 z(f) be the first derivative of -f + 1/10*f**2 + 1/20*f**4 + 3 - 1/100*f**5 - 1/10*f**3. Let u(v) be the first derivative of z(v). Factor u(r).
-(r - 1)**3/5
Factor 6/19 + 10/19*j**2 + 2/19*j**3 + 14/19*j.
2*(j + 1)**2*(j + 3)/19
Let g(q) be the third derivative of 2*q**7/315 - q**6/90 + 10*q**2. Factor g(i).
4*i**3*(i - 1)/3
Factor 16*z**4 - 8*z**3 + 41*z**5 - 12*z**3 - 23*z**5 + 8*z**2 - 22*z**5.
-4*z**2*(z - 2)*(z - 1)**2
Let j = -41 - -206/5. Let i(n) be the first derivative of -j*n**5 - 2 - 1/6*n**6 + 0*n**2 + 0*n + 1/4*n**4 + 1/3*n**3. Factor i(o).
-o**2*(o - 1)*(o + 1)**2
Let b(y) = -2*y**2 + 2 - 2*y + 0*y - 3. Let n be b(-1). Let a(k) = -k**2. Let f(w) = -3*w**2 + 4*w - 1. Let q(o) = n*f(o) - a(o). Factor q(s).
(2*s - 1)**2
Suppose 4/5*g**4 - 96/5*g + 4/5*g**2 + 64/5 + 24/5*g**3 = 0. What is g?
-4, 1
Let h(z) = 3*z + 4. Let w be h(-5). Let a be w/(-3) + 2/6. Suppose 2*r + 5*r**4 + 2*r**5 + 3*r**a + 12*r**3 + 8*r**2 + 0*r**2 = 0. What is r?
-1, 0
Let k be (-1371)/(-36) - 3/(-12). Let a = k - 36. Factor -4*p**2 + 0 - a*p**3 + 4/3*p.
-p*(p + 2)*(7*p - 2)/3
Let w(b) be the third derivative of 0*b**3 + 4*b**2 + 0*b + 0*b**5 + 0 + 0*b**4 - 1/105*b**7 + 1/60*b**6. Suppose w(x) = 0. Calculate x.
0, 1
Let m(l) be the second derivative of -1/600*l**6 - 9/40*l**4 - l**2 + 3/100*l**5 - l + 9/10*l**3 + 0. Let i(n) be the first derivative of m(n). Solve i(c) = 0.
3
Let d(t) be the third derivative of t**9/3780 + t**8/6720 - t**7/630 - t**6/720 + t**4/8 + 7*t**2. Let q(v) be the second derivative of d(v). Factor q(l).
l*(l - 1)*(l + 1)*(4*l + 1)
Determine l so that 0 - 4/9*l**2 - 14/9*l**5 - 4/9*l - 11/9*l**4 + 11/3*l**3 = 0.
-2, -2/7, 0, 1/2, 1
Let x(p) = -p**4 + p**3 - p**2 + p + 1. Let t(i) = -3*i**5 + 6*i**4 - 12*i**3 - 30*i**2 + 39*i + 12. Let g(h) = -t(h) + 12*x(h). Factor g(l).
3*l*(l - 3)**2*(l - 1)*(l + 1)
Let s(a) = -7 + 0*a**3 + 5*a**3 + 2*a - a + a. Let y(c) = -3*c**3 - c + 4. Let o(k) = 4*s(k) + 7*y(k). Factor o(h).
-h*(h - 1)*(h + 1)
Let s(l) be the second derivative of -2*l + 0 + 9/2*l**3 + 1/2*l**2 + 1/20*l**5 - 3/4*l**4. Let m(w) be the first derivative of s(w). Solve m(b) = 0 for b.
3
Let l be -6*((-2)/84)/(10/40). What is h in 6/7*h**2 + 2/7*h**3 + 0 + l*h = 0?
-2, -1, 0
Let t(o) be the first derivative of -o**6/9 - 4*o**5/15 - o**4/6 - 7. Factor t(z).
-2*z**3*(z + 1)**2/3
Let a(j) be the second derivative of 7*j**4/72 + 4*j**3/9 + j**2/3 - 2*j. Let a(d) = 0. Calculate d.
-2, -2/7
Let j(y) be the second derivative of y**5/60 - y**4/6 + y**3/2 - 2*y**2/3 + 3*y. Factor j(t).
(t - 4)*(t - 1)**2/3
Let c(v) = -v**4 - v**2 - v. Let z(h) = -4*h**4 + 2*h**3 + 4*h**2 - 4*h - 4. Let j(w) = 2*c(w) - z(w). Factor j(k).
2*(k - 2)*(k - 1)*(k + 1)**2
Let m(x) be the third derivative of -x**6/120 + x**5/20 + 2*x**2. Let s be m(3). Suppose 0*c**3 - 6*c**2 + s*c**2 + 2*c**3 + 6*c - 2 = 0. Calculate c.
