 - 3*t**5 + 0*t**5 - t**4.
t**4*(2*t - 1)
Let p(n) be the third derivative of 0*n + 1/112*n**8 + 0 - 2*n**2 - 1/210*n**7 + 0*n**5 + 0*n**4 + 0*n**6 + 0*n**3. Determine m, given that p(m) = 0.
0, 1/3
Determine h, given that -1/3*h**2 + h - 2/3 = 0.
1, 2
Let z = -128/7 - -131/7. Factor 0 + 0*k**2 + 0*k - z*k**4 - 9/7*k**3.
-3*k**3*(k + 3)/7
Let i(t) be the second derivative of -t**4/6 + 10*t**3/3 - 25*t**2 + 14*t. Suppose i(d) = 0. What is d?
5
Suppose -h + 16 = -2*h - 4*u, 0 = 4*h + u - 11. Solve 3*w**3 + h*w**4 + 0*w**2 + 0*w**2 + w**3 = 0 for w.
-1, 0
Factor 0 - 1/2*x**3 + x**2 + 0*x.
-x**2*(x - 2)/2
Let i(r) be the second derivative of -1/150*r**5 + 1/15*r**3 + r + 1/2*r**2 + 0 + 0*r**4. Let x(m) be the first derivative of i(m). Let x(d) = 0. What is d?
-1, 1
Suppose -4*s + 2*s - u = -2, 3*s - 29 = 5*u. Suppose 2*p - 3*p = -s*o - 9, 5*p = 4*o + 45. Let 1 - 6*w**2 + p*w**2 - 4*w**2 = 0. Calculate w.
-1, 1
Suppose -27 + 12 = 3*h. Let j = -5 - h. Determine t, given that 4/5*t**2 + 0 + j*t**3 - 4/5*t**4 - 2/5*t**5 + 2/5*t = 0.
-1, 0, 1
Let w = 69 + -41. Factor -4*m**3 - 2*m**4 + 28*m - w*m - 2*m**2.
-2*m**2*(m + 1)**2
Let k be (2/(-15))/((-4)/6). Find o such that -1/5*o + k - 2/5*o**2 = 0.
-1, 1/2
Let o(z) = -3*z - 4. Let d be o(-2). Let 5*k**3 - 4*k**5 - 2*k**2 - k**5 + d*k**4 + 0*k**2 = 0. What is k?
-1, 0, 2/5, 1
Suppose 3*q + 4*l = 8, -8 = 5*q - 6*l + 2*l. Factor -2/7*k**2 - 4/7*k + q.
-2*k*(k + 2)/7
Let l(y) = -13*y**4 + 16*y**3 + 3*y**2 - 9*y - 4. Let z(w) = 9*w**4 - 11*w**3 - 2*w**2 + 6*w + 3. Let t(h) = -5*l(h) - 7*z(h). Factor t(v).
(v - 1)**2*(v + 1)*(2*v - 1)
Let h = -268/5 + 54. Factor 2/5*g - 4/5 + h*g**2.
2*(g - 1)*(g + 2)/5
Find r such that 2/7*r**3 - 2/7 - 2/7*r + 2/7*r**2 = 0.
-1, 1
Suppose -4*x = -2*x. Suppose x*m**3 - 4 + 2*m**3 - 6*m + 5*m - 5*m = 0. Calculate m.
-1, 2
Let n(v) = -v - 2. Let k be n(-6). Let h = k - 1. Factor -m**2 - h + m + m + 2.
-(m - 1)**2
Let z = 10 - 4. Factor c**3 + 1 - 3*c**4 + 0 - z*c + 2 + 5*c**3.
-3*(c - 1)**3*(c + 1)
Suppose -5*r - 10 = -35. Let z(k) be the second derivative of 0 - 1/48*k**4 + 0*k**2 + 0*k**3 - 2*k + 1/80*k**r. Factor z(x).
x**2*(x - 1)/4
Let h(n) be the second derivative of 18*n**7/7 + 18*n**6 + 198*n**5/5 + 116*n**4/3 + 16*n**3 + 18*n. Factor h(u).
4*u*(u + 3)*(3*u + 2)**3
Let a be -4 - (-2 + 2 + 50/(-12)). Let f(l) be the second derivative of -a*l**4 - 1/3*l**3 + l**2 - l + 0 + 1/10*l**5. Factor f(k).
2*(k - 1)**2*(k + 1)
Suppose 2*w - w = -5*s - 14, -3*s = 4*w + 22. Let a = -2 - s. Factor 2/9*g**3 - 2/3*g + a*g**2 + 4/9.
2*(g - 1)**2*(g + 2)/9
Let q(a) be the third derivative of a**7/70 - a**6/10 + a**5/4 - a**4/4 + 11*a**2. Suppose q(g) = 0. What is g?
