50*o**5. Let m(l) be the first derivative of x(l). Factor m(i).
2*i*(i + 1)**2/5
Let p(h) be the second derivative of 3*h + 1/6*h**3 + 0 - 1/24*h**4 + 0*h**2. Let p(g) = 0. Calculate g.
0, 2
Let h(f) be the first derivative of 7*f**4/2 + 46*f**3/3 - 22*f**2 - 16*f + 3. Factor h(x).
2*(x - 1)*(x + 4)*(7*x + 2)
Let a(y) = y**2 - 5*y + 4. Let h be a(4). Factor h - w**2 + 1/4*w.
-w*(4*w - 1)/4
Let n = -844 + 4228/5. Let n*c - 12/5*c**2 + 0 = 0. What is c?
0, 2/3
Let 14/9*i**2 + 0 + 4/9*i**3 + 4/9*i - 2/3*i**4 = 0. What is i?
-1, -1/3, 0, 2
Let b(f) be the second derivative of 4*f + 1/9*f**3 + 0*f**2 + 0 - 1/18*f**4. Let b(n) = 0. Calculate n.
0, 1
Let z = 3 + 2. Let m = z - 1. Solve g**3 - g + 0*g**4 - g**2 - 5*g**4 + m*g**4 + 2*g**4 = 0.
-1, 0, 1
Let -96/7*q**5 - 64/7*q**4 + 68/7*q**2 + 102/7*q**3 - 6/7*q - 4/7 = 0. What is q?
-1, -2/3, -1/4, 1/4, 1
Factor 38/3*j**2 + 8/3 + 1/3*j**5 + 25/3*j**3 + 28/3*j + 8/3*j**4.
(j + 1)**2*(j + 2)**3/3
Let s(c) = -c + 2. Let p be s(1). Factor y**2 + p + 3*y**2 - y + 3*y - 3*y**2.
(y + 1)**2
Let r(v) be the second derivative of 3*v**5/16 - 3*v**4/16 - v**3/4 - 6*v. Factor r(s).
3*s*(s - 1)*(5*s + 2)/4
Let h(b) = -5*b**3 - b**2 + 6*b + 6. Let p(k) = -9*k**3 - 2*k**2 + 11*k + 11. Let i(n) = 11*h(n) - 6*p(n). Factor i(l).
-l**2*(l - 1)
Factor -4*f + 20*f**2 - 45*f - 5*f**3 + 10 + 24*f.
-5*(f - 2)*(f - 1)**2
Let y(r) = r**2 + r - 1. Let b be (2/6)/((-2)/(-12)). Let i(p) = -b*p + 2*p**2 - 2*p + 5 - 6*p**2. Let c(g) = -i(g) - 5*y(g). Factor c(d).
-d*(d + 1)
Let n be (77/28)/(-11)*0. Find c, given that -3/2*c**2 + n + c + 1/2*c**3 = 0.
0, 1, 2
Suppose -3*j + 3 = -3. Let s(d) be the third derivative of 0*d - 11/72*d**4 + 1/9*d**3 + 1/12*d**5 + 0 + j*d**2. Let s(l) = 0. Calculate l.
1/3, 2/5
Let w(k) be the first derivative of k**4/8 + k**3/3 - k**2/4 - k + 4. Factor w(b).
(b - 1)*(b + 1)*(b + 2)/2
Let v(o) be the third derivative of o**5/300 + 7*o**4/120 - 4*o**3/15 - 23*o**2. Factor v(k).
(k - 1)*(k + 8)/5
Factor -1/3*w**4 - 2/3*w**3 + 7/3*w**2 + 0 - 4/3*w.
-w*(w - 1)**2*(w + 4)/3
Let v(z) = 2*z**5 - z**4 - 5*z**3 - 5*z. Let s(g) = g**5 - 2*g**4 - 4*g**3 - 4*g. Let r(f) = 5*s(f) - 4*v(f). Find w, given that r(w) = 0.
-2, 0
Factor -4*c**2 - 4/3*c + 8/3 + 4/3*c**3 + 4/3*c**4.
4*(c - 1)**2*(c + 1)*(c + 2)/3
Suppose 0*z - 10 = -2*z. Suppose -u - 3*s + z*s = 1, 5*u + 3*s = 21. Factor -1/3*h - 2/3*h**2 + 2/3 + 1/3*h**u.
(h - 2)*(h - 1)*(h + 1)/3
Let j(q) be the third derivative of 2*q**7/21 + 14*q**6/15 + 16*q**5/5 + 8*q**4/3 - 32*q**3/3 + 19*q**2. Factor j(h).
4*(h + 2)**3*(5*h - 2)
Let h = 32 - 30. Let m(z) be the first derivative of -2*z - z**2 + 2/3*z**3 + 1/2*z**4 + h. Determine i so that m(i) = 0.
