 = 29 + -17. Let q be (c/16)/(1/4). Factor -2/3*a - 2/3*a**2 + 0 + 2/3*a**q + 2/3*a**4.
2*a*(a - 1)*(a + 1)**2/3
Let z(a) be the third derivative of -5/72*a**4 + 7/180*a**5 - 1/120*a**6 + 0 + 0*a + 3*a**2 + 1/18*a**3. Factor z(s).
-(s - 1)**2*(3*s - 1)/3
Let j = -24 - -12. Let i be j/10*(-15)/2. Factor -3 - i*o - 3*o**3 + 0*o**2 - 6*o**2 - 4*o**2 + o**2.
-3*(o + 1)**3
Factor 25*t**2 - t - 43*t**2 + 19*t**2 - 2.
(t - 2)*(t + 1)
Let k be (-2 - (-1 + -1))*1. Factor -2*o**5 + k*o**3 - 11*o**4 + 6*o**5 + 4*o**3 + 2*o**2 + o**3.
o**2*(o - 2)*(o - 1)*(4*o + 1)
Let v(y) be the second derivative of 9*y - 1/21*y**3 + 0 + 0*y**2 - 2/21*y**4. Factor v(n).
-2*n*(4*n + 1)/7
Let m(v) be the first derivative of -v**8/1680 - v**7/840 + v**3/3 - 3. Let o(d) be the third derivative of m(d). Factor o(i).
-i**3*(i + 1)
Let l(a) be the second derivative of -a**5/20 + 5*a**4/12 - 7*a**3/6 + 3*a**2/2 + 2*a. Factor l(w).
-(w - 3)*(w - 1)**2
Let j(a) = a + 1. Let o(l) = l**2 - 14*l + 10. Let w(t) = -6*j(t) - o(t). Factor w(r).
-(r - 4)**2
Let f(j) be the second derivative of -j**4/90 + j**3/45 + 2*j**2/15 + 6*j. Determine w, given that f(w) = 0.
-1, 2
Let m(t) be the second derivative of t**10/15120 + t**4/6 + 3*t. Let x(o) be the third derivative of m(o). Factor x(f).
2*f**5
Factor 2*k**3 + 0*k**2 + k**2 + 0*k - 14*k - 8 - 5*k**2.
2*(k - 4)*(k + 1)**2
Let w(t) be the first derivative of t**8/7560 - t**6/810 + t**4/108 - 2*t**3/3 + 1. Let y(d) be the third derivative of w(d). Find f, given that y(f) = 0.
-1, 1
Let c(b) be the third derivative of -b**7/945 + b**6/108 - 7*b**5/270 + b**4/36 + 6*b**2. Solve c(j) = 0 for j.
0, 1, 3
Factor 0*b + 0 - 2/5*b**3 + 0*b**2.
-2*b**3/5
Factor -3/8*p**4 + 27/8*p**3 + 33/2*p - 45/4*p**2 - 9.
-3*(p - 3)*(p - 2)**3/8
Let a(l) = -5*l**2 + 40*l + 21. Let r(v) = -v**2 + 8*v + 4. Let w(h) = -2*a(h) + 11*r(h). Let n be w(8). Find j such that j + 0*j + 3*j**3 + 2*j**4 - n*j = 0.
-1, 0, 1/2
Let b(h) be the first derivative of -h**5/5 - h**4/4 + h**3/3 + h**2/2 + 12. Suppose b(m) = 0. Calculate m.
-1, 0, 1
Let b(p) = 48*p**4 + 15*p**3 - 27*p**2 - 69*p - 48. Let k(l) = 7*l**4 + 2*l**3 - 4*l**2 - 10*l - 7. Let m(c) = 4*b(c) - 27*k(c). Factor m(h).
3*(h - 1)*(h + 1)**3
Let p = -358/15 + 24. Let b(v) be the first derivative of p*v**3 + 0*v + 2/5*v**2 - 1. Find y, given that b(y) = 0.
-2, 0
Factor a**2 + 24*a + 2*a**2 - 3*a**3 - 24*a.
-3*a**2*(a - 1)
Let u be ((-5)/30)/(4/(-8)). Let q be (8/(-30))/(2/(-5)). Let 1/3 - q*p**2 + u*p = 0. What is p?
-1/2, 1
Let i(q) be the third derivative of 1/280*q**7 + 0*q**4 + 1/8*q**3 + 0*q**6 + 0*q - q**2 + 0 - 1/40*q**5. Solve i(v) = 0.
-1, 1
Let s(y) = 15*y**4 + 11*y**3 - 45*y**2 - 30*y. Let c(g) = -5*g**4 - 4*g**3 + 15*g**2 + 10*g. Let a(o) = -11*c(o) - 4*s(o). What is l in a(l) = 0?
