Let p(u) be the third derivative of 2*u**7/35 - 3*u**6/20 - 3*u**5/16 - u**4/16 - 34*u**2. Factor p(g).
3*g*(g - 2)*(4*g + 1)**2/4
Let z(c) = c**3 - 14*c**2 + 23*c - 12. Let x(a) = a**3 - 15*a**2 + 24*a - 13. Let s(l) = -2*x(l) + 3*z(l). Factor s(n).
(n - 10)*(n - 1)**2
Let y(n) be the second derivative of -n**8/1400 - n**7/280 - n**6/150 - n**5/200 + 2*n**3/3 - 2*n. Let x(c) be the second derivative of y(c). Factor x(o).
-3*o*(o + 1)**2*(2*o + 1)/5
Suppose 3*f - 6 = 6. Determine l so that 14*l + 2 + f*l**2 + 2*l**2 - 22*l = 0.
1/3, 1
Let j(w) be the first derivative of -w**6/10 - 2*w**5/5 - 3*w**4/5 - 2*w**3/5 - w**2/10 - 21. What is c in j(c) = 0?
-1, -1/3, 0
Let t(z) = z**3 - 9*z**2 + 9*z - 8. Let r be t(8). Let h(q) = q**2 - q + 2. Let o be h(r). Determine j so that j**o + 3*j**2 - 2*j**2 = 0.
0
Let x(c) be the first derivative of -c**7/15 - 3*c**6/20 - c**5/15 + c**2 + 1. Let p(m) be the second derivative of x(m). Suppose p(w) = 0. Calculate w.
-1, -2/7, 0
Let d(w) be the third derivative of -5*w**2 + 0*w + 1/420*w**6 + 2/21*w**3 + 0 + 2/105*w**5 + 5/84*w**4. Let d(i) = 0. What is i?
-2, -1
Suppose 2*a - 12 = -4*r, -2*a = -7*a + 10. Solve w**4 + 7/5*w**r + 0 - 1/5*w**5 - 2/5*w - 9/5*w**3 = 0 for w.
0, 1, 2
Factor -2/5*p**4 + 32/5 + 0*p**2 + 32/5*p - 8/5*p**3.
-2*(p - 2)*(p + 2)**3/5
Let g(s) be the second derivative of -s**4/66 + 5*s**3/33 - 6*s**2/11 + 19*s. Solve g(u) = 0 for u.
2, 3
Let s = 521/4830 + -7/138. Let p(f) be the first derivative of -1/7*f**2 - 2/21*f**3 + s*f**5 + 0*f + 1/14*f**4 - 2. Factor p(k).
2*k*(k - 1)*(k + 1)**2/7
Factor -3*w**4 + 2*w - 14/3*w**2 - 1/3 + 16/3*w**3 + 2/3*w**5.
(w - 1)**4*(2*w - 1)/3
Let v(u) be the second derivative of 0 - 1/12*u**4 + u**2 + 1/60*u**5 + 2*u + 1/6*u**3. Let w(a) be the first derivative of v(a). What is z in w(z) = 0?
1
Let z(v) = v. Let d(j) = -4*j**2 - 15*j - 16. Let r(k) = d(k) - z(k). What is m in r(m) = 0?
-2
Let c(g) be the second derivative of -g**4/6 - g**3 - 2*g**2 + 7*g. Factor c(m).
-2*(m + 1)*(m + 2)
Let l be ((-3)/2)/((-1)/2). Suppose -4*q + 11 = l. Factor 6*y**2 - 7*y**q + 0*y**4 + y**4.
y**2*(y - 1)*(y + 1)
Let g(l) = l**2 + 3*l + 3. Let m be g(-3). Factor -6*z**4 + 14*z**4 + 4*z**m + z**3 + 4*z**5 + z**2.
z**2*(z + 1)*(2*z + 1)**2
Let i be (12/10)/(4/10). Factor 30 + 0*k**3 - 34 - k**3 + i*k**2.
-(k - 2)**2*(k + 1)
Let d be 14/105 - (-56)/30. Let z be 1 + (-3 - -2) + d. Suppose 3/2*k**z - 3/2*k**4 - k + 0 + k**3 = 0. Calculate k.
-1, 0, 2/3, 1
Let p = 297 - 294. Solve 27/5*q**p - 63/5*q**2 - 12/5 + 48/5*q = 0 for q.
2/3, 1
Suppose -32 = -4*d - 0*d. Solve n**5 + 8 - 2*n**3 + n - d = 0 for n.