-1, 1
Let u(h) be the second derivative of -h**6/240 - h**5/60 - 2*h**2 + 2*h. Let j(c) be the first derivative of u(c). Solve j(a) = 0 for a.
-2, 0
Let o(y) be the first derivative of 9*y**6/10 + 36*y**5/25 - 3*y**4/10 - 4*y**3/5 + 3*y**2/10 + 13. Factor o(g).
3*g*(g + 1)**2*(3*g - 1)**2/5
Let c(m) = -4*m**2 - 10*m + 1. Let s(w) = 3*w**2 + 7*w - 1. Let l = 17 + -12. Let o(x) = l*c(x) + 7*s(x). Factor o(k).
(k - 2)*(k + 1)
Let r(h) be the first derivative of h**3/2 + 3*h**2/8 - 3*h/4 - 5. Factor r(f).
3*(f + 1)*(2*f - 1)/4
Let h be ((-42)/(-30))/(-6*(-5)/90). Find g such that h*g**4 - 3/5*g**2 + 6/5*g**3 + 0 + 0*g + 12/5*g**5 = 0.
-1, 0, 1/4
Let c(p) be the first derivative of -1/6*p**4 + 0*p**2 + 0*p**3 + 3 - 2/15*p**5 + 0*p. Solve c(q) = 0 for q.
-1, 0
Suppose -2*d - 36 = -5*d. Factor -10*r**2 - 3*r**3 + 2*r**3 + 3*r**3 + d*r**2.
2*r**2*(r + 1)
Let o = 13 + -6. Determine v so that o + 3*v**4 - 5 - 4*v**2 - v**4 = 0.
-1, 1
Let y(o) be the first derivative of o**6/18 + o**5/5 + o**4/4 + o**3/9 + 18. Find i such that y(i) = 0.
-1, 0
Let q(j) be the third derivative of j**8/60480 + j**7/7560 + j**5/12 - 5*j**2. Let s(n) be the third derivative of q(n). Let s(o) = 0. Calculate o.
-2, 0
Factor -7*g - 2*g**4 + 17*g - 10*g - 2*g**5.
-2*g**4*(g + 1)
Let u(j) be the second derivative of j**5/20 + 11*j**4/36 + j**3/3 + 9*j. Factor u(z).
z*(z + 3)*(3*z + 2)/3
Let m(s) = s**4 - s**3 - s**2 + s. Let a(b) = 3*b**4 - 12*b**3 - 19*b**2 + 12*b + 16. Let c(v) = a(v) - 4*m(v). Find q, given that c(q) = 0.
-4, -1, 1
Let n = -3 + 12. Suppose n = -i - 7*z + 4*z, -2*i - 5*z - 15 = 0. Factor -2*y**2 - 1/2*y - 3/2*y**3 + i.
-y*(y + 1)*(3*y + 1)/2
Let b be (3 + 0)/(3/12). Let o = b + -10. Determine w, given that 1/2*w + 0 + 3/4*w**o = 0.
-2/3, 0
Let i(j) be the first derivative of -3*j**4/8 + j**3 + 3*j**2/4 - 3*j + 2. Let i(b) = 0. Calculate b.
-1, 1, 2
Let u be (3/(-2))/(7/(-14)). Let 18*x**4 - 12*x**2 - 5 - 8 + 21*x - 21*x**u + 7 = 0. What is x?
-1, 1/2, 2/3, 1
Let h(d) be the second derivative of -7*d**6/900 - 19*d**5/300 + d**4/10 + d**3/3 + d. Let u(m) be the second derivative of h(m). Solve u(r) = 0.
-3, 2/7
Factor 6*c + 9/2*c**2 + 2.
(3*c + 2)**2/2
Let q(v) = -v**3 + v**2 + 4*v - 4. Let i(u) = -6*u**3 + 6*u**2 + 27*u - 27. Let s(g) = -4*i(g) + 27*q(g). Suppose s(h) = 0. What is h?
0, 1
Let c(x) be the second derivative of x**4/12 - x**3 + x**2 + x. Let m be c(6). Factor 0*i**3 - 5*i**m - i**3 + 4*i**2.
-i**2*(i + 1)
Factor 0 - 8/5*f - 4/5*f**2.
-4*f*(f + 2)/5
Let o(l) = -2*l + 26. Let a be o(13). Let c(f) be the third derivative of 0*f - 1/210*f**5 + a + 3*f**2 + 0*f**3 - 1/84*f**4. Factor c(v).
-2*v*(v + 1)/7
Let j(s) be the first derivative of -s**8/5040 + s**7/1260 + s**6/360 - s**5/90 - s**4/18 - 8*s**3/3 + 8. Let y(f) be the third derivative of j(f). Factor y(z).
