r q(u).
2*(u + 2)*(3*u - 1)/7
Let t(n) be the third derivative of -n**7/840 + n**4/24 + 2*n**2. Let c(h) be the second derivative of t(h). Determine v, given that c(v) = 0.
0
Suppose -x - 7 = -3*q + 1, -x = -4*q + 11. Let u = 0 + q. Factor -4 - 2*a + 3*a**3 + 8*a**2 + 5*a**u - 2*a**3.
2*(a + 1)**2*(3*a - 2)
Let r(g) be the first derivative of -g**5/10 - g**4/4 - g**3/6 + 9. Factor r(b).
-b**2*(b + 1)**2/2
Let f(p) = -12*p**2 - 21*p. Let n(b) = -3*b**2 - 5*b. Let a(h) = -2*f(h) + 9*n(h). Let a(m) = 0. What is m?
-1, 0
Let z(n) = -9*n**3 - 15*n - 45. Let q(g) = -2*g**3 - 4*g - 11. Let k(j) = -21*q(j) + 5*z(j). Let k(f) = 0. Calculate f.
-1, 2
Let p(n) = 3*n**2 + n - 2. Let d(c) = c**2 - 1. Let l be ((-28)/(-35))/((-2)/10). Let o(y) = l*d(y) + p(y). Factor o(g).
-(g - 2)*(g + 1)
Let v(w) = -w**3 - 4*w**2 + w + 7. Let t be v(-4). Let h(k) be the second derivative of -1/18*k**3 - 1/36*k**4 + 0 + 0*k**2 + t*k. Factor h(c).
-c*(c + 1)/3
Let 104*b**2 - 205*b**2 + 105*b**2 - b**5 + 5*b**4 - 8*b**3 = 0. Calculate b.
0, 1, 2
Let o(l) be the second derivative of -l**5/50 + l**4/15 + l**3/15 - 2*l**2/5 - 10*l. Factor o(j).
-2*(j - 2)*(j - 1)*(j + 1)/5
Let u(q) be the second derivative of -7/15*q**6 + 3*q + 2/3*q**3 + 7/6*q**4 - 5/21*q**7 + 0 + 3/10*q**5 + 0*q**2. Determine k, given that u(k) = 0.
-1, -2/5, 0, 1
Suppose 2*m = -3*y + 23, -2*y - 6 = -3*m - m. Find u, given that 1/5*u**m + 0 + 0*u**3 + 0*u**2 + 0*u = 0.
0
Factor -2/3*m**2 - 722/3 + 76/3*m.
-2*(m - 19)**2/3
Let n(c) = -11*c**3 + 19*c**2 - 35*c + 17. Let o(j) = 16*j**3 - 29*j**2 + 52*j - 25. Let g(b) = 7*n(b) + 5*o(b). Solve g(u) = 0 for u.
1, 2
Factor -53*j**5 - 2*j + 2*j + 56*j**5 - 3*j**3.
3*j**3*(j - 1)*(j + 1)
Suppose 8/5*h**2 + 2/5*h**5 + 2*h**4 + 0*h + 0 + 16/5*h**3 = 0. Calculate h.
-2, -1, 0
Factor -6*m**3 + 6*m + 24*m**2 + 2*m**4 - 12*m**2 - 14*m**2.
2*m*(m - 3)*(m - 1)*(m + 1)
Find r such that 3/4*r**3 + 1/4*r**2 - 1/4*r**5 - 1/4*r**4 - 1/2*r + 0 = 0.
-2, -1, 0, 1
Solve -9*f**3 - 5*f**4 + 9*f**5 + 0*f**4 - 3*f**2 + 8*f**4 = 0.
-1, -1/3, 0, 1
Let k = 509/52 - 124/13. Factor -k*u + 1/4*u**3 - 3/4*u**2 + 1/4*u**4 + 1/2.
(u - 1)**2*(u + 1)*(u + 2)/4
Let -2/5*h**2 + 0 - 4/5*h = 0. Calculate h.
-2, 0
Let j(z) be the third derivative of -z**5/60 + z**4/24 - 13*z**2. Find o such that j(o) = 0.
0, 1
Factor 2/3*t**3 - 2/3 + 2/3*t**2 - 2/3*t.
2*(t - 1)*(t + 1)**2/3
Let i be 3/((-3)/(-2)) - 0. Let g = 13 - 10. Let -4*j**2 + 4*j**2 - j**i + g*j**2 = 0. Calculate j.
0
Suppose -l = 1, -3 = -3*a + l - 4*l. Determine y, given that -5*y**5 + 3*y + y**5 + 10*y**a - 6*y**4 - 4*y**2 + y**5 = 0.