0, 1, 2
Let z(f) be the first derivative of 44/15*f**3 + 14/5*f**4 + 34/25*f**5 + 4 + 4/15*f**6 + 8/5*f**2 + 2/5*f. Solve z(w) = 0.
-1, -1/4
Let m be 20/(-110) - (-35)/11. Let c(h) be the first derivative of -1/5*h**2 + 4/15*h**m + 1 + 0*h. Factor c(q).
2*q*(2*q - 1)/5
Let p(d) be the second derivative of d**5/100 - d**4/60 - 2*d**3/15 + 2*d**2/5 + 27*d. Factor p(h).
(h - 2)*(h - 1)*(h + 2)/5
Let j(h) be the second derivative of h - 1/2*h**2 + 0 + 1/12*h**3 + 1/24*h**4. Factor j(a).
(a - 1)*(a + 2)/2
Let a(q) = -1. Let p(b) = 3*b**2 + 4*b + 3. Let r(v) = -2*a(v) - p(v). Suppose r(d) = 0. What is d?
-1, -1/3
Let h be -2*-7*5/(-2). Let s be h/14*(-4)/5. Factor 4*y**3 + 3*y**4 + 5*y**3 + 3*y + 6*y**2 + 3*y**s.
3*y*(y + 1)**3
Let m(w) be the third derivative of 1/30*w**5 - 5*w**2 + 0*w**3 + 0*w - 1/60*w**4 + 0 - 1/75*w**6. Factor m(g).
-2*g*(g - 1)*(4*g - 1)/5
Let z(b) be the first derivative of b**3/18 - 5*b**2/6 + 25*b/6 - 9. Factor z(w).
(w - 5)**2/6
What is c in -12*c + 10 + 2*c**2 + 7 - 7 = 0?
1, 5
Suppose 5*u - 5 = -4*n + 2*u, -3*n - 2*u = -4. Determine a so that a - 14*a**5 - 10*a**n - 2*a - 3*a + 18*a**3 + 10*a**4 = 0.
-1, -2/7, 0, 1
Let f(a) be the first derivative of -2*a**2 + 2/3*a**3 + 2*a + 1. Let f(v) = 0. Calculate v.
1
Let x(p) = p - 4. Let o be 2/5 - 56/(-10). Let v be x(o). Let -n**v + n**2 + 2*n**2 - 4*n + 0*n = 0. What is n?
0, 2
Let j be (-9 - -6)/(1/(-4)*2). Let u(m) be the second derivative of 0 + 0*m**3 - 1/40*m**5 + 0*m**2 + 1/84*m**7 - 1/24*m**4 - 3*m + 1/60*m**j. Factor u(q).
q**2*(q - 1)*(q + 1)**2/2
Let 0 + 1/4*m**4 + 1/2*m + 5/4*m**2 + m**5 - 3*m**3 = 0. What is m?
-2, -1/4, 0, 1
Let p be (5/3)/(2/24*10). Factor 1/2*t + 0 - 1/4*t**p.
-t*(t - 2)/4
Let x(w) be the second derivative of -3*w**5/100 - w**4/20 + w**3/10 + 3*w**2/10 - 6*w. What is g in x(g) = 0?
-1, 1
Let t(a) be the first derivative of 2*a**5/25 - a**4/2 + 16*a**3/15 - 4*a**2/5 + 35. Factor t(h).
2*h*(h - 2)**2*(h - 1)/5
Let y(d) be the second derivative of d**5/20 - d**4/6 - d**3/6 + d**2 - 8*d. Factor y(f).
(f - 2)*(f - 1)*(f + 1)
Let a(q) be the third derivative of q**10/75600 + q**9/7560 + q**8/2016 + q**7/1260 - q**5/20 + 2*q**2. Let l(d) be the third derivative of a(d). Factor l(n).
2*n*(n + 1)**2*(n + 2)
Factor 0*j - 4/7*j**3 + 12/7*j**2 + 0.
-4*j**2*(j - 3)/7
Let a(p) = 2*p**2 - 14*p + 16. Let s(m) = 4*m**2 - 29*m + 31. Let z = 6 + -11. Let w(o) = z*a(o) + 2*s(o). Factor w(i).
-2*(i - 3)**2
Let x(u) be the third derivative of u**7/1155 + u**6/220 + u**5/110 + u**4/132 + u**2 + 10*u. Suppose x(h) = 0. What is h?
-1, 0
What is d in -1/3*d**3 + 1/6 - 1/6*d**5 + 1/3*d**2 + 1/2*d - 1/2*d**4 = 0?
-1, 1
Let u(x) = -x**3. Let l(g) be the first derivative of -11*g**4/2 + 2*g**3 - 1. Let t(r) = -l(r) + u(r). Factor t(m).
