3, 3
Suppose h + 4*h = 70. Solve 2*o**3 - h*o - 2*o - 8 - 10*o**2 - 4*o**3 = 0.
-2, -1
Let t = -141/2 - -71. Find p, given that 1/2*p**3 + 0*p - 1/2*p**4 + 1/2*p**2 + 0 - t*p**5 = 0.
-1, 0, 1
Suppose -6 = -4*s + 2*y, 0 = 4*s + 4*y - 22 - 14. Solve -3/5*j**2 + 3/5*j**s + 0*j**3 + 0*j + 0 = 0.
-1, 0, 1
Let u(b) be the second derivative of b**6/2 - 5*b**5/4 + 5*b**4/12 + 5*b**3/6 + 14*b. Let u(x) = 0. Calculate x.
-1/3, 0, 1
Let w(o) be the second derivative of o**7/2940 - o**6/1260 - o**5/420 + o**4/84 - o**3 + 6*o. Let f(h) be the second derivative of w(h). Factor f(a).
2*(a - 1)**2*(a + 1)/7
Determine s, given that 4/13*s**3 + 2/13*s**4 + 2/13*s**2 + 0 + 0*s = 0.
-1, 0
Let q(g) be the second derivative of -g**4/54 + g**3/9 + 4*g**2/9 - 4*g. Factor q(u).
-2*(u - 4)*(u + 1)/9
Let z(k) be the third derivative of k**5/30 - k**4/6 - k**2. Find s, given that z(s) = 0.
0, 2
Let g(m) be the first derivative of 0*m**2 + 2/3*m**3 + 0*m + 1 - 1/36*m**4 + 1/540*m**6 + 0*m**5. Let o(k) be the third derivative of g(k). Factor o(b).
2*(b - 1)*(b + 1)/3
Factor -4*m**2 - 6 + m**2 + 15*m - 6*m.
-3*(m - 2)*(m - 1)
Let x be -3 + -2 + 2 - 3. Let r be (-14)/x - 3/9. Factor -5/3*m + 2/3 + 2/3*m**r + 1/3*m**5 - 4/3*m**4 + 4/3*m**3.
(m - 2)*(m - 1)**3*(m + 1)/3
Let f(j) = j**3 - 3*j**2 + j - 1. Let u(z) = 2 - z - 4 + 2*z**3 + 2*z - 4*z**2. Let a(p) = p + 2. Let s be a(0). Let d(o) = s*u(o) - 3*f(o). Factor d(n).
(n - 1)*(n + 1)**2
Let d be -1*3/9*-12. Factor d - 3*b**2 - 2 - 2.
-3*b**2
Let o(t) be the third derivative of -t**7/2940 + t**5/140 - t**4/42 - 2*t**3/3 + 3*t**2. Let g(y) be the first derivative of o(y). Suppose g(p) = 0. What is p?
-2, 1
Let q = -3/553 - -8875/4977. What is y in -q*y**4 + 8/9*y - 20/9*y**3 + 2/3*y**2 - 2/9 = 0?
-1, 1/4, 1/2
Let r(n) = -n - 7. Let g be r(-7). Suppose -11 = -5*i + 4, g = 3*c - 2*i. What is p in -2/3*p**3 + 0 + 2/3*p - 2/3*p**4 + 2/3*p**c = 0?
-1, 0, 1
Solve -4*a + 4*a**3 + 12 - 4*a - 12*a**2 + 4*a + 0*a**3 = 0.
-1, 1, 3
Let k(d) be the third derivative of -2*d**7/105 - 2*d**6/15 - d**5/3 - d**4/3 - 16*d**2. Factor k(z).
-4*z*(z + 1)**2*(z + 2)
Let s = 5 - 7. Let g be 0 - (12/(-3) - s). Determine d, given that 1/4*d + 1/4*d**g + 0 = 0.
-1, 0
Let d(n) be the second derivative of -5*n**5/18 + 5*n**4/6 - 8*n**3/9 + 4*n**2/9 + 9*n. Factor d(v).
-2*(v - 1)*(5*v - 2)**2/9
Let d(w) = w**2 + 4*w - 2. Suppose 3*a + 5 = 2*a. Let t be d(a). What is i in 5 + 2 + 6*i - t*i**4 - 4 - 6*i**3 = 0?
-1, 1
Let h(r) be the third derivative of r**8/112 - r**7/40 - r**6/80 + r**5/10 - r**4/16 - r**3/8 + 11*r**2. Suppose h(a) = 0. Calculate a.
-1, -1/4, 1
Let t(y) be the third derivative of 0 - 1/20*y**5 + 0*y + 1/6*y**3 + 1/12*y**4 - 2*y**2. Factor t(v).
