i).
4*(i - 5)*(i - 1)*(i + 1)**3
Let v(w) = -6*w**3 + 12*w**2. Let k(f) = f**2 + 4*f**3 + 3*f**2 - 6*f**3. Let j = -12 + 22. Let c(s) = j*k(s) - 3*v(s). Let c(i) = 0. Calculate i.
0, 2
Find s such that -3*s + 14*s**2 - 10*s**2 - s = 0.
0, 1
Let k(t) be the first derivative of t**6/14 + 6*t**5/35 - 3*t**4/14 - 4*t**3/7 + 3*t**2/14 + 6*t/7 - 40. Let k(d) = 0. Calculate d.
-2, -1, 1
Let y(z) = -z**3 + z**2 + z - 1. Let i(n) = 8*n**4 + 16*n**3 + 2*n**2 + 13*n**2 + n**2 + 2*n - 6. Let b(t) = -i(t) + 6*y(t). Factor b(p).
-2*p*(p + 1)*(p + 2)*(4*p - 1)
Let z(p) = p**2 + p + 1. Let q(t) = -15*t + 938*t**3 - 943*t**3 - 18 - 30*t**2 + 3. Let s(o) = -q(o) - 15*z(o). Factor s(n).
5*n**2*(n + 3)
Let q = 17357 + -190671/11. Factor 92/11*t**2 + 320/11*t - q + 6/11*t**3.
2*(t + 8)**2*(3*t - 2)/11
Solve -13*j + 25*j - 3*j**2 - 62*j + j**2 = 0 for j.
-25, 0
Let z be -22 + 7 + 3 + (-272)/(-12). Find f such that -12 - z*f + 4/3*f**2 = 0.
-1, 9
Let u = -242/7 + 989/28. Let s(n) be the first derivative of n + 1/6*n**3 + 12 - u*n**2. Find h, given that s(h) = 0.
1, 2
Let q(h) be the first derivative of -1/15*h**3 - 1/150*h**5 + 1/30*h**4 + 0*h + 2 + 1/2*h**2. Let y(p) be the second derivative of q(p). Factor y(f).
-2*(f - 1)**2/5
Let x(u) = u**3 + u**2 + 4*u. Let j(l) = -3*l**3 - 19*l**2 - 32*l. Let o(m) = 5*j(m) + 20*x(m). Factor o(d).
5*d*(d - 16)*(d + 1)
Let m(f) be the second derivative of -f**4/48 - f**3/2 - 5*f**2/2 - 4*f + 41. Factor m(z).
-(z + 2)*(z + 10)/4
Let z be ((-10)/(-25))/((-1)/10). Let f be ((-6)/(-50))/(z*(-1)/20). Find n such that 0*n - f*n**2 + 0 = 0.
0
Let r(c) be the second derivative of -c**7/1260 + c**6/540 + c**5/90 + c**3/6 + 12*c. Let a(v) be the second derivative of r(v). Factor a(z).
-2*z*(z - 2)*(z + 1)/3
Suppose -2*x - 2*r + 11 = -3*r, -4*x = -5*r - 37. Let m(w) = w + 6. Let q be m(-3). Solve -u**q + u**2 + x*u**3 + u**3 + 8*u**2 = 0 for u.
-3, 0
Let w(s) be the second derivative of 8*s**6/45 + s**5/3 - s**4/6 - 4*s**3/9 + s**2/3 - 127*s. Suppose w(l) = 0. What is l?
-1, 1/4, 1/2
Let a(s) = -s**2 + 25. Let l be a(-5). Let t(r) be the second derivative of -3*r - 1/6*r**4 + 0 + 0*r**2 - 1/10*r**5 + l*r**3. Factor t(n).
-2*n**2*(n + 1)
Suppose 0 = 20677*m - 20676*m - 3. Suppose 1/4 + 3/2*q**2 + 1/4*q**4 + q + q**m = 0. What is q?
-1
Let n(y) be the first derivative of -y**4/2 - y**3/2 + y**2 + 3*y/2 - 280. Determine a so that n(a) = 0.
-1, -3/4, 1
Solve 1/3*d**2 + 2/3 - d = 0 for d.
1, 2
Suppose -19*b + 18*b = 4*t - 13, -13 = -3*t - 4*b. Let n(x) be the first derivative of 3*x**2 + t*x - 3/2*x**4 + 4 - x**3. Solve n(g) = 0 for g.
-1, -1/2, 1
Let r(q) = -q**3 - 6*q**2 + 6*q - 3. Let v be r(-7). Let j(c) be the second derivative of -1/8*c**2 + 0 - 3*c + 1/48*c**v - 1/80*c**5 + 1/24*c**3. Factor j(w).