-(z - 2)**2*(z + 1)**2/3
Let d(o) = o**5 - o**4 + o**2 - o + 1. Let c(h) = -6*h**5 + 10*h**4 - 7*h**3 - 2*h**2 + 5*h - 5. Let y(m) = -2*c(m) - 10*d(m). Factor y(p).
2*p**2*(p - 3)*(p - 1)**2
Suppose -2*n + 6 = -n. Let b(s) be the third derivative of 1/140*s**n + 0*s + 0*s**4 + 0*s**3 - s**2 + 1/105*s**5 + 1/735*s**7 + 0. Factor b(j).
2*j**2*(j + 1)*(j + 2)/7
Let w(k) = k**3 - k**2 + k - 1. Let t(q) = -4*q**3 - 3*q**2 - 15*q - 5. Let b(d) = 4*t(d) + 12*w(d). Determine r so that b(r) = 0.
-2
Suppose -2*j - 3 = f - 0, -f - 5 = 0. Let u(g) be the first derivative of 2/7*g + 2/7*g**2 + 2/21*g**3 + j. Solve u(n) = 0 for n.
-1
Let d(w) be the first derivative of w**3/27 - 2*w**2/9 + 19. Factor d(s).
s*(s - 4)/9
Let h(i) be the second derivative of -i**4/72 + i**3/12 - i**2/6 - 8*i. Factor h(s).
-(s - 2)*(s - 1)/6
Let s(i) be the third derivative of 0*i - 1/3*i**3 + 3*i**2 + 1/60*i**6 + 0 + 1/4*i**4 - 1/10*i**5. Factor s(w).
2*(w - 1)**3
Let h be 36/(-8)*(-1)/(6/4). Factor 2/5*s**h - 2/5*s**2 + 0 + 2/5*s**4 - 2/5*s.
2*s*(s - 1)*(s + 1)**2/5
Let z(h) = 10*h**2 - 15*h - 5. Let w(k) = -5*k**2 + 7*k + 2. Let a(v) = -5*w(v) - 2*z(v). Let a(i) = 0. What is i?
0, 1
Let o(h) = -h + 16. Let g be o(14). Let u(w) be the first derivative of -g + 1/6*w**3 + 0*w + 1/8*w**4 + 0*w**2. Factor u(x).
x**2*(x + 1)/2
Let u(j) be the second derivative of -j**7/42 + j**6/15 + j**5/10 - j**4/3 - j**3/6 + j**2 - 9*j. Let u(w) = 0. What is w?
-1, 1, 2
Let f be (-1)/4*(-130)/(-30). Let p = f - -89/60. Factor 0 + p*m**5 + 0*m + 4/5*m**4 + 2/5*m**3 + 0*m**2.
2*m**3*(m + 1)**2/5
Let o(a) = -a**3 + 5*a**2 - 7*a + 5. Let h(t) = -2*t**3 + 10*t**2 - 14*t + 11. Let f(p) = 4*h(p) - 10*o(p). Let f(g) = 0. What is g?
1, 3
Let o(u) be the second derivative of -u**7/210 - u**6/30 - u**5/25 + 4*u**4/15 + 16*u**3/15 + 8*u**2/5 - 3*u. Factor o(q).
-(q - 2)*(q + 1)*(q + 2)**3/5
Let t(r) = -r**5 + r**4 - r**3 - r**2. Let h(n) = 6*n**5 + 10*n**4 - 30*n**3 + 50*n**2 - 20*n + 4. Let u(a) = h(a) + 10*t(a). Factor u(v).
-4*(v - 1)**5
Let i(c) = -2*c**2 - 2*c + 12. Let f(b) = 1. Let k(j) = 12*f(j) - i(j). Factor k(y).
2*y*(y + 1)
Let h(t) be the second derivative of -t**7/7560 - t**6/2160 - 5*t**4/12 + 5*t. Let n(o) be the third derivative of h(o). Factor n(s).
-s*(s + 1)/3
Factor 1/6*s**4 - 1/6*s**3 + 1/3 + 1/6*s - 1/2*s**2.
(s - 2)*(s - 1)*(s + 1)**2/6
Let l(s) be the second derivative of 0 - 1/48*s**4 + 1/8*s**3 - 1/4*s**2 + 4*s. Let l(o) = 0. Calculate o.
1, 2
Suppose 3*q - 16 = 8. Let u be ((-10)/q)/((-3)/12). Determine t, given that 8/9 + 20/9*t**3 + 2*t**4 - 38/9*t**2 - 8/3*t - 8/9*t**u = 0.
-1, 1/4, 2
Let k = -495015/44 - -11251. Let a = k - -1/132. Factor -2/3*p**2 - a - 4/3*p.
-2*(p + 1)**2/3
Let s be (-1)/(-20) + 1/4. L