3*m**2*(7*m - 2)
Let f = 474 + -7106/15. Let h(k) be the first derivative of -1/9*k**6 + 0*k**4 + 1/3*k**2 + 0*k - 4/9*k**3 - 1 + f*k**5. Factor h(z).
-2*z*(z - 1)**3*(z + 1)/3
Let z(c) be the first derivative of 8/15*c**5 - 8/9*c**6 - 8 + 0*c**3 + 0*c - 1/12*c**4 + 0*c**2. Factor z(f).
-f**3*(4*f - 1)**2/3
Let u be (-1 + 1)/((-2)/(-2)). Let b be 2 + u/((-1)/1). Find c such that 1 - b*c**2 + 1 + 0 = 0.
-1, 1
Suppose -1/2 - 1/6*h + 1/6*h**3 + 1/2*h**2 = 0. What is h?
-3, -1, 1
Suppose -2*j - 52 = -60. Suppose 0 + 2/3*y**2 + 2/3*y**3 - 2/3*y - 2/3*y**j = 0. What is y?
-1, 0, 1
Determine z so that -10*z - 17*z + 2*z**4 - 69*z**3 + 2*z**2 - 107*z**2 + 7*z**4 = 0.
-1, -1/3, 0, 9
Factor 27/2*o + 3/2*o**3 + 9*o**2 + 6.
3*(o + 1)**2*(o + 4)/2
Suppose c = -2*g, -g + 2*c - 10 = 5*c. Suppose -1 = -3*d - a, 3*d - 18 = -d + g*a. Determine m so that m**2 + 2*m**d - 2*m**5 + 2*m + m**2 - 4*m**4 = 0.
-1, 0, 1
Let m(p) = 1 - 5*p + 0*p + 4*p. Let c be m(-3). Factor 0 + 6*y**2 - c*y - 2*y + 2 - 2*y**3.
-2*(y - 1)**3
Let d(v) = v**2 + 5*v. Let r be d(-5). Let q(c) be the second derivative of r + c + 0*c**4 + 0*c**3 + 1/50*c**5 + 0*c**2. Let q(p) = 0. What is p?
0
Let z(b) be the second derivative of -14*b**4/45 + 17*b**3/45 + b**2/5 - 18*b. Solve z(x) = 0 for x.
-1/7, 3/4
Let x(g) be the first derivative of g**5/20 - g**4/8 - 3*g**2/2 - 3. Let p(b) be the second derivative of x(b). Suppose p(k) = 0. Calculate k.
0, 1
Suppose 4*v + 12 = 0, 5*v + 10 = 2*a - 5. Suppose 2*j + 0 - 4 = a. Let 2/3 + 2*q**2 - j*q - 2/3*q**3 = 0. What is q?
1
Suppose -s = 2*m - 5*m, 4*m - s = 0. Solve 2/13*h + 2/13*h**2 + m = 0.
-1, 0
Determine p so that 3/2 + 11/2*p - 2*p**2 = 0.
-1/4, 3
Let c be (15 - 14)*34/6 + -5. Let q be ((-6)/2)/((-18)/4). Factor v - c + q*v**2.
(v + 2)*(2*v - 1)/3
Let z be 122/(-21) + 4/6. Let r = 208/35 + z. Solve r*w - 2/5*w**2 - 2/5 = 0 for w.
1
Let x be 38/88 + 1/(-4). Let q = -1/3 - -17/33. Factor -2/11*u - 2/11*u**2 + x + q*u**3.
2*(u - 1)**2*(u + 1)/11
Let k = 422/665 + -6/95. Suppose -2/7*a + 2/7*a**2 - k = 0. What is a?
-1, 2
Let r(w) = -w**3 - 2*w. Let z(d) = -6*d**3 - 11*d. Let h = -64 + 98. Let f(g) = h*r(g) - 6*z(g). Factor f(m).
2*m*(m - 1)*(m + 1)
Let j(p) = 10*p**3 + 40*p**2 - 14*p - 4. Let u(y) = 3*y**3 + 13*y**2 - 5*y - 1. Let a(i) = -5*j(i) + 16*u(i). What is n in a(n) = 0?
1, 2
Let u be (-2 + (-12)/(-2))*-2. Let i = -6 - u. Factor -6*q**4 + 0*q**3 - q**3 - i*q**5 - 2*q**2 - q**3 - 4*q**3.
-2*q**2*(q + 1)**3
Factor -13*p**4 - 3*p**4 - 3*p**4 - 2*p**4 - 6*p**2 + 27*p**3.
-3*p**2*(p - 1)*(7*p - 2)
Let g(u) be the third derivative of u**6/45 + u**5/6 + u**4/3 - 4*u**3/9 + 29*u**2. Factor g(z).
2*(z + 2)**2*(4*z - 1)/3
Determine r, given that -5*r - r + 6*r + 10*r**3 - 5*r**4 = 0.
0, 2
Let r(i) be the second derivative of i**4/5