12*y**3 + 0*y**2. Factor t(m).
-m*(m - 1)**4/2
Let o = 0 + 2. Let k(a) be the first derivative of 0*a**o + 0*a + 6/5*a**5 - 3/2*a**4 - 1 - 1/3*a**6 + 2/3*a**3. Factor k(b).
-2*b**2*(b - 1)**3
Suppose 3*y = 4*n + 22, n = -y - 0*n - 2. Let a(z) be the second derivative of -4/11*z**y - 2*z - 1/66*z**4 + 0 + 4/33*z**3. Find k such that a(k) = 0.
2
Let k(u) be the first derivative of u**6/1800 + u**5/150 + u**4/30 - u**3 + 4. Let f(d) be the third derivative of k(d). Let f(y) = 0. What is y?
-2
Suppose j**2 - 9*j**2 + 12 + 3*j**4 + 6*j**3 - 12*j + 0 - j**2 = 0. What is j?
-2, 1
Solve -4/7*j**3 + 8/7*j**2 - 32/7 + 16/7*j = 0 for j.
-2, 2
Suppose -4*x = 5*i - 39, -3*i + 52 = i - 2*x. Determine a, given that 14*a**2 - 1 - 10*a**4 - 3 + 5*a + 6*a**3 - i*a = 0.
-1, -2/5, 1
Let x(h) = h**2 + 3*h - 7. Let d be x(-5). Let u(g) be the second derivative of 2/5*g**2 + 0 + 1/15*g**d + g - 1/30*g**4. Factor u(z).
-2*(z - 2)*(z + 1)/5
Let t be (-5)/15 - (-85)/12. Factor 0 + t*v - 9/2*v**2 + 3/4*v**3.
3*v*(v - 3)**2/4
Let k(o) = o**2 + 7*o + 7. Let v be k(-5). Let s = 0 - v. What is j in 6/5*j**2 + 2/5 - 6/5*j - 2/5*j**s = 0?
1
Let g(t) be the third derivative of t**7/140 - t**6/16 + t**5/5 - t**4/4 - 12*t**2. Factor g(j).
3*j*(j - 2)**2*(j - 1)/2
Let m(g) be the third derivative of 0*g**3 + 0*g + 1/21*g**4 + 1/15*g**7 + 1/20*g**6 + 3*g**2 + 0 - 4/35*g**5. What is f in m(f) = 0?
-1, 0, 2/7
Factor 0*v**2 + 3*v**2 - v - 2*v**2.
v*(v - 1)
Let m(c) be the first derivative of c**3 + 6*c**2 + 12*c + 8. Factor m(q).
3*(q + 2)**2
Let s(v) be the second derivative of -v**9/16632 + v**7/2310 - v**5/660 - v**3/6 + 2*v. Let h(i) be the second derivative of s(i). Factor h(n).
-2*n*(n - 1)**2*(n + 1)**2/11
Let t = -1333/3 - -446. What is z in -1/3*z**2 + 2/3*z + 0 - t*z**3 + z**5 + 1/3*z**4 = 0?
-1, 0, 2/3, 1
Let x = -402/11 + 3662/99. Determine s, given that -2/9*s**3 + 2/9*s**2 + 0 + x*s = 0.
-1, 0, 2
Let d = 3 - 5. Let t be (3 + d)/((-9)/(-2)). Factor -50/9*p**2 - 14/9*p**4 + 38/9*p**3 - 8/9 + t*p**5 + 32/9*p.
2*(p - 2)**2*(p - 1)**3/9
Let m(y) be the second derivative of 8*y**7/105 + 4*y**6/15 + 17*y**5/100 + y**4/30 - 10*y. Factor m(f).
f**2*(f + 2)*(4*f + 1)**2/5
Let v(c) be the first derivative of 0*c**4 + 2 + 0*c + 1/5*c**5 + c**2 - c**3. Solve v(g) = 0.
-2, 0, 1
Let m(p) be the third derivative of -p**8/672 + p**7/84 - 3*p**6/80 + 7*p**5/120 - p**4/24 - 40*p**2. Find j such that m(j) = 0.
0, 1, 2
Let n(u) = u**2 - 4. Let f be n(3). Find o such that f + 3*o**2 + 5*o + 3 + 7*o + 4 = 0.
-2
Let y(a) be the second derivative of -5*a**4/24 + 5*a**3/6 - 5*a**2/4 + 10*a. Solve y(q) = 0.
1
What is b in 1/7*b - 1/7*b**2 + 0 + 1/7*b**4 - 1/7*b**3 = 0?
-1, 0, 1
Let z(i) be the first derivative of -i**6/8 + 7*i**5/20 - 5*i**4/16 + i**3/12 - 4. Factor z(r).
