
Let l(s) be the third derivative of -12*s**2 + 0*s + 1/3*s**4 + 2/3*s**3 + 0 + 1/15*s**5. Let l(g) = 0. Calculate g.
-1
Let w(a) be the third derivative of a**8/1008 + a**7/90 - a**6/120 - 19*a**5/180 + 7*a**4/36 - 119*a**2. Factor w(s).
s*(s - 1)**2*(s + 2)*(s + 7)/3
Let l(p) = 2*p**2 + 95*p - 18. Let f(i) = -3*i**2 - 94*i + 17. Let m(w) = -5*f(w) - 4*l(w). Factor m(r).
(r + 13)*(7*r - 1)
Let g be (15/9)/(10/18). Determine k so that -4*k**5 - 28*k**2 + 223 + 4*k**g + 4*k - 215 - 4*k**5 + 20*k**4 = 0.
-1, -1/2, 1, 2
Let y(a) be the first derivative of 3*a**6 - 3*a**5/5 - 21*a**4/4 + a**3 + 3*a**2/2 - 701. Let y(z) = 0. Calculate z.
-1, -1/3, 0, 1/2, 1
Let q = 224 + -219. Suppose -5*o - q = 4*s + s, -o = -2*s + 7. Let -3/4*j**3 - 3/2*j**s - 3/4*j + 0 = 0. Calculate j.
-1, 0
Let u(b) be the third derivative of -2/45*b**3 + 0 + 0*b + 1/2520*b**8 - 2/525*b**7 + 7/450*b**6 - 9*b**2 + 1/20*b**4 - 8/225*b**5. Factor u(f).
2*(f - 2)*(f - 1)**4/15
Let o be (-2)/(3 + 43/(-14)). Let s = -22 + o. Factor -2*y**2 - 6*y - s*y**2 + 5*y**2.
-3*y*(y + 2)
Let c = -213 - -213. Let k(p) be the third derivative of c - 1/60*p**6 + 0*p**4 - 1/42*p**7 + 0*p + 0*p**3 + 0*p**5 - p**2 - 1/112*p**8. Factor k(t).
-t**3*(t + 1)*(3*t + 2)
Suppose -174*a + 1299 = -83*a + 342*a. Solve -8/15*g**2 + 2/3*g - 4/15 + 2/15*g**a = 0 for g.
1, 2
Let j = 1745 + -12213/7. Factor 8/7*i**2 + j*i + 0 + 8/7*i**3.
2*i*(2*i + 1)**2/7
Factor -15*d**2 - 55/4*d**3 + 5/4*d**4 + 0*d + 0.
5*d**2*(d - 12)*(d + 1)/4
Let t = -67 + 67. Let a(h) be the third derivative of 2*h**2 + 0 - 1/588*h**8 + 1/42*h**4 - 2/105*h**6 - 1/105*h**7 + 1/21*h**3 - 1/105*h**5 + t*h. Factor a(g).
-2*(g + 1)**4*(2*g - 1)/7
Solve 3*g**5 + 4 + 21*g**4 - 11*g**5 - 62*g**3 - 59*g**4 - 38*g**2 - 2*g = 0.
-2, -1, 1/4
Let r = 30 + -33. Let c be ((-1)/r)/(45/(-12) + 4). Determine k so that k - c*k**3 - 8/3*k**2 + 3 = 0.
-3/2, 1
Suppose -14 - 86 = -50*w. Factor -7/8*s**w + 1/2 + 3/2*s.
-(s - 2)*(7*s + 2)/8
Let l(u) = -5*u**3 - 10*u**2 + 41*u - 14. Let i(n) = 5*n**3 + 10*n**2 - 40*n + 15. Let p(a) = -6*i(a) - 5*l(a). Let p(t) = 0. Calculate t.
-4, 1
Factor -50*w**3 + 3*w**4 - 29*w**3 + 121*w**3.
3*w**3*(w + 14)
Let i(p) be the second derivative of -21*p**5/4 + 641*p**4/4 + 226*p**3 + 114*p**2 + 6*p - 1. Let i(n) = 0. What is n?
-2/5, -2/7, 19
Let s = 1874065/198 - 9465. Let y = s + 1721/198. Solve -14/3*g**3 - 8/3*g**5 + 22/3*g + 22/3*g**2 - y*g**4 + 4/3 = 0.
-2, -1, -1/4, 1
Let o(p) = -p**2 + 2*p + 50. Suppose -3*v = 3*h - 1 - 38, -4*h = -4*v + 12. Let u be o(v). Factor 0 - 3/5*f**u - 1/5*f**3 - 2/5*f.
-f*(f + 1)*(f + 2)/5
Let v = -2269/5 - -3179/7. Let q = 32/35 - v. Factor -2/7*k**2 - 2/7*k + q.
-2*(k - 1)*(k + 2)/7
Let b(s) be the third derivative of 0*s + 11*s**2 + 5/336*s**8 - 5/12*s**4 + 1/24*s**6 + 1/14*s**7 + 0 - 1/4*s**5 + 0*s**3. Factor b(i).
