 + 5*v + 6*v**3.
(v + 1)**2*(v + 2)**2
Let y(u) be the second derivative of -u**9/15120 + u**7/1260 - u**5/120 + u**4/12 - 3*u. Let t(f) be the third derivative of y(f). Find k such that t(k) = 0.
-1, 1
Let d(z) = -5*z**2 + 6*z - 1. Let f(n) = 4*n**2 - 5*n. Let w(o) = -3*d(o) - 4*f(o). Find y such that w(y) = 0.
-1, 3
Let z(f) = 20*f - 2*f**2 - 13*f - 17*f. Let v be z(-5). Factor 0*o**4 - 2/7*o**5 + 2/7*o**3 + 0*o**2 + 0*o + v.
-2*o**3*(o - 1)*(o + 1)/7
Let z = -5 + 7. Determine r so that 10*r**z - 56*r**3 - r - 3*r - 40*r**2 = 0.
-2/7, -1/4, 0
Let p = -19314 - -2027986/105. Let o = p - -2/15. Solve 2/7*w**2 + 4/7*w**3 + 0 + 0*w + o*w**4 = 0.
-1, 0
Let i(f) be the third derivative of 3/16*f**4 + 0*f**3 - f**2 + 0 - 1/20*f**5 + 0*f + 1/240*f**6. Factor i(g).
g*(g - 3)**2/2
Let u = 25 + -20. Suppose -1 = 2*v + u*n, 3*v + 3 = 5*v + n. What is g in -8/3*g**2 - v*g + 2/3 = 0?
-1, 1/4
Let f(s) be the first derivative of 35*s**6/6 + 2*s**5 - 35*s**4/2 - 20*s**3/3 + 35*s**2/2 + 10*s - 9. Solve f(t) = 0 for t.
-1, -2/7, 1
Let 2/3*t**2 + 1/3*t**4 + 4/3*t - 4/3*t**3 - 1 = 0. Calculate t.
-1, 1, 3
What is k in -1/2*k**4 + 0 + 0*k**2 + 0*k - k**3 = 0?
-2, 0
Let i(d) be the second derivative of 1/30*d**4 + 2/5*d**2 + 0 - 1/5*d**3 + 9*d. Factor i(z).
2*(z - 2)*(z - 1)/5
Let h(i) be the first derivative of 3*i**4/20 - 2*i**3/3 + 2*i**2/5 + 8*i/5 - 34. Factor h(v).
(v - 2)**2*(3*v + 2)/5
Let d(o) be the first derivative of -4*o**5/45 - 2*o**4/3 - 16*o**3/9 - 20*o**2/9 - 4*o/3 - 8. Factor d(a).
-4*(a + 1)**3*(a + 3)/9
Suppose 4*q = 2 + 10. Determine g, given that -6*g**3 - 24*g**2 + 3*g**5 + g**q + 5*g**3 + 6*g**4 - 21*g - 6*g**3 - 6 = 0.
-1, 2
Let n be (42/9)/(4/6). Suppose n = 2*z + 3. Solve 2/3*l**4 + 0 + z*l**3 + 2*l**2 + 2/3*l = 0.
-1, 0
Let t(y) be the second derivative of y**9/105840 - y**7/8820 + y**5/840 + 3*y**4/4 - y. Let p(g) be the third derivative of t(g). Let p(l) = 0. What is l?
-1, 1
Let n(f) be the first derivative of 4*f**5/35 - 5*f**4/7 + 4*f**3/3 - 6*f**2/7 + 20. Let n(j) = 0. What is j?
0, 1, 3
Let r(k) be the third derivative of -k**5 + 0 - 19/30*k**6 + 4/3*k**3 - 2/15*k**7 - 1/6*k**4 + 0*k + 5*k**2. Find w, given that r(w) = 0.
-1, 2/7
Let z(p) be the second derivative of -p**4/4 - 8*p. Let z(n) = 0. Calculate n.
0
Factor -2/5*n**3 + 6/5*n**5 + 0*n + 0 - 4/5*n**2 + 8/5*n**4.
2*n**2*(n + 1)**2*(3*n - 2)/5
Let c(o) be the second derivative of -4*o**6/45 - o**5/2 - 2*o**4/3 + 4*o**3/9 + 38*o. Suppose c(d) = 0. What is d?
-2, 0, 1/4
Find s, given that 56*s + 5*s**5 + 5*s**2 - 20*s**4 - 76*s + 15*s**3 + 15*s**2 = 0.
-1, 0, 1, 2
Let k(d) be the third derivative of d**5/15 + 5*d**4/24 + d**3/6 + 16*d**2. Factor k(i).
(i + 1)*(4*i + 1)
Suppose 3*p = t + 4, 4*t - p - p - 4 = 0. Solve 2/9*y + 0 + 10/9*y**t + 8/9*y**3 = 0 for y.
