t q(h) be the first derivative of h**6/135 + h**5/90 + h + 2. Let c(d) be the first derivative of q(d). Factor c(z).
2*z**3*(z + 1)/9
Let b(g) = -19*g**5 - 11*g**4 + g**3 + 11*g**2 + 18*g - 13. Let d(n) = -9*n**5 - 6*n**4 + 6*n**2 + 9*n - 6. Let p(v) = 6*b(v) - 13*d(v). Factor p(t).
3*t*(t - 1)*(t + 1)**2*(t + 3)
Let x(c) be the third derivative of -c**5/180 - 13*c**4/72 + 38*c**2. Factor x(f).
-f*(f + 13)/3
Let d = 515341/210 - 2454. Let i(m) be the second derivative of 0*m**4 + 0*m**2 - 3*m + 0*m**6 - d*m**7 + 1/100*m**5 + 0 + 0*m**3. Factor i(r).
-r**3*(r - 1)*(r + 1)/5
Let t be (-22)/(-8) - (-12)/(-16). Let p = 2 + -2. Factor 2/9 + p*o - 2/9*o**t.
-2*(o - 1)*(o + 1)/9
Let j(m) be the first derivative of -2*m**3/27 + 2*m**2/9 - 2*m/9 - 6. Factor j(p).
-2*(p - 1)**2/9
Let y(u) be the first derivative of 0*u**3 + 0*u + 0*u**2 - 5 + 2/65*u**5 + 1/13*u**4 - 1/39*u**6. Factor y(l).
-2*l**3*(l - 2)*(l + 1)/13
Let c(p) be the second derivative of p + p**3 - 1/10*p**5 - 2*p**2 + 0*p**4 + 0. Factor c(i).
-2*(i - 1)**2*(i + 2)
Let o = 4 + -1. Suppose -2*d - 5*i + 1 = 5, 3*d - 3 = -o*i. Factor -2*z**2 + z**2 + d*z**2 - 3*z**2.
-z**2
Let u be (10/5 - 0) + (-4)/2. Determine g, given that 10/3*g**3 + u - 8/3*g**5 - 2*g**2 + 2*g**4 - 2/3*g = 0.
-1, -1/4, 0, 1
Let k = 18 + -10. Let g be ((-4)/(-12))/(k/12). Factor 0*o - g*o**2 - 1/2*o**4 + 0 + o**3.
-o**2*(o - 1)**2/2
Let y(p) = 5*p**2 - 15*p + 10. Let w(d) = d - 1. Let h(z) = -10*w(z) - y(z). Factor h(o).
-5*o*(o - 1)
Let b(z) be the third derivative of -z**5/30 + z**4/3 - 4*z**3/3 + 13*z**2. Determine q, given that b(q) = 0.
2
Let b(t) be the third derivative of t**10/201600 + t**9/120960 - t**8/80640 + t**5/30 + 3*t**2. Let v(z) be the third derivative of b(z). Factor v(g).
g**2*(g + 1)*(3*g - 1)/4
Let y(p) be the second derivative of p**5/110 + 5*p**4/66 + 2*p**3/11 - 14*p. Solve y(n) = 0 for n.
-3, -2, 0
Let i(m) be the first derivative of -m**3/21 + m**2/14 - 5. Let i(y) = 0. What is y?
0, 1
Determine m, given that -9*m**2 - 25*m**3 + 4*m**2 - 55*m**4 + 15*m**2 - 20*m**5 = 0.
-2, -1, 0, 1/4
Let z be 10/12 + 10/60. Let h(v) be the first derivative of 0*v**2 + z + 0*v + 1/16*v**4 - 1/12*v**3. Factor h(a).
a**2*(a - 1)/4
Suppose a + a = 4. Factor -a*x + 0 + 3 - x**2 + 0 + 0*x**2.
-(x - 1)*(x + 3)
Let h be (6/10)/((-1)/5). Let y(b) = 3*b**2 - 3. Let x(z) = 3*z**2 + z - 2. Let f(q) = h*x(q) + 2*y(q). Determine v, given that f(v) = 0.
-1, 0
Let z(n) be the third derivative of -n**8/504 - n**7/105 - n**6/180 + n**5/30 + n**4/18 + 13*n**2. What is k in z(k) = 0?
-2, -1, 0, 1
Let n(m) be the first derivative of 2*m**5/17 - 12*m**4/17 + 70*m**3/51 - 12*m**2/17 - 8*m/17 - 20. Determine f so that n(f) = 0.
-1/5, 1, 2
Let r(w) be the second derivative of -w**6/15 + w**4/2 - 2*w**3/3 + 27*w. Factor r(h).