-(w - 1)**2*(w + 1)/4
Let f(x) be the third derivative of 1/24*x**3 + 0*x**4 - 1/240*x**5 + 0 + 0*x + 19*x**2. Factor f(p).
-(p - 1)*(p + 1)/4
Let m(p) = 2*p**4 + 7*p**3 + 10*p**2 + 3*p. Let t(s) = s**2 - 2*s - 1. Let j(l) = 5*m(l) - 5*t(l). Factor j(r).
5*(r + 1)**3*(2*r + 1)
Let d(v) = 30*v**3 + 91*v**2 + 66*v + 11. Let m(u) = u**2 + 2*u - 1. Let n(q) = -2*d(q) - 6*m(q). What is a in n(a) = 0?
-2, -1, -2/15
Let o(f) be the third derivative of -1/168*f**8 - 1/30*f**5 + 8*f**2 + 0*f**4 + 0*f**3 - 1/20*f**6 + 0 - 1/35*f**7 + 0*f. Factor o(d).
-2*d**2*(d + 1)**3
Let r(p) be the second derivative of p**7/504 + p**6/72 - p**5/8 + 13*p**4/12 - 6*p. Let x(s) be the third derivative of r(s). Factor x(v).
5*(v - 1)*(v + 3)
Let i(d) be the first derivative of d**4/8 + 3*d**3/2 + 15*d**2/4 - 25*d/2 + 181. Solve i(a) = 0 for a.
-5, 1
Let u(y) be the first derivative of -y**4/8 - y**3/6 + y**2/2 + 95. Let u(v) = 0. Calculate v.
-2, 0, 1
Let o = -27 - -31. Suppose -o*p + 2 = -6. Factor -21*b**2 - 7*b**3 + 29*b**p + 3*b**3 - 4*b**4.
-4*b**2*(b - 1)*(b + 2)
Let l = 166/11 + -494/33. Let p(o) be the second derivative of 8*o - l*o**3 + 4/11*o**2 + 0 + 1/66*o**4. Suppose p(h) = 0. Calculate h.
2
What is m in 57/5*m + 78/5*m**2 + 3/5*m**4 + 3 + 42/5*m**3 - 3/5*m**5 = 0?
-1, 5
Let c(h) be the first derivative of -7/3*h**3 - 9/5*h**5 - 1/2*h**2 + 26 + 0*h - 15/4*h**4. Factor c(g).
-g*(g + 1)*(3*g + 1)**2
Suppose 2*n - 32 = -k + 5, n - 4*k = -4. Let -9*b**3 + 14*b**3 - n - 8*b + 7*b**2 - 6*b**3 = 0. What is b?
-1, 4
Let 35*b**3 - 46*b**3 + 141*b + 5*b**2 + b**2 + 3*b**5 - 133*b**3 + 66*b**4 - 72 = 0. What is b?
-24, -1, 1
Factor 26/5*v**2 - 54/5*v**3 - 14/5*v**5 + 46/5*v**4 - 4/5*v + 0.
-2*v*(v - 1)**3*(7*v - 2)/5
Let x = 6/505 + 1503/1010. Let p(m) be the first derivative of x*m**2 - 3/4*m**4 - 2*m**3 + 10 + 6*m. Find c, given that p(c) = 0.
-2, -1, 1
Let w = -13734 + 13737. Factor -10/3*r**2 - 8/3 + 16/3*r + 2/3*r**w.
2*(r - 2)**2*(r - 1)/3
Let s(t) be the first derivative of t**6/12 - 3*t**5/5 + 3*t**4/2 - 4*t**3/3 - 565. Factor s(h).
h**2*(h - 2)**3/2
Let u be (2 - -1) + 0 - -6. Suppose 11 = 5*l - u. Factor 0*a**l - 3/4*a**3 + 0 + a**5 + 1/4*a**2 + 0*a.
a**2*(a + 1)*(2*a - 1)**2/4
Let q = -1794 + 16150/9. Suppose 4/9*l - 8/3 + q*l**2 = 0. What is l?
-3, 2
Let s be 2/6 + ((-275)/(-15))/5. Factor 6*u**2 - s*u - u**2 + 8*u - 9*u.
5*u*(u - 1)
Factor -3/7*k**3 + 69/7*k + 36/7 + 30/7*k**2.
-3*(k - 12)*(k + 1)**2/7
Let k(d) be the third derivative of 0 - 1/120*d**5 + 0*d**3 - 1/24*d**4 + 1/240*d**6 + 14*d**2 + 0*d. Factor k(w).
w*(w - 2)*(w + 1)/2
Suppose -16*d - 20 = -r - 21*d, -5*r + 5*d - 20 = 0. Factor 0*p + 1/3*p**5 + 0 + r*p**3 - p**4 + 4/3*p**2.
p**2*(p - 2)**2*(p + 1)/3
Let x = 77 + -59. Find b such that -x*b + 2*b - 23*b + 12 - 9*b**3 - 9*b + 39*b**2 = 0.