-1, 0, 1
Let a(w) be the third derivative of w**9/10080 + w**8/6720 - w**7/1680 - w**6/720 + w**4/8 + 4*w**2. Let i(u) be the second derivative of a(u). Factor i(h).
h*(h - 1)*(h + 1)*(3*h + 2)/2
Let k(g) be the second derivative of 1/21*g**3 + 19/70*g**5 + 3*g - 1/15*g**6 + 0 - 5/14*g**4 + 2/7*g**2. Find q such that k(q) = 0.
-2/7, 1
Let k be 2/8 - (-598)/40. Determine n, given that -64/5*n**2 + k*n**3 + 26/5*n - 44/5*n**4 - 4/5 + 2*n**5 = 0.
2/5, 1
Let l(x) be the third derivative of x**6/540 + x**5/135 + x**4/108 - 5*x**2. Find v such that l(v) = 0.
-1, 0
Let h(k) be the first derivative of k**4/12 - 2*k**2/3 - 7. Factor h(x).
x*(x - 2)*(x + 2)/3
Let i = -240 - -721/3. Suppose 1/6*n**2 - 1/6*n - i = 0. Calculate n.
-1, 2
Factor 2*k**5 - 9*k**3 - 5*k - 3*k**4 - 2*k + 15*k**2 + k**5 + k.
3*k*(k - 1)**3*(k + 2)
Let h(o) be the first derivative of -o**3/6 - o**2/2 - o/2 - 7. Factor h(g).
-(g + 1)**2/2
Suppose -3*z = -15 - 3. Find u, given that -z*u**2 + 4*u**2 + 0*u**2 = 0.
0
Let m(z) be the first derivative of -2*z**5/95 + 4*z**3/57 - 2*z/19 - 30. Factor m(j).
-2*(j - 1)**2*(j + 1)**2/19
Factor -32*k - 36*k - 67 + 44*k**2 + 91.
4*(k - 1)*(11*k - 6)
Let y be (5/(4 + -19))/(-1). Let -1/3*u**4 + 1/3*u**2 + y*u**3 + 0 - 1/3*u = 0. What is u?
-1, 0, 1
Let j(y) be the first derivative of -y**4/22 - 2*y**3/33 + 6. Factor j(b).
-2*b**2*(b + 1)/11
Suppose -6*c + 2*c - 24 = 0. Let y be c/9 + (-4)/(-6). Factor 0*a - a + a**2 + y*a**2.
a*(a - 1)
Let d(o) be the third derivative of o**6/960 + o**5/60 + o**4/12 + 2*o**2. Factor d(s).
s*(s + 4)**2/8
Let u(j) be the first derivative of -5*j**7/147 + 4*j**6/35 - 9*j**5/70 + j**4/21 + 2*j + 1. Let f(b) be the first derivative of u(b). Factor f(o).
-2*o**2*(o - 1)**2*(5*o - 2)/7
Let r = -862 + 14648/17. Let p = 5/34 - r. Factor 0 + 1/2*b**4 + p*b**2 + b**3 + 0*b.
b**2*(b + 1)**2/2
Let n be -3*183/(-108) + 203/(-116). Factor n*t**4 + 2/3*t**2 + 4/3*t + 0 - 16/3*t**3.
2*t*(t - 1)**2*(5*t + 2)/3
Let z(f) be the first derivative of -f**4/8 - f**3/3 + 5*f**2/4 + 3*f + 24. What is g in z(g) = 0?
-3, -1, 2
Let i(f) = f**3 - 5*f**2 + 6*f - 5. Let n be i(4). Suppose -n*y - 8 = -5*y. Solve z**4 + y*z**2 - 2*z**2 - 3*z**4 = 0 for z.
-1, 0, 1
Let v(y) be the third derivative of -y**6/2160 - y**5/240 - y**4/72 - y**3/3 - 5*y**2. Let t(u) be the first derivative of v(u). Solve t(q) = 0.
-2, -1
Let t(a) be the first derivative of -5*a**4/16 + 5*a**3/12 + 15*a**2/4 + 7. Factor t(u).
-5*u*(u - 3)*(u + 2)/4
Suppose 0 = 3*z + 17 - 11. Let c be ((-3)/((-3)/(-4)))/z. Solve 1/2*s**3 - 1/4*s - 1/4*s**5 + 0*s**4 + 0 + 0*s**c = 0.
-1, 0, 1
Find n, given that 3/5*n - 2/5 - 1/5*n**2 = 0.
1, 2
Find o such that -2*o**3 + 3*o**2 + 8*o**3 - 9*o**3 + 3*o**5 - 3*o**4 = 0.
-1, 0, 1
Suppose 0 = 5*a - b + 4*b + 3, 5 = -5*b. Let u = -117 + 119. Factor -1/4*l**u + a*l + 0 + 1/4*l**3.
l**2*(l - 1)/4
Suppose 3*q + 4 = -g, 4*q + 22 = 4*g + 6. Factor -3/2*j**3 + 3/2*j - 3/2*j**g + 3/2.