-2*h*(h - 1)**2*(h + 2)
Let t(l) be the third derivative of 1/60*l**5 + 0*l + 1/6*l**3 + 2*l**2 + 1/12*l**4 + 0. Factor t(r).
(r + 1)**2
Suppose 5*g + 4*r - 30 = -r, -3*r = 5*g - 32. Let i be -1*(0 - -2) + 2. Factor 6*u**2 - 1 + i - g*u**2 - 2*u.
-(u + 1)**2
Let r(f) be the second derivative of -f**7/2520 - f**6/1440 - f**4/4 - 4*f. Let x(d) be the third derivative of r(d). Suppose x(w) = 0. Calculate w.
-1/2, 0
Factor -14/13*v**2 - 18/13 + 30/13*v + 2/13*v**3.
2*(v - 3)**2*(v - 1)/13
Let s(v) be the second derivative of 5/168*v**7 - 7/80*v**5 + 1/40*v**6 - 1/16*v**4 + 0 + 1/12*v**3 + 3*v + 0*v**2. Let s(x) = 0. Calculate x.
-1, 0, 2/5, 1
Let s be (-6)/3*42/4. Let c be (s + 20)*1/(-5). Factor -2/5*i + 1/5*i**2 + c.
(i - 1)**2/5
Let z(w) be the first derivative of 2 + 0*w**2 + 0*w + 2/15*w**5 + 2/9*w**3 + 1/3*w**4. Find c such that z(c) = 0.
-1, 0
Solve -24*r**3 - 2*r**3 + 4*r + 5*r**3 + 15*r**2 + 2*r = 0 for r.
-2/7, 0, 1
Suppose -5*r - 2*d = -5, 0*r = 4*r - 4*d - 32. Let w(v) be the first derivative of 0*v**r + 0*v**2 - 3 - 1/4*v**4 + 0*v. Solve w(l) = 0 for l.
0
Let s(n) be the third derivative of n**5/240 + n**4/96 + n**2. Solve s(d) = 0.
-1, 0
Factor -2/5 + 1/5*i + 1/5*i**2.
(i - 1)*(i + 2)/5
Let j(q) be the first derivative of q**6/8 - 3*q**4/4 - q**3/2 + 9*q**2/8 + 3*q/2 - 5. Find i, given that j(i) = 0.
-1, 1, 2
Let l be 3 + (-175)/20 - -6. Factor 1/4*g**2 + 0*g - l.
(g - 1)*(g + 1)/4
Factor -1/6*y + 1/6*y**2 - 1/6 + 1/6*y**3.
(y - 1)*(y + 1)**2/6
Let a(i) be the third derivative of i**6/420 - i**4/84 - i**2. Let a(u) = 0. Calculate u.
-1, 0, 1
Let i = 6/97 - 320/2037. Let m = 29/84 + i. Factor 1/4*s - 1/2*s**3 - 1/4 - 1/4*s**4 + 1/2*s**2 + m*s**5.
(s - 1)**3*(s + 1)**2/4
Suppose 0 + 9/4*c - 3/8*c**2 = 0. What is c?
0, 6
Let g(k) be the second derivative of 0 + 1/21*k**7 - 1/6*k**4 + 0*k**3 - 1/10*k**5 + 0*k**2 - k + 1/15*k**6. Factor g(n).
2*n**2*(n - 1)*(n + 1)**2
Factor -3*t + 9*t**3 - 3 + 92*t**2 - 6*t - 89*t**2.
3*(t - 1)*(t + 1)*(3*t + 1)
Let q(h) be the second derivative of -h**6/10 + 3*h**5/10 + h**4/4 - h**3 - 8*h. Find p, given that q(p) = 0.
-1, 0, 1, 2
Let d(i) = -9*i**3 + 15*i**2 - 13*i - 4. Let v(x) = -5*x**3 + 8*x**2 - 7*x - 2. Let b(o) = 6*d(o) - 11*v(o). Factor b(u).
(u - 1)*(u + 1)*(u + 2)
Let r(z) = z**2 - 11*z + 2. Let v be r(11). Let j = 4 - 0. Factor s**4 + s**3 + 2*s**2 - j*s**v + 1 - s**5 + s**3 - s.
-(s - 1)**3*(s + 1)**2
Suppose 4*t = 3*u - 25, -4*u - t + 52 = 3*t. Let n be 3/9 - u/(-3). Factor -2*j + 5*j**2 - 4*j**n - 3*j**5 + 5*j**5 - j**2.
2*j*(j - 1)**3*(j + 1)
Let c(m) = -m**2 - 7*m - 10. Let x be c(-4). Let 2/7*b + 0 - 2/7*b**x = 0. What is b?
0, 1
Let k(j) = -153*j**2 - 84*j - 18. Let u(z) = -152*z**2 - 84*z - 17. Suppose 4*x = 6*x - 12. Let y(q) = x*u(q) - 5*k(q). Find i such that y(i) = 0.