-(v - 1)*(3*v + 1)
Let g(z) = z**3 - 2*z**2 + 3*z - 4. Let f be g(2). Let h(b) be the first derivative of 0*b + 1/2*b**3 - 1/2*b**2 + 3/2*b**4 + 7/10*b**5 - f. Factor h(a).
a*(a + 1)**2*(7*a - 2)/2
Let z = -9 + 8. Let s = 1 - z. Factor -3*c**3 - 2*c**2 - 2*c**s + 5*c**3.
2*c**2*(c - 2)
Let h(k) = k**3 - 12*k**2 + 21*k - 8. Let q be h(10). Let g(f) be the second derivative of 0 - 1/54*f**4 + 1/9*f**2 + 0*f**3 - q*f. Factor g(u).
-2*(u - 1)*(u + 1)/9
Let u(s) be the first derivative of 2 + 0*s**2 + 0*s + 0*s**4 + 2/15*s**3 - 2/25*s**5. Solve u(i) = 0 for i.
-1, 0, 1
Let s(m) = -m**2 + 6*m + 2. Let p be s(6). Solve y**2 - 1 + 0*y**p + 0*y**2 = 0.
-1, 1
Let o(y) be the third derivative of -y**5/210 - y**4/28 - 2*y**3/21 - 24*y**2. Factor o(h).
-2*(h + 1)*(h + 2)/7
Let b be ((-22)/33)/((-21)/14). Factor 2/9*d**2 + 2/9 - b*d.
2*(d - 1)**2/9
Let u(w) = 7*w**5 - 5*w**4 - 4*w**3 + 7*w - 5. Let s(q) = 6*q**5 - 4*q**4 - 4*q**3 + 6*q - 4. Let j(t) = 5*s(t) - 4*u(t). Factor j(g).
2*g*(g - 1)**2*(g + 1)**2
Let o(g) be the first derivative of g**6/1440 + g**5/80 + 3*g**4/32 + 2*g**3 - 1. Let j(f) be the third derivative of o(f). Solve j(k) = 0 for k.
-3
Let h = 7 - 5. Suppose -h*k + 8 + 42 = 0. Factor n**2 + k - 25 + 2*n.
n*(n + 2)
Suppose 7*i + 0 = 14. Let f(t) = t - 2. Let y be f(i). Find j, given that 0*j + y + 2/5*j**2 - 6/5*j**3 - 2/5*j**5 + 6/5*j**4 = 0.
0, 1
Let h = 85 + -80. Let z(b) be the third derivative of 1/120*b**h + 0*b**4 - 1/420*b**7 + 0*b**6 + 0 + 0*b + b**2 + 0*b**3. Factor z(n).
-n**2*(n - 1)*(n + 1)/2
Suppose -5*v = 5*x - 40, -2*v + 3*v = 3*x - 12. Let n(c) be the first derivative of c + 2 + 0*c**2 - 1/3*c**v. Factor n(i).
-(i - 1)*(i + 1)
Find b, given that 25 - 43 + 34 - 36*b**2 - 64*b = 0.
-2, 2/9
Let w be -1 + 3 + -1 + 2. Factor 2*y**w - 17*y**2 - 3*y**2 - 16*y + 2 + 14 + 10*y**3.
4*(y - 2)*(y + 1)*(3*y - 2)
Let x(a) be the first derivative of -a**6/360 + a**4/24 - 2*a**3/3 + 1. Let q(c) be the third derivative of x(c). Determine y so that q(y) = 0.
-1, 1
Let z(o) be the first derivative of 6 - 9/16*o**4 + o**3 - 3/5*o**5 + 0*o + 3/2*o**2 - 1/8*o**6. What is p in z(p) = 0?
-2, -1, 0, 1
Factor -2/3*v**3 + 0 - 4/3*v**2 - 2/3*v.
-2*v*(v + 1)**2/3
Let p(t) be the third derivative of -t**8/1344 + t**6/480 - 4*t**2. Factor p(n).
-n**3*(n - 1)*(n + 1)/4
Let l(z) be the second derivative of 0 - 2*z + 0*z**2 + 0*z**4 - 3/20*z**5 + 1/2*z**3. Determine r so that l(r) = 0.
-1, 0, 1
Factor 6*o**4 - 2*o**5 + 2*o**3 - 6*o**4.
-2*o**3*(o - 1)*(o + 1)
Let l be (3/(-10))/(12/(-32)*2). Find m, given that l*m**2 - 8/5*m + 8/5 = 0.
2
Let a be -4*-1*12/16. Suppose -4*u**a - u**3 + 3*u**3 + 2 + 6*u**2 - 2*u - 4*u = 0. Calculate u.
1
Suppose 0 = 2*i - k - 0 - 5, -3*k + 5 = -i. Let w = -1 + i. Factor 8/7*g**4 + 2/7*g**5 + 0 + 12/7*g**w + 2/7*g + 8/7*g**2.