-1, 0, 1
Suppose 4*p - 6 = 6. Suppose 0 = -p*y + y. Factor -x**3 + y*x**2 + 0*x**2 - 2*x**5 + 3*x**3.
-2*x**3*(x - 1)*(x + 1)
Let f(w) be the third derivative of 0 + 0*w - 1/30*w**5 - 16/3*w**3 - 11*w**2 + 2/3*w**4. Factor f(v).
-2*(v - 4)**2
Let -1/3*n**3 + 1/3*n - 1/6 + 1/6*n**2 = 0. Calculate n.
-1, 1/2, 1
Let h(q) be the third derivative of -q**7/1260 - q**4/12 - 4*q**2. Let t(d) be the second derivative of h(d). Factor t(r).
-2*r**2
Let t(q) be the second derivative of -q**9/1008 + q**8/1120 + q**7/168 - q**6/120 + q**4/6 + q. Let c(a) be the third derivative of t(a). Factor c(r).
-3*r*(r - 1)*(r + 1)*(5*r - 2)
Let w(q) be the second derivative of q**7/63 + q**6/9 + q**5/3 + 5*q**4/9 + 5*q**3/9 + q**2/3 + 4*q. Factor w(k).
2*(k + 1)**5/3
Let w(c) = -c**3 - c**2 - c - 1. Let s(o) = o**4 + 11*o**3 + 11*o**2 + o. Let r(m) = -s(m) - 6*w(m). Let r(i) = 0. What is i?
-3, -2, -1, 1
Solve -8*r - 6*r**2 + 10*r**2 - 4*r**3 + 8*r**2 = 0 for r.
0, 1, 2
Let h = -10251 - -112859/11. Let -14*o**4 - 12*o**3 - 16/11*o + h*o**5 + 0 + 104/11*o**2 = 0. What is o?
-1, 0, 2/7, 2
Let c = -1683/2 - -816. Let t = -25 - c. Let 0 + t*d + 1/2*d**2 = 0. Calculate d.
-1, 0
Let c(u) be the second derivative of -u**4/90 - 4*u**3/45 - u**2/5 - 5*u. Determine z so that c(z) = 0.
-3, -1
Let x(q) = -11*q**3 - 15*q**2 - 5*q + 1. Let b(z) = z**3 - 1. Let j(s) = b(s) + x(s). Factor j(t).
-5*t*(t + 1)*(2*t + 1)
Let j(o) = -o**2 - 4*o + 4. Let z be j(-5). Let g = 2 - z. Factor -4*c**3 - 7*c**4 - 2*c**g + 3*c**2 + 10*c**4.
3*c**2*(c - 1)**2
What is u in 0*u + 0*u**2 - 1/4*u**4 - 1/4*u**3 + 0 = 0?
-1, 0
Let l(y) be the first derivative of -y**4/4 - 4*y**3/3 + 2*y - 1. Let s be l(-4). Factor 3*j + 0*j + 2*j**s - 5*j.
2*j*(j - 1)
Let u(b) be the first derivative of -10 - 16*b - 10*b**2 - 4/3*b**3. Find l, given that u(l) = 0.
-4, -1
Suppose 0 = 13*x - 12*x - 3. Solve 1 + 1/2*g - 1/2*g**x - g**2 = 0 for g.
-2, -1, 1
Let g(m) be the second derivative of m**8/17920 - m**7/1344 + m**6/640 + 9*m**5/320 + m**4/4 - 10*m. Let x(v) be the third derivative of g(v). Factor x(b).
3*(b - 3)**2*(b + 1)/8
Let y be (100/15)/((-2)/(-3)). Factor -y*d**3 + 7*d + 6*d + 27*d + 4*d**2 - 16.
-2*(d - 2)*(d + 2)*(5*d - 2)
Let o(a) be the first derivative of -a**6/60 - 3*a**5/20 - a**4/2 - 2*a**3/3 + 2*a + 1. Let c(z) be the first derivative of o(z). Factor c(s).
-s*(s + 2)**3/2
Determine f so that -2/3*f**4 + 2/3*f**5 + 0 + 2/3*f**2 + 0*f - 2/3*f**3 = 0.
-1, 0, 1
Let c(x) be the second derivative of -x**7/1050 + x**5/300 - 5*x**2/2 - 5*x. Let w(s) be the first derivative of c(s). Find t such that w(t) = 0.