1
Suppose 4*i - 36 = 4*s, -s = -5*i - 3*s + 24. Suppose 5*j + 2*t - 12 - i = 0, t - 15 = -4*j. Let -z**3 - 3*z**j - 3*z**4 - z**5 + 4*z**4 = 0. Calculate z.
-1, 0
Let y = -6 - -11. Suppose y*o - o = 8. Factor -3*w**2 + 7*w**3 - 2*w + 0*w - 2*w**o.
w*(w - 1)*(7*w + 2)
Let n(l) = -6*l**3 + 6*l**2. Let b(f) = -6*f**3 + 7*f**2 - f. Suppose -4 = -2*v, 3*u + 0*v = -2*v + 19. Let h(p) = u*n(p) - 4*b(p). Factor h(t).
-2*t*(t - 1)*(3*t + 2)
Let n = -2/21 + 52/105. Let v = 10 + -10. Factor -n*s**2 + 4/5*s**3 + v + 0*s - 2/5*s**4.
-2*s**2*(s - 1)**2/5
Suppose -6*i = i - 14. Let h be (-6)/(-4 - -1) - i. Factor 2/7*s**2 - 2/7 + h*s.
2*(s - 1)*(s + 1)/7
Let m(c) be the first derivative of -25*c**4 + 20*c**3/3 + 32*c**2 + 16*c - 22. Factor m(d).
-4*(d - 1)*(5*d + 2)**2
Let i = 8/7 - 10/21. Let u(s) = s**2 + 29*s + 30. Let w be u(-28). Suppose i*j**w + 2/3*j**3 + 0*j + 0 = 0. What is j?
-1, 0
Let j(s) = s + 1. Let v be j(1). Suppose 8*y = v*y + 18. Suppose 4/3 - 2/3*k**2 + 2*k - 2/3*k**4 - 2*k**y = 0. Calculate k.
-2, -1, 1
Let m = -629 - -37741/60. Let n(f) be the third derivative of 1/3*f**3 + 0 + 0*f + 1/4*f**4 + m*f**6 + 1/10*f**5 - f**2. Find l such that n(l) = 0.
-1
Suppose -25*r = -35 - 65. Factor -1/4*v**3 + 0 + 1/4*v**r + 1/4*v - 1/4*v**2.
v*(v - 1)**2*(v + 1)/4
Let h(g) = 6*g**2 - 2*g - 10. Let t(q) = q**3 - q - 1. Let d(f) = 2*h(f) - 4*t(f). Factor d(s).
-4*(s - 2)**2*(s + 1)
Let o(k) = -1 - k**2 + 0 + 7 - 4*k. Let i be o(-6). Let r(n) = -n - 1. Let j(d) = -d**3 - d**2 - 5*d - 5. Let s(v) = i*r(v) + j(v). Factor s(b).
-(b - 1)*(b + 1)**2
Let k(m) be the third derivative of -m**7/42 + m**6/60 + m**5/12 - m**4/12 + 4*m**2. Factor k(i).
-i*(i - 1)*(i + 1)*(5*i - 2)
Let a(s) be the first derivative of 2*s**5/5 - 3*s**4/2 + 2*s**3/3 + 3*s**2 - 4*s + 6. Let a(i) = 0. Calculate i.
-1, 1, 2
Let q(s) = -6*s**2 + s. Let n(g) = -5*g**2 + g. Let i(j) = -7*n(j) + 6*q(j). Let h(w) = -w - 1. Let k(c) = -2*h(c) - 2*i(c). Factor k(d).
2*(d + 1)**2
Let g(q) be the second derivative of 5*q**4/12 + 25*q**3/18 + 5*q**2/3 - 15*q. Factor g(u).
5*(u + 1)*(3*u + 2)/3
Let n(w) be the second derivative of w**4/20 + 3*w**3/10 - w + 43. What is r in n(r) = 0?
-3, 0
Let b(l) = l**3 + l**2 - l. Let y(f) = -8*f**3 - 6*f**2 + 11*f - 4. Let s(q) = -21*b(q) - 3*y(q). Factor s(o).
3*(o - 2)*(o - 1)*(o + 2)
Let i be 68/400 + (-1)/(-12)*-2. Let c(m) be the third derivative of 0 + 0*m - 3*m**2 + 1/1050*m**7 - 1/600*m**6 + 1/120*m**4 + 0*m**3 - i*m**5. Factor c(a).
a*(a - 1)**2*(a + 1)/5
Let m(r) be the second derivative of -r**4/8 + 8*r. Factor m(q).