-1, -1/4, 0
Suppose -4*z = z + 11*z. Find j such that 4/7*j + 2/7*j**3 + z - 6/7*j**2 = 0.
0, 1, 2
Suppose a - 2*t - 15 = 0, -25 = -4*a + 3*t - 2*t. Let o(c) be the first derivative of -c**2 - 2/3*c**3 + 1/2*c**4 - 1 + 2/5*c**a + 0*c. Factor o(u).
2*u*(u - 1)*(u + 1)**2
Let t be (-8 - 0)/((-6)/(-45)). Let i be 12/t + (-23)/(-15). Factor -4/3*y**3 - 2/3 + 2/3*y**5 + i*y**2 + 2/3*y - 2/3*y**4.
2*(y - 1)**3*(y + 1)**2/3
Let k(h) be the second derivative of -11*h**4/16 - 13*h**3/8 - 3*h**2/4 - 5*h. Solve k(w) = 0 for w.
-1, -2/11
Let s(q) = -5*q**3 + 6*q**2 + 2*q + 2. Let y(n) = 10*n**3 - 11*n**2 - 3*n - 5. Let x(o) = 5*s(o) + 2*y(o). Factor x(a).
-a*(a - 2)*(5*a + 2)
Let s(x) = -9*x**3 + 6*x + 3. Let o = 15 + -19. Let f(n) = -9*n**3 + n**2 + 6*n + 4. Let b(g) = o*s(g) + 3*f(g). Factor b(q).
3*q*(q + 1)*(3*q - 2)
Factor -16/9*d**2 + 0*d + 0 - 32/9*d**3 - 20/9*d**4 - 4/9*d**5.
-4*d**2*(d + 1)*(d + 2)**2/9
Let n(a) be the second derivative of -a**7/70 + a**6/30 - a**5/50 - a. Let n(x) = 0. Calculate x.
0, 2/3, 1
Let c(l) be the third derivative of -l**8/10080 - l**7/1260 - l**6/540 - l**4/24 - 5*l**2. Let b(j) be the second derivative of c(j). Factor b(h).
-2*h*(h + 1)*(h + 2)/3
Let w(a) = -2*a - 2. Let p be w(2). Let t = -6 - p. Factor 0 + 135*j**5 - 22*j**2 + 216*j**4 - 52*j**3 + 124*j**3 - 15*j + t*j - 2.
(j + 1)*(3*j + 1)**3*(5*j - 2)
Find j such that -4/9*j**2 - 2/9*j + 0 - 2/9*j**3 = 0.
-1, 0
Let u(t) be the first derivative of 2/11*t + 2/55*t**5 - 1/11*t**2 + 1/11*t**4 + 3 - 4/33*t**3 - 1/33*t**6. Find s, given that u(s) = 0.
-1, 1
Let n be ((-8)/(-10))/(2/5). Solve -3 + 3 + 8*w + 2 - 4*w + 2*w**n = 0 for w.
-1
Let d(l) be the first derivative of l**4/4 + 10*l**3 + 150*l**2 + 1000*l - 48. Find u, given that d(u) = 0.
-10
Let j = 15 + -10. Factor 0*i**j + i**5 - 2*i**3 - 4*i**4 - 3*i**5.
-2*i**3*(i + 1)**2
Let t(h) = 8*h**3 - 2*h**2 + 10*h + 10. Let o(b) = b**3 + b + 1. Let j(z) = -20*o(z) + 2*t(z). Factor j(p).
-4*p**2*(p + 1)
Let r(z) be the first derivative of 0*z**4 + 0*z**3 - 2 + 1/110*z**5 + 0*z**2 + 3*z. Let a(x) be the first derivative of r(x). Solve a(l) = 0 for l.
0
Let v(a) be the third derivative of -5*a**2 - 1/330*a**5 + 1/132*a**4 + 0*a + 1/33*a**3 - 1/660*a**6 + 0. Factor v(w).
-2*(w - 1)*(w + 1)**2/11
Suppose -5*n - 4 = -19. Suppose 0*r + 4*c = r - 20, -3*r = -n*c - 15. Solve r - 2/5*p - 2/5*p**3 + 4/5*p**2 = 0 for p.
0, 1
Let u = 18 - 1. Factor -74*b**3 + 11*b - 12 - 10*b**2 + u*b**3 - 59*b - 3*b**5 - 65*b**2 - 21*b**4.
-3*(b + 1)**3*(b + 2)**2
Factor 1/3*a**3 + 0 - 3*a**5 + 0*a + 0*a**2 + 0*a**4.
-a**3*(3*a - 1)*(3*a + 1)/3
Suppose 36*j = 20*j + 64. Suppose -2*y**j - 14/3*y**3 - 16/3*y**2 - 2/3 - 3*y - 1/3*y**5 = 0. What is y?