5*i*(i - 1)*(i + 1)**2*(i + 2)
Let y(i) = -2*i**2 + 3*i**3 - 3 - 5 + 2 + 2. Let u(n) = 4*n**3 - 2*n**2 - 5. Let k(m) = 4*u(m) - 5*y(m). Factor k(g).
g**2*(g + 2)
Let s = -16469/3 - -5490. Factor -1/3 + 1/3*l**3 + 1/3*l**2 - s*l.
(l - 1)*(l + 1)**2/3
Let a = 705 - 7753/11. Suppose -6/11*y + 4/11*y**3 - 2/11 + a*y**5 - 4/11*y**2 + 6/11*y**4 = 0. Calculate y.
-1, 1
Factor 1/8*k**2 - 17/8*k + 0.
k*(k - 17)/8
Let w = -73 - -76. Suppose 0 = w*d - 10*d + 21. Suppose -4/3*h**d - 4/3*h**2 + 2*h - 2/3 - 2/3*h**5 + 2*h**4 = 0. What is h?
-1, 1
Find z, given that -z**2 + 3*z + 0 - 1/4*z**4 - 7/4*z**3 = 0.
-6, -2, 0, 1
Suppose 0 = -3*w + 3, 5*g + 2 = 3*w - 1. Suppose g = -34*u + 43*u. Factor -32/5*h**2 - 4/5*h**3 + u - 64/5*h.
-4*h*(h + 4)**2/5
Let a(t) = -15*t**3 - 368*t**2 + 11*t - 11. Let n(g) = -5*g**3 - 122*g**2 + 4*g - 4. Let o(c) = -4*a(c) + 11*n(c). Find p such that o(p) = 0.
-26, 0
Suppose -3*y = -x - 33 - 100, -2*x - 266 = -4*y. Let r = -125 - x. Suppose -20 + r*n - 4/5*n**2 = 0. Calculate n.
5
Let c(k) = -2*k - 5. Let y be c(-4). Let z(i) = i**3 - 24 + 2*i + 51 - 27 - i**2. Let x(q) = -2*q**3 - 3*q. Let f(h) = y*z(h) + 2*x(h). Let f(p) = 0. What is p?
-3, 0
Let n(p) be the second derivative of -2*p**7/21 + 4*p**6/15 + 6*p**5/5 - 4*p**4/3 - 26*p**3/3 - 12*p**2 + 119*p. Factor n(g).
-4*(g - 3)*(g - 2)*(g + 1)**3
Let b(j) = 4*j**4 + 7*j**3 - 4*j**2 + 3*j. Let q be 4/18 - 752/144. Let y(c) = 3*c**4 + 6*c**3 - 3*c**2 + 2*c. Let l(v) = q*y(v) + 4*b(v). Factor l(a).
a*(a - 2)*(a - 1)*(a + 1)
Let u(o) = -5*o**3 + 6*o**2 - 18*o + 5. Let a(s) = -22*s**3 + 24*s**2 - 73*s + 19. Let t(i) = 6*a(i) - 26*u(i). What is z in t(z) = 0?
-8, 1
Let v(f) be the first derivative of 1/15*f**3 + 0*f + 11 + 1/10*f**4 - 1/25*f**5 - 1/5*f**2. Suppose v(t) = 0. What is t?
-1, 0, 1, 2
Let v be (2 - 36/10)*((-1022)/56 + 18). Solve 8/5*w + 8/5 - 2/5*w**2 - v*w**3 = 0.
-2, -1, 2
Factor -8*k + 2*k**2 + 27*k - 21*k.
2*k*(k - 1)
Let x = -2084 - -2084. Let q(i) be the first derivative of 0*i - 1 + x*i**2 + 0*i**3 - 3/8*i**4. Factor q(l).
-3*l**3/2
Let d(r) be the third derivative of r**10/75600 - r**8/5040 + r**6/360 + 2*r**5/15 - 13*r**2. Let v(a) be the third derivative of d(a). Factor v(h).
2*(h - 1)**2*(h + 1)**2
Let o = -24 - -24. Suppose 5*m - 19 - 16 = o. Factor 7*y + 1 - m*y - y**2.
-(y - 1)*(y + 1)
Let k = 168/65 + -31/13. Determine o so that 1/5 - 1/5*o - k*o**2 + 1/5*o**3 = 0.
-1, 1
Let f = -115 - -119. Factor 13*c**3 - 12*c + 5*c**3 - 2*c**f - 16*c**2 + 18 - 6*c**3 + 0*c**4.
-2*(c - 3)**2*(c - 1)*(c + 1)
Let l = 91 - 89. Let p(a) be the first derivative of 0*a + 1/18*a**4 - l - 1/9*a**2 - 2/45*a**5 + 2/27*a**3. Factor p(y).