-3*q**2/2
Let n(h) be the second derivative of h**7/2520 + h**6/540 - h**5/360 - h**4/36 - 2*h**3/3 - 6*h. Let y(t) be the second derivative of n(t). Factor y(m).
(m - 1)*(m + 1)*(m + 2)/3
Let z(y) = -y**3 + 12*y**2 - 10*y + 7. Let u be z(11). Let o = u - 15. Factor -1/5*c + 3/5*c**o + 2/5 - 4/5*c**2.
(c - 1)**2*(3*c + 2)/5
Let t(i) be the third derivative of -i**8/2800 + i**7/1400 - 3*i**3/2 + i**2. Let r(u) be the first derivative of t(u). Factor r(y).
-3*y**3*(y - 1)/5
Let t(r) be the first derivative of 4*r**3/33 + 3*r**2/11 + 2*r/11 + 4. Find w, given that t(w) = 0.
-1, -1/2
Let t(n) be the first derivative of 0*n - 3 + 0*n**2 + 3/4*n**4 - 2/3*n**3. Let t(o) = 0. Calculate o.
0, 2/3
Let -2/3*t**3 + 0 - 8/3*t**2 - 8/3*t = 0. What is t?
-2, 0
Let v(t) be the third derivative of 1/120*t**6 - 1/60*t**5 + 0*t + 0 - 2*t**2 + 0*t**3 + 0*t**4. Let v(u) = 0. Calculate u.
0, 1
Let o = -336 - -2356/7. Factor -2/7*r**3 - 2/7*r + o*r**2 + 0.
-2*r*(r - 1)**2/7
Let o(q) = 6*q**2 + 4*q. Let k(h) be the third derivative of -h**5/12 - h**4/6 + 2*h**2. Let t(y) = -4*k(y) - 3*o(y). Solve t(z) = 0 for z.
-2, 0
Determine h so that 4*h**3 - 2*h**5 - 417*h**4 - 4*h**3 + 429*h**4 = 0.
0, 6
Let v(i) be the first derivative of -i**2 - 8*i - 1. Let m be v(-6). Factor 4*j**m + 2*j**5 - 4*j**2 + 0*j**2 - 2*j + 0*j.
2*j*(j - 1)*(j + 1)**3
Let p(y) be the first derivative of 3/4*y**4 + 0*y - 2*y**2 + 0*y**3 - 3 + 1/5*y**5. Factor p(c).
c*(c - 1)*(c + 2)**2
Let o = 8 + -2. Factor -o*y**3 - 5*y**5 - 5*y**4 + 2*y**5 + 14*y**4.
-3*y**3*(y - 2)*(y - 1)
Let h(j) = -4*j**2 - j - 5. Let v(o) be the first derivative of 2*o**3 + o**2/2 + 7*o - 4. Let b(z) = 7*h(z) + 5*v(z). Factor b(s).
2*s*(s - 1)
Factor 0 + 6*r**3 + 0*r + 6*r**4 + 3/2*r**2.
3*r**2*(2*r + 1)**2/2
Let z(d) = -3*d**5 - 26*d**4 - 43*d**3 - 41*d**2 - 5. Let k(t) = -15*t**5 - 129*t**4 - 216*t**3 - 204*t**2 - 24. Let o(f) = 5*k(f) - 24*z(f). Factor o(h).
-3*h**2*(h + 2)**2*(h + 3)
Let z be ((-12)/(-14))/(150/140). What is d in 4/5*d**3 + z*d**2 - 2/5*d - 2/5 - 2/5*d**5 - 2/5*d**4 = 0?
-1, 1
Let s be (-156)/(-42) + 4/14. Suppose 3*f + s*t = 12, 4*f + t - 3*t - 16 = 0. Factor 0*u - 4/9*u**2 + 2/9*u**f + 0*u**3 + 2/9.
2*(u - 1)**2*(u + 1)**2/9
Let n(b) = 25*b**3 - 12*b**2 - 10*b. Let p(t) = -50*t**3 + 23*t**2 + 20*t. Let i(u) = -7*n(u) - 3*p(u). Factor i(v).
-5*v*(v - 1)*(5*v + 2)
Suppose 0 = 3*l - 2*l. Let r be (8 - l)/4 - 0. Factor 8/5*s**r + 4/5 + 2/5*s**3 + 2*s.
2*(s + 1)**2*(s + 2)/5
Let o be 136/28 - (-6)/(-7). Factor -2/3*w**2 - 6 + o*w.
-2*(w - 3)**2/3
Solve 1/10*z + 3/10 - 3/10*z**2 - 1/10*z**3 = 0 for z.
-3, -1, 1
Let v(j) be the second derivative of j**7/2100 - j**6/450 - j**5/75 - j**4/6 - 2*j. Let i(m) be the third derivative of v(m). Suppose i(q) = 0. Calculate q.
-2/3, 2
Let o(a) be the third derivative of