892*z**2 - 1849*z - 890. Factor x(n).
-(n - 43)**2*(n - 1)**2
What is t in -48*t**3 + 16*t**4 + 42*t**2 + 16*t**4 - 21*t**2 + 2 + 12*t - 19*t**2 + 0*t = 0?
-1/4, 1
Let q(l) be the first derivative of 1/2*l**2 + 2/3*l**3 - 4 + 0*l + 1/4*l**4. Factor q(p).
p*(p + 1)**2
Let b(d) be the third derivative of 0 + 1/80*d**6 + 0*d - 1/6*d**3 + 12*d**2 - 1/16*d**4 + 1/420*d**7 + 1/120*d**5. Determine s so that b(s) = 0.
-2, -1, 1
Factor 6/5*s + 0 + 3/5*s**3 - 9/5*s**2.
3*s*(s - 2)*(s - 1)/5
Let s be (12/15)/((-4)/200). Let w(d) = d**3 - d**2 - 1. Let t(k) = -4*k**3 + 11*k**2 - 9*k + 10. Let p(h) = s*w(h) - 5*t(h). Let p(o) = 0. What is o?
-2, 1/4, 1
Let x(f) be the first derivative of 4*f**3/9 + 32*f**2/9 + 80*f/9 - 44. Factor x(d).
4*(d + 2)*(3*d + 10)/9
Let y = -44 - -24. Let c be y/(-6)*((-77)/(-105))/11. Solve -c - 2/9*m**2 - 4/9*m = 0 for m.
-1
Let f(b) = 47*b - 83. Let l be f(2). Let i = -12 - -8. Let r(u) = 19*u**2 - 31*u + 12. Let v(j) = 6*j**2 - 10*j + 4. Let h(q) = i*r(q) + l*v(q). Factor h(y).
-2*(y - 1)*(5*y - 2)
Let z = 845 - 845. Let l(b) be the second derivative of 0*b**2 - 7*b - 2*b**3 - 3/20*b**5 + z + b**4. Determine g so that l(g) = 0.
0, 2
Suppose 106/17 + 2/17*r**2 - 108/17*r = 0. What is r?
1, 53
Let f = -312 + 137. Let j be (-1)/2 - f/250. Determine q, given that 2/5*q - j - 1/5*q**2 = 0.
1
Suppose -1/4*h**3 - 11/4*h**2 - 35/4*h - 25/4 = 0. Calculate h.
-5, -1
Let g(m) be the second derivative of m**6/120 - 3*m**5/40 + m**4/12 + m**3/4 - 5*m**2/8 - 477*m. Solve g(k) = 0.
-1, 1, 5
Let d(p) be the first derivative of -1/3*p**4 + 2/15*p**5 - 10/3*p - 14/3*p**2 - 17 - 8/3*p**3. Factor d(q).
2*(q - 5)*(q + 1)**3/3
Let y(i) = -4*i - 3*i - i**2 - 2*i + 10*i. Let w(r) = r**3 - 3*r**2 - r. Let p(d) = -5*w(d) - 5*y(d). Find u, given that p(u) = 0.
0, 4
Factor -61*w - 215*w**3 - 66*w - 52*w + 179*w - 105*w**2 - 10*w**4.
-5*w**2*(w + 21)*(2*w + 1)
Let d = -18470 - -18473. Let -4*b - 32/7*b**2 - 8/7 - 12/7*b**d = 0. What is b?
-1, -2/3
Factor 1/3*g**3 + 8 + 26/3*g + 3*g**2.
(g + 2)*(g + 3)*(g + 4)/3
Let k(g) be the second derivative of -g**8/112 + 23*g**2 + 45*g. Let j(z) be the first derivative of k(z). Factor j(c).
-3*c**5
Factor 1/10*g**4 + 0 - 3/10*g**2 - 1/5*g + 0*g**3.
g*(g - 2)*(g + 1)**2/10
Let w be (4/8)/(3/246). Suppose 4*h - 2*t + 9 = w, -3*h - 4*t = -2. Suppose -h*a**2 - 3*a**3 - 4*a + 3*a**2 + 8*a**3 - 5*a**2 = 0. What is a?
-2/5, 0, 2
Factor -1692*w**4 - 567*w**2 - 1188*w**4 + 562*w**2 + 240*w**3.