-1, 0, 2
Factor -2*d + 2*d**2 + 2/3 - 2/3*d**3.
-2*(d - 1)**3/3
Suppose 7*f = r + 2*f - 30, -5 = f. Let y be (-6)/15 - (-12)/r. Let 2/7*u**y + 2/7 - 4/7*u = 0. What is u?
1
Let l(a) be the third derivative of a**7/1155 - a**6/165 + a**5/110 + 9*a**2. Factor l(i).
2*i**2*(i - 3)*(i - 1)/11
Let a be (-15)/(-6)*(-40)/25. Let i be (a/2)/((-20)/8). Determine l, given that 6/5*l**2 + 1/5 + 1/5*l**4 - i*l - 4/5*l**3 = 0.
1
Let f(x) be the first derivative of -8/7*x**3 - 4/7*x + 11/7*x**2 - 9/14*x**4 - 1. Determine m so that f(m) = 0.
-2, 1/3
Suppose 15*u - 194 = -194. Factor 3/2*h - 3/4*h**2 - 3/4*h**3 + u.
-3*h*(h - 1)*(h + 2)/4
Let p(i) = 2*i - 4. Let n be p(4). Suppose 0 = 3*q, 0*r = -3*r - n*q. Factor 0 + 1/5*a**5 + 0*a**2 + 1/5*a - 2/5*a**3 + r*a**4.
a*(a - 1)**2*(a + 1)**2/5
Let p(d) be the first derivative of d**6/240 + d**5/120 - d**4/48 - d**3/12 - 3*d**2/2 - 4. Let y(l) be the second derivative of p(l). Factor y(b).
(b - 1)*(b + 1)**2/2
Let u(t) = 3*t**2 - 4*t - 9. Let b(i) = -4*i**2 + 6*i + 14. Let w(a) = -5*b(a) - 8*u(a). Determine q so that w(q) = 0.
-1/2, 1
Factor -2*i**2 + 50*i**2 + 78*i**4 - 36 + 102*i**3 + 30 + 21*i**5 - 3*i.
3*(i + 1)**4*(7*i - 2)
Let p(w) be the third derivative of -w**11/443520 + w**9/40320 - w**7/6720 + w**5/12 + w**2. Let h(x) be the third derivative of p(x). Factor h(u).
-3*u*(u - 1)**2*(u + 1)**2/4
Suppose 0 = -7*j - 23 + 51. Let o(f) be the third derivative of 1/180*f**5 + 1/9*f**3 + j*f**2 - 1/24*f**4 + 0*f + 0. Let o(i) = 0. What is i?
1, 2
Let d(t) = t**3 - 2*t**2 + t. Let q be (-1)/(-3 + (-15)/(-6)). Let x be d(q). Let -8/3*c**x - 4*c**3 + 2*c + 2*c**5 + 4/3*c**4 + 4/3 = 0. What is c?
-1, -2/3, 1
Let a be (-10)/(-65) + (-174)/1300. Let i(g) be the second derivative of -1/30*g**4 + 0 + a*g**5 + 0*g**2 - 3*g + 0*g**3. Factor i(o).
2*o**2*(o - 1)/5
Let t = 44344/75327 + -2/4431. Factor 16/17*y**3 + 2/17*y**5 + 0 + 0*y - t*y**4 - 8/17*y**2.
2*y**2*(y - 2)**2*(y - 1)/17
Let q(x) be the first derivative of 3*x**5/5 - 6*x**4 + 16*x**3 + 4. Let q(n) = 0. Calculate n.
0, 4
Let y(r) be the first derivative of 1/1080*r**6 + 1/120*r**5 + 1/36*r**4 - 2/3*r**3 + 0*r**2 + 1 + 0*r. Let l(c) be the third derivative of y(c). Factor l(i).
(i + 1)*(i + 2)/3
Let j(z) be the second derivative of z**8/56 + 3*z**7/70 + z**6/40 + 2*z**2 - 3*z. Let u(t) be the first derivative of j(t). Suppose u(w) = 0. Calculate w.
-1, -1/2, 0
Suppose 5*p - 2*p = -4*m - 3, 0 = 3*m + 9. Suppose -o = -p*o + 4. Factor 3*w + 2*w**o - 2 - 3*w.
2*(w - 1)*(w + 1)
Let f = 1422/7 - 202. Let o be -30*(-3)/(-42)*-2. Factor f*n**3 + 0*n + 0 + 32/7*n**4 + 0*n**2 + o*n**5.
2*n**3*(3*n + 2)*(5*n + 2)/7
Let j(u) = -u**4 - 7*u**3 + 5*u - 1. Let w(l) = 2*l**4 + 6*l**3 - l**2 - 4*l + 1. Let i(v) = 2*j(v) + 3*w(v). Factor i(z).