1/3, 2
Let c(x) = -5*x**2 - 261*x - 48. Let y be c(-52). Let g(o) be the first derivative of 5/3*o**3 - 3/8*o**y + o + 2 - 9/4*o**2. Suppose g(w) = 0. Calculate w.
1/3, 1, 2
Let a(z) be the first derivative of 3*z**4/16 - 3*z**3/4 - 3*z**2/8 + 9*z/4 - 91. Factor a(q).
3*(q - 3)*(q - 1)*(q + 1)/4
Let r(w) be the first derivative of -2*w**3/3 + w**2 + 12*w + 79. Factor r(m).
-2*(m - 3)*(m + 2)
Let q = 1/60 - -7/60. Let v(j) be the first derivative of 4 - 3/5*j**2 + 0*j - q*j**3. Suppose v(g) = 0. What is g?
-3, 0
Let g(d) = 2*d**2 - 181*d - 189. Let z(v) = -5*v**2 + 365*v + 380. Let y(p) = 5*g(p) + 3*z(p). Let y(n) = 0. What is n?
-1, 39
Let w(d) be the second derivative of d**7/70 - d**5/10 + d**3/2 + 15*d**2 - 8*d. Let a(i) be the first derivative of w(i). Factor a(l).
3*(l - 1)**2*(l + 1)**2
Let v(o) be the first derivative of 3*o**4/8 + 3*o**3 + 9*o**2 + 12*o + 573. Determine i, given that v(i) = 0.
-2
Let o(i) be the first derivative of -2/5*i**5 + 3/4*i**4 - 1/2*i**6 + 0*i**2 + 2/3*i**3 - 16 + 0*i. Suppose o(c) = 0. Calculate c.
-1, -2/3, 0, 1
Suppose -205 + 205 = 71*f. Factor -2/5*p + f - 2/15*p**2.
-2*p*(p + 3)/15
Let k(u) be the third derivative of 0*u + 2/15*u**6 + 1/3*u**5 - 1/3*u**4 + 0 - 2*u**3 + 37*u**2. Suppose k(i) = 0. What is i?
-1, 3/4
Let p = 1491 - 1466. Determine l so that -p*l - 5/2*l**2 - 125/2 = 0.
-5
Suppose 0 = 2*a - 4*d - 52, 0 = -0*a - 3*a - 5*d + 56. Determine i, given that -4*i**4 + 11*i**2 - 39*i**3 + a*i**3 - 9 + 21*i**3 - 6*i = 0.
-1, 3/2
Let t(o) be the third derivative of -o**7/525 + 8*o**6/75 + 17*o**5/25 + 26*o**4/15 + 7*o**3/3 + 2*o**2 - 397*o. Factor t(h).
-2*(h - 35)*(h + 1)**3/5
Let g(t) = -2*t**2 - 9*t. Let k be g(-4). Let 20 - 16*w + 4*w**2 + k*w**3 - 3*w**2 - 3*w**3 = 0. Calculate w.
-5, 2
Let i(c) be the third derivative of c**6/60 - 4*c**5/5 + 7*c**4 - 80*c**3/3 + 45*c**2. Solve i(u) = 0.
2, 20
Determine c, given that 0 + 13/4*c**2 - 1/2*c = 0.
0, 2/13
Let o(n) be the third derivative of -n**6/300 - 64*n**5/25 - 4096*n**4/5 - 2097152*n**3/15 - 207*n**2. What is x in o(x) = 0?
-128
Let h(r) be the third derivative of r**6/600 + 2*r**5/75 + 13*r**4/120 + r**3/5 + 59*r**2. Factor h(p).
(p + 1)**2*(p + 6)/5
Let b = 702 + -694. Let z(v) be the second derivative of -7/4*v**5 + 5*v**2 + 0 - 5/4*v**4 + b*v + 5/2*v**3 - 1/2*v**6. Factor z(p).
-5*(p + 1)**3*(3*p - 2)
Let n(j) = j**2 - 4. Suppose -5*w - 2 = -4*w. Let f be n(w). Solve f*m - 2/3*m**2 + 2/3 = 0.
-1, 1
Let b = -2768 - -8305/3. Factor 7/3*i**2 + 5/3*i**4 - 2/3*i - b*i**5 - 3*i**3 + 0.
-i*(i - 2)*(i - 1)**3/3
Let q(g) = 6*g**2 + 88*g - 28. Let y be q(-15). Suppose 2*k + 6 = 4*k. Factor 0*m**y + 1/5*m - 1/5*m*