-2*y*(y - 1)**2*(y + 1)/9
Let y(z) be the second derivative of -1/12*z**3 - 5/72*z**4 - 1/120*z**5 + 0*z**2 + 1/180*z**6 + 0 + 30*z. Let y(g) = 0. Calculate g.
-1, 0, 3
Let b(x) = x**2 - 26. Let y be b(-6). Let q be (y/(-15))/((-2)/9). Determine j, given that 0*j + 6/7*j**3 + 0 + 3/7*j**2 - q*j**4 + 12/7*j**5 = 0.
-1/4, 0, 1
Factor 12*b + 0*b + 432*b**2 + 46 - 10 - 219*b**2 - 212*b**2.
(b + 6)**2
Let j(f) = 84*f**2 - 124*f. Let q(d) = 20*d - 16*d**2 + 3*d**2 - d. Let g(h) = -5*j(h) - 32*q(h). Factor g(s).
-4*s*(s - 3)
Find f, given that -10 + 13*f - 48*f**2 - 39*f**2 - f**3 + 85*f**2 = 0.
-5, 1, 2
Let b(r) = 8*r**2 - 82*r - 10. Let u(z) = 9*z**2 - 84*z - 12. Let w(j) = 6*b(j) - 5*u(j). Solve w(g) = 0 for g.
0, 24
Let h(o) be the third derivative of -o**8/8400 + o**6/900 + o**4/24 + 13*o**2. Let x(f) be the second derivative of h(f). Solve x(v) = 0 for v.
-1, 0, 1
Let a(w) = -w**4 - 3*w**3 + 3*w**2 + w. Let h(t) = -t**4 + t**3 - t**2 + t. Suppose 3*m + 26 - 23 = 0. Let x(j) = m*h(j) - a(j). Factor x(s).
2*s*(s - 1)*(s + 1)**2
Let c = 1/643 + 1921/5144. Find t, given that -3/4 + c*t**2 - 3/8*t = 0.
-1, 2
Suppose -20*f = -31*f. Let k(q) be the third derivative of 1/120*q**6 - 1/180*q**5 + 0*q - 2*q**2 + 1/18*q**3 - 1/24*q**4 + f. Solve k(w) = 0 for w.
-1, 1/3, 1
Let v(l) = 66 + 4*l**2 + 4*l**3 - 4*l + 59 - 129. Let m(r) = 4*r**3 + 4*r**2 - 3*r - 3. Let t(q) = -4*m(q) + 3*v(q). Factor t(p).
-4*p**2*(p + 1)
Let m(i) = -i**3 + 7*i. Let l be m(3). Let p be 20/132 - l/33. Factor -5/3*o**2 - 7/3*o**4 + 0 - 3*o**3 - 2/3*o**5 - p*o.
-o*(o + 1)**3*(2*o + 1)/3
Solve -15 + 15 + 3*h**5 - 8*h**2 + 3*h**4 - 4*h**2 - 5*h**3 - 7*h**3 = 0.
-2, -1, 0, 2
Let r(f) = -f**5 + f**4 + f**3 - f**2 + f - 1. Let i(d) = 8*d**5 - 5*d**4 + 57*d**3 + 97*d**2 + 14*d + 21. Let t(q) = 4*i(q) + 68*r(q). Solve t(c) = 0.
-1, -1/3, 4
Let l = -89 - -629/7. Let n = 1349/5 + -9398/35. Let -9/7*u**3 + 3/7*u**4 + n*u + 3/7*u**2 - l = 0. What is u?
-1, 1, 2
Let o(u) = 7*u**4 - 28*u**3 + 67*u**2 - 60*u + 24. Let d(z) = -z**4 - z**3 - z**2 - 2. Let a(v) = -2*d(v) - o(v). Solve a(f) = 0 for f.
1, 2
Suppose z - 7 = -2*m, -5*m + 2*z + 4 = -0*m. Find x, given that -8 - 7*x + 10*x**2 + 7*x + m*x**2 - 20*x = 0.
-1/3, 2
Factor -236 + 224 + 38*w**3 - 41*w**3 + 9*w**2.
-3*(w - 2)**2*(w + 1)
Let z(k) be the third derivative of -k**7/420 + 17*k**6/240 + k**5/120 - 17*k**4/48 + 254*k**2. Solve z(o) = 0 for o.
-1, 0, 1, 17
What is g in 18*g**2 - 28/3*g**3 + 10/9*g**4 + 8/3 - 112/9*g = 0?
2/5, 1, 6
Let f = 4 + 5. Suppose 3*a + 5*x + f = 0, 4*x + 8 = a - 3*a. Factor a*j**4 - 6*j**2 - 4 + 12*j - 2*j - 2*j**3 + 0*j**2.
2*(j - 1)**3*(j + 2)
Let s(t) = t**2 + 6*t - 21. Let v be s(3). Factor 14*q**2 - v*q**2 - 3*q**2 - 2*q**2.
3*q**2
Let b be (-10)/(-55)