-2/7
Let a = 173/252 + -5/252. Factor 10/9*j - a*j**2 - 4/9.
-2*(j - 1)*(3*j - 2)/9
Let i be (9 - 1 - 4)*1. Suppose 0 = 2*f + 14 - 4, i*h + 2*f + 2 = 0. Determine b, given that 2/9*b**h + 0*b + 0 + 2/9*b**3 = 0.
-1, 0
Let k = -75 - -51. Let b be (-1)/((-4)/k*-3). Suppose 4/3*x**3 + 0*x**b - 2/3*x**4 - 4/3*x + 2/3 = 0. Calculate x.
-1, 1
Let n be ((-5)/(-225))/(4/5). Let w(u) be the second derivative of 2*u + 1/6*u**2 - 1/9*u**3 + 0 + n*u**4. Let w(z) = 0. Calculate z.
1
Let y be (-26)/39*(-102)/4. Factor z + 11*z**3 + 5*z**3 - y*z**3.
-z*(z - 1)*(z + 1)
Let v(d) be the second derivative of -d**5/20 - 3*d**4/8 - d**3 + 3*d**2/2 + 7*d. Let n(x) be the first derivative of v(x). Factor n(o).
-3*(o + 1)*(o + 2)
Let g be (150/20)/(-3)*6/(-20). Suppose -3/4*f**2 + 3/4*f**3 + g - 3/4*f = 0. Calculate f.
-1, 1
Let s(u) be the third derivative of -u**7/1575 - u**6/900 + u**5/50 - 11*u**4/180 + 4*u**3/45 + 43*u**2. Solve s(l) = 0.
-4, 1
Suppose -17678*s + 17678*s + 4*s**3 + 8*s**2 = 0. What is s?
-2, 0
Let 4 - 2*k - 4 - 2*k**3 + 0*k**3 - 4*k**2 = 0. What is k?
-1, 0
Let l be 33*4*3/9. Let r = l + -40. Solve -2/3*y**r + 0 + 0*y + 0*y**3 + 2/3*y**2 = 0.
-1, 0, 1
Let m be (-5)/2*(-4)/5. Factor -4*i**3 - i**5 + 6*i**2 - 2*i**4 + 3*i**3 - 6*i**m.
-i**3*(i + 1)**2
Factor 0 - 2/5*k**3 - 4/5*k**2 - 2/5*k.
-2*k*(k + 1)**2/5
Let w(b) be the third derivative of 0*b - 3*b**2 + 7/240*b**6 + 0 + 2/15*b**5 + 11/48*b**4 + 1/6*b**3. Find p such that w(p) = 0.
-1, -2/7
Let h(l) = -l**4 - 5*l**3 - l**2 - l - 2. Let k(y) = 2*y**4 + 11*y**3 + y**2 + 2*y + 5. Let j = 10 - 6. Let o(n) = j*k(n) + 10*h(n). Factor o(d).
-2*d*(d + 1)**3
Suppose 4*w = -3*o + 17 + 57, 2*w - 10 = 0. Determine f so that 0*f**4 + o*f**3 - 4*f**4 - 10*f**3 - 4*f**2 = 0.
0, 1
Let u(d) be the second derivative of -1/15*d**4 + 2/15*d**3 + 0 + 4/5*d**2 - 3*d. Determine g so that u(g) = 0.
-1, 2
Factor -3*t - 3/2*t**2 + 12.
-3*(t - 2)*(t + 4)/2
Let k = -282 - -136. Let z be k/(-20) - (-3)/(-6). Suppose 16/5*n + 8/5*n**5 + 56/5*n**3 - z*n**4 - 44/5*n**2 - 2/5 = 0. What is n?
1/4, 1
Let p(r) be the second derivative of r**7/98 + r**6/70 - 3*r**5/70 + 21*r. Factor p(i).
3*i**3*(i - 1)*(i + 2)/7
Let m(w) be the third derivative of -w**8/1680 + w**7/350 - w**6/300 - 11*w**2. Determine a, given that m(a) = 0.
0, 1, 2
Determine p so that -1/5 - 1/5*p**2 - 2/5*p = 0.
-1
Let v(k) = -k**2 - 3*k - 2. Let x be v(-1). Factor -1/6*d**4 + 1/6*d**2 + x*d + 0 + 0*d**3.
-d**2*(d - 1)*(d + 1)/6
Factor 8/11*k**2 + 2/11*k**3 + 8/11*k + 0.
2*k*(k + 2)**2/11
Let g(k) be the second derivative of k**5/60 - k**4/18 + k**3/18 + k. Factor g(w).
w*(w - 1)**2/3
Let n(a) be the