-r**2*(r - 1)**2*(3*r - 1)/4
Let j(n) = -n**2 - 26*n - 150. Let l be j(-9). Determine h so that -432/7*h + 216/7*h**2 + 4/7*h**4 + 324/7 - 48/7*h**l = 0.
3
Factor -3*v - 4*v + 12*v + 4*v**3 + 7*v + 4 + 12*v**2.
4*(v + 1)**3
Factor 0 + 100/3*v**5 + 0*v + 16/3*v**2 + 32*v**3 + 60*v**4.
4*v**2*(v + 1)*(5*v + 2)**2/3
Let q be (-2)/(-8) - (-29)/4. Let v = 9 - q. Find l, given that -1 + 5/2*l - v*l**2 = 0.
2/3, 1
Let l(a) be the second derivative of a**7/126 + a**6/90 + 9*a. Factor l(y).
y**4*(y + 1)/3
Let v(n) be the third derivative of n**7/49 - 13*n**6/140 + 9*n**5/70 + n**4/28 - 2*n**3/7 + 8*n**2. Solve v(c) = 0.
-2/5, 1
Let k(d) = -2*d**3 - 3*d**2 - d - 2. Let v be k(-2). Let l(q) be the first derivative of -1/3*q**3 + 0*q + 0*q**2 + 2 + 1/4*q**v. Solve l(h) = 0 for h.
0, 1
Let a(n) = 4*n - 9. Let k be a(3). Let f(g) be the first derivative of 1/10*g**4 - 2/15*g**k - 3 + 0*g**2 + 0*g. Solve f(i) = 0 for i.
0, 1
Let y(m) = 20*m**3 + 5*m**2 - 5*m + 55. Let c(d) = d**3 + d**2 + d + 1. Let t(h) = 15*c(h) - y(h). Suppose t(g) = 0. What is g?
-2, 2
Let n(q) be the first derivative of q**6/8 - 3*q**5/20 - 15*q**4/16 - 3*q**3/4 - 4. Determine o so that n(o) = 0.
-1, 0, 3
Let v(x) be the third derivative of -x**6/720 - x**5/360 + x**4/36 + x**3/9 - 2*x**2. Factor v(k).
-(k - 2)*(k + 1)*(k + 2)/6
Let u = 5/878 - 296789/4390. Let v = u + 68. Factor -4/5*n - 2/5 - v*n**2.
-2*(n + 1)**2/5
Solve 12*z - 332*z**2 - 4*z**3 - 2*z**3 + 2*z**3 + 324*z**2 = 0.
-3, 0, 1
Find u, given that 0*u + 1/5*u**2 + 0 = 0.
0
Suppose j + 27 = -5*f, -5*f = 5*j - j + 33. Let y be (19/(-95))/(2/f). Find s, given that 0*s**2 + 0 + 0*s**3 - y*s**5 + 1/2*s**4 + 0*s = 0.
0, 1
Let u = 3 + 1. Factor 2*i**u - 3*i**4 - 5*i**2 + 2*i**3 + 4*i**2.
-i**2*(i - 1)**2
Factor 0*f + 0 + 1/2*f**3 + 0*f**2 - 5/4*f**4.
-f**3*(5*f - 2)/4
Let u(f) be the third derivative of -f**9/45360 - f**8/20160 + f**7/7560 + f**6/2160 - f**4/8 - 3*f**2. Let y(i) be the second derivative of u(i). Factor y(z).
-z*(z - 1)*(z + 1)**2/3
Let a = 3 + -6. Let c = a - -5. Factor -i**4 + 2*i - 6*i**2 - 3*i - 3*i**3 + 3*i**c.
-i*(i + 1)**3
Suppose 0 = -3*j - 2*j + 2*f + 10, -4*j + 8 = -5*f. Let p be (1 - 1 - 0)/2. Suppose -1/2 + p*g**3 + g**j - 1/2*g**4 + 0*g = 0. What is g?
-1, 1
Factor -4/3*r**3 + 0 + 0*r**4 + 2/3*r + 2/3*r**5 + 0*r**2.
2*r*(r - 1)**2*(r + 1)**2/3
Let d(p) be the second derivative of p**6/33 - p**5/55 - 5*p**4/66 + 2*p**3/33 - 2*p - 28. Solve d(c) = 0.
-1, 0, 2/5, 1
Suppose 4*p + 0 + 1/2*p**2 = 0. Calculate p.
-8, 0
Suppose 3*x - 2 = -c, 0*x = 4*c + 4*x - 8. Let y be 2 - 1 - (-4 - -5). Determine u, given that -u**2 - 3*u - 2*u**c + y + 4*u**2 + 2 = 0.
1, 2
Determine p so that 21/4*p**3 - 21/4*p + 3/2*p**2 - 3/2 = 0.
-1, -2/7, 1
Let h(w) = -w**4 - w + 1. Let j = 18 - 31. Let u = 18 + j. Let c(o) = 7*o**4 - 2*o**3 + 5*o - 5. Let s(v) = u*h(v) + c(v). Factor s(b).