2*g*(g + 1)**4/7
Solve 4/7*n - 8/7*n**2 + 2/7*n**4 + 6/7 - 4/7*n**3 = 0.
-1, 1, 3
Let z(r) be the first derivative of -4*r**6/3 + 4*r**5/5 + 9*r**4 - 16*r**3/3 - 8*r**2 - 11. Determine g, given that z(g) = 0.
-2, -1/2, 0, 1, 2
Let w(b) be the third derivative of 5*b**8/84 - 8*b**7/105 - 31*b**6/30 + 14*b**5/15 + 22*b**4/3 + 16*b**3/3 - 38*b**2. Suppose w(g) = 0. Calculate g.
-2, -1, -1/5, 2
Let w(f) = 3*f + 30. Let i be w(-10). Let p(o) be the first derivative of 0*o**4 + 1/20*o**5 + 0*o**3 + i*o**2 - 1 + 0*o. Find b such that p(b) = 0.
0
Let q(u) be the first derivative of 5/2*u**2 + 2 + u + 25/12*u**3. Suppose q(v) = 0. Calculate v.
-2/5
Let u(a) be the third derivative of -a**5/20 - a**4/4 - 8*a**2 + 3*a. Let u(d) = 0. What is d?
-2, 0
Let v be 50/12 + -3 - 1. Factor 0*k + 1/6*k**2 - v*k**4 + 1/6*k**5 - 1/6*k**3 + 0.
k**2*(k - 1)**2*(k + 1)/6
Let n(j) = j**3 - 2*j**2 - 7*j - 1. Let f be n(4). Suppose i**f + i**2 + 1/2 + 1/2*i**5 - 3/2*i**4 - 3/2*i = 0. What is i?
-1, 1
Let h(l) = -4 - 5 - 4 + 4 + 3*l**4 - 9*l**3 - 12*l**5 + 9*l. Let f(o) = -3*o**5 + o**4 - 2*o**3 + 2*o - 2. Let s(q) = 9*f(q) - 2*h(q). What is k in s(k) = 0?
0, 1
Let 0*k + 0*k**2 + 4*k - k**2 + k = 0. Calculate k.
0, 5
Let t be ((-6)/(-6))/((-2)/(-6)). Let h = -2 + t. Factor 0 - 4*v**2 - 1 - 67*v - v**3 + 62*v - h.
-(v + 1)**2*(v + 2)
Let t(y) be the second derivative of -5/21*y**3 - 1/70*y**5 + 2/7*y**2 - 4*y + 0 + 2/21*y**4. Let t(z) = 0. Calculate z.
1, 2
Let w(y) = -2*y**5 + 2*y**4 + 10*y**3 - 16*y**2 + 6*y - 1. Let j(p) = -p**5 + p**4 - p**3 + p**2 + 1. Let k(a) = -j(a) - w(a). Suppose k(d) = 0. Calculate d.
-2, 0, 1
Find d, given that 8/5 - 48/5*d + 42/5*d**2 + 98/5*d**3 = 0.
-1, 2/7
Let b(f) be the third derivative of f**6/300 - f**5/75 + f**4/60 + 7*f**2. Factor b(t).
2*t*(t - 1)**2/5
Let t be 12/(-30) + 14/10. Let v be t/((-2)/(-3)) - 1. Factor 0 - 1/2*s**2 + v*s - 1/2*s**3 + 1/2*s**4.
s*(s - 1)**2*(s + 1)/2
Let y be -3 + ((-157)/4 - 4). Let v = -46 - y. Factor -1 - v*q**2 + q.
-(q - 2)**2/4
Let k(j) = 27*j**3 + 11*j**2 + 7*j. Let s(d) = 13*d**3 + 5*d**2 + 4*d. Let n = -3 - 2. Let h(m) = n*s(m) + 3*k(m). Factor h(i).
i*(4*i + 1)**2
Let g(c) be the second derivative of -c**6/180 - c**5/15 - c**4/3 + c**3/3 - 2*c. Let i(l) be the second derivative of g(l). Factor i(m).
-2*(m + 2)**2
Let t be (-6 + 2 - -2)/(-4). Let u be (0 - 0)/(1 + -2). Factor t*n + 1/2*n**2 + u.
n*(n + 1)/2
Find f, given that 2/3*f - 4/3*f**2 + 4/3 - 2/3*f**3 = 0.
-2, -1, 1
Let t(r) be the first derivative of -r**3 - 3/4*r**4 + 0*r**2 + 0*r - 7 + 1/2*r**6 + 3/5*r**5. Factor t(l).
3*l**2*(l - 1)*(l + 1)**2
Let s(z) be the first derivative of z**8/840 + z**7/210 + z**6/180 - 2*z**3/3 - 3. Let a(y) be the third deriv