(z + 1)**2*(2*z - 1)**2
Let z(c) be the first derivative of -c**3 - c**2 - 2*c + 2. Let n(t) = t**3 + t - 1. Let w(r) = n(r) - z(r). Suppose w(s) = 0. Calculate s.
-1
Let m(r) be the first derivative of r**6/2 + 2*r**5/5 - r**4/4 + 2. Solve m(u) = 0.
-1, 0, 1/3
Let d(u) be the second derivative of u**8/11760 + u**7/2940 + u**6/2520 - 5*u**3/3 - u. Let m(j) be the second derivative of d(j). Factor m(y).
y**2*(y + 1)**2/7
Let r(h) = 3*h**2 - 9*h - 1. Let d be (-2 - 7)/(1/1). Let k = -5 - d. Let z(q) = q**2 - 3*q. Let b(s) = k*r(s) - 14*z(s). Factor b(w).
-2*(w - 2)*(w - 1)
Suppose -5*b = -59 + 4. Let h = 11 - b. Factor 1/4*u**2 + h + 0*u.
u**2/4
Let r(s) be the second derivative of -s**6/10 - 3*s**5/20 + 3*s**4/4 + 5*s**3/2 + 3*s**2 - 40*s. Determine t, given that r(t) = 0.
-1, 2
Factor 1 + 15 + 16*g**3 - 20*g + 8*g**2 - 16*g**4 + 0*g**2 - 8 + 4*g**5.
4*(g - 2)*(g - 1)**3*(g + 1)
Let q(w) be the second derivative of -w**6/120 + w**4/8 - w**3/3 + 5*w**2/2 + 4*w. Let l(v) be the first derivative of q(v). Find f, given that l(f) = 0.
-2, 1
Let v(c) be the second derivative of c**8/560 - c**7/175 + c**5/50 - c**4/40 - 3*c**2/2 - 8*c. Let q(o) be the first derivative of v(o). Factor q(k).
3*k*(k - 1)**3*(k + 1)/5
Let u be (-2)/4*(-2 + -2). Suppose -8 = -2*q, -2*x - u*q = -0*x - 14. Factor 1/4*t**x - 1/4*t + 0*t**2 + 0.
t*(t - 1)*(t + 1)/4
Let c(t) = t**3 + 8*t**2 - 10*t - 7. Let k be c(-9). Factor -2*u**3 - 27*u + 14*u**k + 4*u**2 - u**3.
-3*u*(u - 3)**2
Factor -1 - 8*u - 45/4*u**2 + 81/4*u**3.
(u - 1)*(9*u + 2)**2/4
Suppose -n + 4 = n + 3*i, -4*i = 0. Factor -3*a**2 - a**3 - 2*a**2 + 4*a**n.
-a**2*(a + 1)
Let w(c) be the first derivative of -3*c**4/16 + c**3 - 14. Solve w(i) = 0 for i.
0, 4
Let n = -11 - -16. Suppose -6 + n + 5*k**2 + 4*k + 3 - 3*k**2 = 0. What is k?
-1
Suppose -4*x + 1 = -19. Suppose x*d = -2*h + 23, 2*d + 3 = -3*h + 7*d. Let 3*w**2 + 1/2 + 1/2*w**h + 2*w**3 + 2*w = 0. What is w?
-1
Let a(m) be the second derivative of -1/3*m**3 + 0*m**2 + 0 - 1/3*m**4 + 3*m. Factor a(q).
-2*q*(2*q + 1)
Suppose -2/9*l**2 + 0*l - 2/3*l**3 - 2/9*l**5 + 0 - 2/3*l**4 = 0. Calculate l.
-1, 0
Factor 3*h**2 + 36/5 - 96/5*h.
3*(h - 6)*(5*h - 2)/5
Let s(l) be the second derivative of -3/4*l**4 + 1/10*l**6 - 3/20*l**5 + 0 + l + 1/2*l**3 + 3*l**2. Let s(r) = 0. What is r?
-1, 1, 2
Let i(v) = -2*v**4 + 7*v**3 + 5*v**2 - 2*v. Let k(r) = -3*r**4 + 15*r**3 + 9*r**2 - 4*r. Let g(s) = -10*i(s) + 4*k(s). Solve g(d) = 0.
-1, 0, 1/4, 2
Solve -2/3*f**2 + f**4 - 1/3 + 1/3*f**5 + 2/3*f**3 - f = 0.
-1, 1
Let y(n) = -n + 5. Let m be y(6). Let z(b) = 2*b**2 + b + 0*b - 3*b**2 - b**3. Let u(s) = -6*s**3 - 4*s**2 + 6*s - 1. Let d(a) = m*u(a) + 5*z(a). Facto