-2, -1
Let m be 2/14*(16 - 13). Solve 0 + 6/7*h**4 - 6/7*h**2 + 0*h**3 - 3/7*h + m*h**5 = 0 for h.
-1, 0, 1
Let i(b) be the first derivative of -3*b**5/20 + 3*b**4/4 - 3*b**3/4 + 20. Factor i(o).
-3*o**2*(o - 3)*(o - 1)/4
Let y(u) be the first derivative of -u**7/21 - u**6/15 + u**5/10 + u**4/6 - 2*u + 10. Let r(f) be the first derivative of y(f). Factor r(s).
-2*s**2*(s - 1)*(s + 1)**2
Suppose 3*o + 23 = 167. Let f be o/70*21/6. Find y, given that -18/5*y**2 + f*y - 2/5 = 0.
1/3
Let k(d) be the second derivative of -d**5/90 - 5*d**4/54 - 7*d**3/27 - d**2/3 - 11*d. Determine g, given that k(g) = 0.
-3, -1
Factor -2/3*i**2 + 0*i + 2/3*i**3 + 0 - 2/3*i**5 + 2/3*i**4.
-2*i**2*(i - 1)**2*(i + 1)/3
Let v(l) be the third derivative of l**8/84 - 2*l**7/35 + l**6/15 + 2*l**5/15 - l**4/2 + 2*l**3/3 - 4*l**2. Factor v(x).
4*(x - 1)**4*(x + 1)
What is d in d**2 + 0*d**2 + d**2 + 4*d + 2*d**2 = 0?
-1, 0
Let d(p) = p**2 + 7*p - 12. Let k be d(-9). Suppose 3*g = k*g - 6. Solve -5*r**3 + 2*r**2 + 3*r**4 + 0*r**3 + 0*r**g = 0.
0, 2/3, 1
Let w(t) = -28*t**3 - 18*t**2 + 6*t + 6. Let p(i) = -28*i**3 - 19*i**2 + 7*i + 7. Let r(x) = 6*p(x) - 7*w(x). Determine y so that r(y) = 0.
-3/7, 0
Suppose -24/11 + 2/11*d**2 - 2*d = 0. What is d?
-1, 12
Suppose c - 3*c - 6 = -2*p, c - 15 = -2*p. Let -h - 3*h - h**3 - h**3 + p*h**2 = 0. Calculate h.
0, 1, 2
Let q(s) be the third derivative of s**5/42 - s**4/7 + 4*s**3/21 - 5*s**2. Let q(g) = 0. What is g?
2/5, 2
Let l(g) = -g + 14. Let f be l(10). Factor -f*c - 12*c**3 - 4*c**2 + 5*c - c - 9*c**4 - 2*c**5.
-c**2*(c + 2)**2*(2*c + 1)
Let n be (0/1)/(-2)*-1. Let f = -21 - -21. Factor n + 2/7*w**3 + f*w - 2/7*w**2.
2*w**2*(w - 1)/7
Let i(b) be the third derivative of -b**6/40 - b**5/20 + b**4/8 + b**3/2 - 20*b**2. What is f in i(f) = 0?
-1, 1
Factor 5/7*s - 1/7*s**2 - 4/7.
-(s - 4)*(s - 1)/7
Let w = -408 + 1226/3. Solve w*z - 2/3*z**2 + 4/3 = 0 for z.
-1, 2
Let t be 2/(-22) + (-5 - -5). Let p = t - -14/33. Factor 0*h + 0 + p*h**2.
h**2/3
Solve -2*x**2 + 31*x - 18*x - 15*x = 0 for x.
-1, 0
Let q = -14 - -18. Let 1/2*h**q + 0 + 0*h - 1/2*h**2 + 0*h**3 = 0. What is h?
-1, 0, 1
Let v = 370/873 + 2/97. Find q, given that -2/9*q**2 + 0 + 0*q - 2/9*q**4 - v*q**3 = 0.
-1, 0
Let r(j) = 2*j - 4. Let v be r(4). Let 2/3*a**3 + 0 + 1/3*a**2 + 1/3*a**v + 0*a = 0. Calculate a.
-1, 0
Factor -1/4*a**2 + 1/4*a**4 + 0 + 1/2*a - 1/2*a**3.
a*(a - 2)*(a - 1)*(a + 1)/4
Let k = -3/818 - -1645/2454. Factor k*l**2 + 0*l + 0.
2*l**2/3
Let t be (48/120)/((-8)/(-10)). Find b such that -t*b**4 + 0*b**2 - b**3 + b + 1/2 = 0.
-1, 1
Suppose -2*l = -5*l + 6. Let h be 14/4 + 3/l. What is o in o + 2*o**2 + o**h + 5 - 2*o**3 - 4 - o**4 - 2 = 0?
-1, 1
Suppose -2 + 27 = 5*w. Factor -m**2 + 3*m**3 + 0*m*