-3*(j - 1)*(j + 1)**2/2
Let o(p) be the third derivative of -p**6/480 - 13*p**5/240 - 35*p**4/96 + 49*p**3/24 - 33*p**2. Factor o(z).
-(z - 1)*(z + 7)**2/4
Let s be (-4)/(-6) + 16/12. Solve -2*j - 4*j + 2*j**3 + 0*j - s*j**2 + 2*j = 0.
-1, 0, 2
Suppose -4*j - j = -15. Factor -8*r + j*r**2 + 6 - 2 - r**3 + 4*r**2 - 2*r**2.
-(r - 2)**2*(r - 1)
What is z in -2/7*z**2 + 4/7*z + 0 - 2/7*z**3 = 0?
-2, 0, 1
Let z(n) = n**3 - n**2 + 1. Let h(g) = -5*g**4 + 25*g**3 - 25*g**2 + 5*g + 10. Let p(q) = h(q) - 10*z(q). Factor p(m).
-5*m*(m - 1)**3
Let b = 18 + -18. Determine x, given that 1/5*x + 7/5*x**3 + b + 3/5*x**4 + x**2 = 0.
-1, -1/3, 0
Suppose -4*o + 5*g = 4 - 1, 5*o - 18 = -g. Suppose 3*f**5 + o*f - 4*f**4 - 2*f**4 - 3*f = 0. Calculate f.
0, 2
Let m be -6 + 2 - (-1 - 8). Let p(i) be the third derivative of 3/40*i**m + 0 + 1/12*i**3 - 1/8*i**4 + 2*i**2 + 0*i. Determine w, given that p(w) = 0.
1/3
Let c = 97 - 52. Let z be 2/(-3)*c/(-6). Factor 0*y**2 - z*y - 2*y**2 + 5*y.
-2*y**2
Factor 0 + 1/2*t**3 - 1/2*t + 1/2*t**4 - 1/2*t**2.
t*(t - 1)*(t + 1)**2/2
Let 12*s + 9*s**5 + 156*s**3 - 24 - 23*s**2 + 149*s**2 - 15*s**3 + 60*s**4 = 0. What is s?
-2, -1, 1/3
Factor 2*u + 10/7*u**2 + 4/7.
2*(u + 1)*(5*u + 2)/7
Let n be 82/(-120) - (-3)/4. Let t(l) be the third derivative of l**2 + 0*l**3 + 0 + n*l**5 - 1/60*l**6 - 1/12*l**4 + 0*l. Determine x, given that t(x) = 0.
0, 1
Let m(g) be the first derivative of -2/45*g**3 + 0*g + 2/75*g**5 + 0*g**2 + 0*g**4 - 6. Factor m(y).
2*y**2*(y - 1)*(y + 1)/15
Find l, given that -8/11 - 10/11*l**2 + 16/11*l + 2/11*l**3 = 0.
1, 2
Let u be 0 + ((-20)/28 - -1). Let c be (2/21)/((-3)/(-9)). Determine t so that u - c*t - 2/7*t**2 + 2/7*t**3 = 0.
-1, 1
Let y = 459 + -457. Factor 0*c + 1/5*c**y - 1/5.
(c - 1)*(c + 1)/5
Let 3/4*t**2 + 0*t**3 + 3/8*t + 0 - 3/4*t**4 - 3/8*t**5 = 0. What is t?
-1, 0, 1
Let s be (-6)/9*3 - 7. Let t = -17/2 - s. Factor 1/2*f**2 - 1/4*f**5 - 1/4*f**4 + t*f**3 - 1/4 - 1/4*f.
-(f - 1)**2*(f + 1)**3/4
Factor -10 + 7*p - 4*p**3 - p**3 + 9*p - p.
-5*(p - 1)**2*(p + 2)
Let f(a) be the first derivative of -1/2*a**3 - 1/30*a**5 - 8 - 7/12*a**2 - 5/24*a**4 - 1/3*a. Determine u so that f(u) = 0.
-2, -1
Let v(z) = 8*z - 38. Let f be v(5). Find s such that 1/4*s**f + 0*s + 0*s**3 - 1/4*s**4 + 0 = 0.
-1, 0, 1
Let h(n) be the first derivative of n**6/6 + n**5/5 - n**4/2 - 2*n**3/3 + n**2/2 + n + 7. Factor h(k).
(k - 1)**2*(k + 1)**3
Let g(r) be the first derivative of 6*r - 9/2*r**2 + r**3 + 4. Factor g(w).
3*(w - 2)*(w - 1)
Find l such that -3*l**2 + 4*l**4 + 15*l**2 - 6*l**3 - 4*l**3 - 4*l - 2*l**3 = 0.
0, 1
Suppose -3*k = -k - 8. Factor -2*t**2 - 2*t**2 + 0*t**3 - 2*t + k*t**4 + 0*t**3 + 2*t**5.
2*t*(t - 1)*(