-5*w**2*(24*w - 1)**2
Let s = 41 + -39. Suppose -19*q**4 - 2 + 154*q**4 + 270*q**3 - 405*q**5 + 55*q - 3 - 210*q**s = 0. Calculate q.
-1, 1/3
Let f be (2/6)/((-10)/(-420)). Suppose -j = -2*y + 8, 4*y - j - 2 - f = 0. Let 1 + 2*v**2 - 1 - y*v = 0. Calculate v.
0, 2
Let s(w) be the first derivative of -w**7/70 - 3*w**6/70 - 3*w**5/140 + w**4/28 + 5*w**2 - 3. Let t(a) be the second derivative of s(a). Solve t(j) = 0 for j.
-1, 0, 2/7
Suppose -4*k = -0*k. Suppose -3*x + 33 = 5*u, k*x + 2*u = -4*x + 58. Solve 8 + 0*a**3 - 20*a - 2*a**3 - a**3 + x*a**2 - a**3 = 0.
1, 2
Let u(k) be the second derivative of 5*k**7/252 - k**6/36 - 45*k. Factor u(y).
5*y**4*(y - 1)/6
Let z(p) = -12*p**2 + 44*p + 48. Let q(f) = 2*f**2 - 311 - 22*f + 7*f + 295 + 2*f**2. Let a(g) = -8*q(g) - 3*z(g). Factor a(r).
4*(r - 4)*(r + 1)
Let z(x) be the second derivative of 3*x**5/40 + x**4/8 - 5*x**3/4 + 9*x**2/4 - 77*x. What is h in z(h) = 0?
-3, 1
Let v(k) be the second derivative of k**8/33600 - k**7/2100 + k**6/400 - k**5/150 - 2*k**4 - 21*k. Let b(c) be the third derivative of v(c). Factor b(o).
(o - 4)*(o - 1)**2/5
Let g be (-4)/18 - (-202)/18. Let h = g + -9. Let 0 + 0*l**h + 0*l + 1/5*l**3 = 0. What is l?
0
Let i(x) be the second derivative of x**5/4 + 35*x**4/6 + 50*x**3 + 180*x**2 + 171*x. Factor i(b).
5*(b + 2)*(b + 6)**2
Let u(o) be the third derivative of 3/14*o**4 - 2/7*o**3 - 11/140*o**5 - 14*o**2 + 3/280*o**6 + 0*o + 0. Solve u(f) = 0 for f.
2/3, 1, 2
Let b(a) be the second derivative of -a**9/13608 + a**3/3 + 11*a. Let z(u) be the second derivative of b(u). Factor z(f).
-2*f**5/9
Let d(o) = -o**3 - 2*o**2 + 99*o. Let f be d(-11). Factor -3/2*a**2 + 3/2*a**3 + f - 3*a.
3*a*(a - 2)*(a + 1)/2
Let h(g) be the third derivative of g**6/60 + 13*g**5/30 + 4*g**4/3 - 64*g**3 - 271*g**2. Factor h(i).
2*(i - 3)*(i + 8)**2
Factor 1/4*y**3 + 0 + 23/4*y + 6*y**2.
y*(y + 1)*(y + 23)/4
Let w(s) be the first derivative of 0*s**2 + 0*s - 5 + 4/9*s**3 + 4/5*s**5 - 2/9*s**6 - s**4. Solve w(u) = 0.
0, 1
Let g(n) be the second derivative of 0*n**2 - 8*n + 0 + 0*n**3 + 1/126*n**7 + 1/30*n**6 + 1/20*n**5 + 1/36*n**4. Let g(y) = 0. Calculate y.
-1, 0
Let k be (-8)/(-14) - 60/(-42). Suppose k*j + 9 = 5*j. Factor 3*g**j + g**2 - 3*g**2 + 5*g**3 - 2*g - 4*g**2.
2*g*(g - 1)*(4*g + 1)
Let p = -30514/5 - -6103. Factor -1/5*u**2 + p*u + 6/5.
-(u - 3)*(u + 2)/5
Let b = 6596 - 6596. Find h such that -3/2*h**2 + b*h + 0 + 3/2*h**3 = 0.
0, 1
Suppose 0 = 4*l + 5*i + 25, 238*l - 55 = 241*l + 11*i. Let l + 1/5*g**2 - 7/5*g = 0. Calculate g.