2*b**3*(b - 1)
Determine z, given that -276*z**4 + 254*z**4 - 2*z**2 + 3*z**5 - 22*z**3 - 9*z**5 + 4*z = 0.
-2, -1, 0, 1/3
Let t(h) = -h**5 - 8*h**4 - 8*h**3 + 4*h**2 + 11*h + 3. Let o(b) = -b**5 - b + 1. Let u(p) = -o(p) - t(p). Factor u(k).
2*(k - 1)*(k + 1)**3*(k + 2)
Let r(h) be the first derivative of -3*h**5/5 + 3*h**4/4 + 4*h**3 - 6*h**2 - 15. Factor r(l).
-3*l*(l - 2)*(l - 1)*(l + 2)
Let x(k) be the third derivative of 0*k - 4*k**2 + 1/30*k**5 + 0 + 1/4*k**4 + 2/3*k**3. Let x(n) = 0. Calculate n.
-2, -1
Let o be -3*5/(-9)*2/10. Let y(l) be the third derivative of 1/30*l**5 - 1/6*l**4 + 2*l**2 + 0*l + 0 + o*l**3. Factor y(n).
2*(n - 1)**2
Suppose -m + 21 - 6 = 5*j, -5*m - 12 = -4*j. Let o = j + -1. Solve -2*r**2 + 2 + 0*r**2 + r**3 - o = 0 for r.
0, 2
Let n be (-2)/(-11) - (-210)/(-66). Let l be 3/1 + (n - -4). What is j in -2/7*j**2 + 0 + 2/7*j**3 - 2/7*j + 2/7*j**l = 0?
-1, 0, 1
Let i(p) be the third derivative of -1/24*p**4 + 1/30*p**5 - 2*p**2 + 1/60*p**6 - 1/210*p**7 - 1/6*p**3 - 1/336*p**8 + 0 + 0*p. Find q, given that i(q) = 0.
-1, 1
Suppose 2*g + 4*s - 16 = 0, -19 = 2*g - 8*s + 5*s. Let o be (1/g)/((-6)/36). Factor 0*r + 2/3*r**5 + 0*r**2 + 0*r**o + 2/3*r**4 + 0.
2*r**4*(r + 1)/3
Suppose -21 = -4*m - 1. Let q = 2 - -17. Solve q*l**3 - 11*l**4 + l**5 + 16*l + 1 + 4*l**4 - m - 25*l**2 = 0 for l.
1, 2
Let m(q) be the first derivative of 0*q**4 + 1/25*q**5 - 1/5*q**3 + 0*q - 1/5*q**2 + 1. Find j, given that m(j) = 0.
-1, 0, 2
Suppose 11*u - 90 = 8*u. Solve 3 + 27/2*i**3 + 39/2*i + u*i**2 = 0 for i.
-1, -2/9
Let k(v) be the first derivative of -v**3 - 3*v**2 - 3*v - 4. Find m such that k(m) = 0.
-1
Let n(k) = -7*k**4 + 3*k**3 - 9*k**2 - k - 6. Let x(p) = -20*p**4 + 8*p**3 - 26*p**2 - 3*p - 17. Let q(u) = -17*n(u) + 6*x(u). Factor q(s).
-s*(s + 1)**3
Suppose -8*s - 7 + 31 = 0. Factor 1/2*q**4 + 0 + 1/2*q**2 + q**s + 0*q.
q**2*(q + 1)**2/2
Let m(n) = -n**3 - n**2 + n. Let f be 0*(2 - -2 - 5). Let c be m(f). Find x, given that 0*x**2 + 0*x + c - 1/5*x**4 + 1/5*x**3 = 0.
0, 1
Let u = 143/420 - 1/140. Factor u*o**3 + 5*o - 3 - 7/3*o**2.
(o - 3)**2*(o - 1)/3
Let w(y) be the third derivative of 6*y**2 + 0 - 2/735*y**7 + 0*y**4 - 4/105*y**5 - 2/105*y**6 + 0*y**3 + 0*y. What is d in w(d) = 0?
-2, 0
Let k be 29/6 - 5/6. Factor 49/4*s**3 - 2 + 19*s - 105/2*s**2 + 343/4*s**k.
(s + 1)*(7*s - 2)**3/4
Factor -2*v + 0 + 3 + 0 - 2 + v**2.
(v - 1)**2
Let o(z) = -z + 8. Let l be o(6). What is m in 3*m**2 + l*m**3 + 2*m**2 + 4*m + m**2 = 0?
-2, -1, 0
Let s be -5*(-5)/(250/(-15)) - -2. Factor -s*y**2 + 1/2*y**3 + 1/4*y**4 - 1/4*y**5 - 1/4*y 