0, 7
Factor -17 - 8 + 12*q + 12 - 3 - 2*q**2.
-2*(q - 4)*(q - 2)
Let q(p) = p**2 - 12*p + 24. Let k be q(10). Let a(z) be the third derivative of 0*z + 2*z**2 - 1/180*z**5 + 0 - 1/18*z**3 + 1/36*z**k. Factor a(g).
-(g - 1)**2/3
Suppose 67 - 61 = 2*c. Let a(s) be the first derivative of -6 - 3/4*s**5 + 0*s - 7/8*s**6 + 27/16*s**4 - 3/4*s**2 + 5/4*s**c. Determine w, given that a(w) = 0.
-1, 0, 2/7, 1
Factor -5/2 + 17/12*n - 1/12*n**2.
-(n - 15)*(n - 2)/12
Let a be -1*(2 - (2 - -5)). Let n = a - 3. Factor 1/2*q**n + 1/2 - q.
(q - 1)**2/2
Let b(z) be the third derivative of z**6/4140 + z**5/230 - 11*z**3/3 - 8*z**2. Let s(g) be the first derivative of b(g). Let s(v) = 0. What is v?
-6, 0
Let z(d) be the first derivative of -3*d**4/20 + 5*d**3 - 141*d**2/10 + 69*d/5 + 146. Find o, given that z(o) = 0.
1, 23
Let f(q) be the third derivative of 21*q**2 + 0*q**3 - 1/42*q**7 + 5/6*q**4 + 0 + 0*q + 1/12*q**6 + 7/12*q**5. Factor f(k).
-5*k*(k - 4)*(k + 1)**2
Factor 10*x**3 + 0*x**3 - x**4 + 36*x + 108 + 11*x**3 - 21*x**2 - 41*x**3 + 10*x**3.
-(x - 2)*(x + 3)**2*(x + 6)
Let s(m) = -38*m + 570. Let g be s(15). Let r(u) be the third derivative of 0*u**4 - 10*u**2 + 0*u**3 + 1/300*u**5 + g + 0*u. What is a in r(a) = 0?
0
Factor -1/4*c**2 - 1/2 - 3/4*c.
-(c + 1)*(c + 2)/4
Let s = -157/576 - -21/64. Let m(t) be the first derivative of -1/27*t**6 + s*t**4 + 2/27*t**3 + 0*t - 11 + 0*t**2 - 2/45*t**5. Find w such that m(w) = 0.
-1, 0, 1
Factor -201/5 - 1218/5*a**2 - 822/5*a**3 - 3/5*a**5 - 213/5*a**4 - 807/5*a.
-3*(a + 1)**4*(a + 67)/5
Let z be (8 + -10 + 2)/(-10 + 11). Let k = 7/2 + -31/10. Factor 6/5*p + z + k*p**2.
2*p*(p + 3)/5
Let b(a) be the second derivative of -1/5*a**5 + 0 + 0*a**2 + 12*a + 2/15*a**6 + 2/3*a**3 - 1/3*a**4. Factor b(w).
4*w*(w - 1)**2*(w + 1)
Suppose 0 = -b + 4*b - 27. Suppose i + b = -3*a, 6*a - a + 5 = -5*i. Solve 4/3*n + 0 - 10/3*n**2 - 2/3*n**5 + 2*n**i + 2/3*n**4 = 0 for n.
-2, 0, 1
Let d(k) = 2*k**2 + 22*k - 36. Let p(n) = n**2 + 2*n + 1. Let v(x) = 2*d(x) + 6*p(x). Factor v(w).
2*(w - 1)*(5*w + 33)
Let g(t) be the second derivative of 2*t**7/7 - 23*t**6/10 + 153*t**5/20 - 55*t**4/4 + 29*t**3/2 - 9*t**2 + 380*t. Factor g(k).
3*(k - 2)*(k - 1)**3*(4*k - 3)
Let v be (-18)/(-24) - (-2)/(-24). Let y(w) be the second derivative of 0 + 0*w**2 - v*w**3 + 2/3*w**4 - 8*w - 1/5*w**5. Factor y(x).
-4*x*(x - 1)**2
Let l(r) = -r + 1 + 6 + 4 + 5. Let v be l(13). Solve 0 - 1/6*j**4 + 1/6*j**v - 1/6*j + 1/6*j**2 