-1, 0, 1
Let b be -10*(-2)/8 - (114 + -112). Factor 5/2*n + 1 + b*n**3 + 2*n**2.
(n + 1)**2*(n + 2)/2
Let x(i) be the second derivative of i**6/720 - i**5/120 - i**3/3 + 2*i. Let u(p) be the second derivative of x(p). What is r in u(r) = 0?
0, 2
Factor 3*r + 7/3*r**2 + 2/3.
(r + 1)*(7*r + 2)/3
Let x(f) be the third derivative of -1/600*f**6 - 1/150*f**5 + 0 - 2*f**2 + 1/120*f**4 + 0*f + 1/15*f**3. Factor x(d).
-(d - 1)*(d + 1)*(d + 2)/5
Let l be 0*((-3)/9 + 10/12). Let 2/9*a**4 - 4/9*a**3 + 0 + 2/9*a**2 + l*a = 0. What is a?
0, 1
Let w(c) be the first derivative of c**4/8 - 3*c**2/4 - c - 5. Solve w(a) = 0 for a.
-1, 2
Let i(v) be the second derivative of 0*v**2 - 4*v + 0 + 1/27*v**3 + 2/27*v**4. Factor i(d).
2*d*(4*d + 1)/9
Suppose 2/17*w**2 - 2/17*w**3 - 8/17 + 8/17*w = 0. What is w?
-2, 1, 2
Let z be (0/13)/(-4 - -1*2). Suppose k - 4 = -2. Factor 0 - 2/3*w**3 + z*w + 2/3*w**k.
-2*w**2*(w - 1)/3
Suppose -4 + 1 = -k. Factor -3*g**2 + 17*g**2 - 8*g**k + 6*g - 2*g.
-2*g*(g - 2)*(4*g + 1)
Let l = 16 - -4. Let o = l + -18. Factor 0 + 1/4*p**o - 3/4*p**3 + 1/2*p.
-p*(p - 1)*(3*p + 2)/4
Let d be ((-3)/2)/(11/(-22)). Let l(m) = m. Let w(h) = -h**2 - 3*h + 1. Let u(b) = d*l(b) + w(b). Factor u(i).
-(i - 1)*(i + 1)
Suppose -2/3*l**3 + 0 - 1/2*l**2 + 1/6*l = 0. Calculate l.
-1, 0, 1/4
Let u(k) = -8*k**3 - 2*k**2 + 3*k + 3. Let q be u(-2). Factor -32*o**2 - 12 + 20*o + 76*o**3 + q*o**2 + 71*o**2 + 16*o**4.
4*(o + 1)**2*(o + 3)*(4*o - 1)
Let q(h) = -h**5 + h**4 - h**2 - h. Let j(y) = 15*y**5 - 15*y**4 + 9*y**3 + 3*y**2 + 24*y. Let m(u) = j(u) + 18*q(u). Factor m(z).
-3*z*(z - 1)**3*(z + 2)
Let d(o) be the first derivative of 5*o**3 + 3/5*o**5 + 3*o**4 + 5 + 3*o**2 + 0*o. Determine q, given that d(q) = 0.
-2, -1, 0
Solve -1/2*k**2 + 0 - 1/2*k = 0 for k.
-1, 0
Let w(c) be the second derivative of 7/48*c**4 + 0 + 1/168*c**7 + 1/12*c**3 + 9/80*c**5 + 2*c + 1/24*c**6 + 0*c**2. Factor w(m).
m*(m + 1)**3*(m + 2)/4
Suppose i + 4*i - 90 = 0. Let m = -14 + i. Factor 4/3*a**m - 2/3*a - 10/3*a**3 + 8/3*a**2 + 0.
2*a*(a - 1)**2*(2*a - 1)/3
Let l(o) be the third derivative of -o**5/240 + o**4/48 - 11*o**2. Factor l(r).
-r*(r - 2)/4
Let a(m) be the second derivative of -m**5/50 - m**4/5 - 15*m. Suppose a(q) = 0. What is q?
-6, 0
Let y(l) be the second derivative of -2*l + 1/3*l**3 + 0*l**2 + 0 - 1/4*l**4 + 1/20*l**5. Factor y(u).
u*(u - 2)*(u - 1)
Solve -30*u - 29*u - 5*u**2 - u**3 + 53*u = 0 for u.
-3, -2, 0
Suppose 0 = -3*t, -3*i + 4*t - 8*t + 72 = 0. Let r be ((-3)/i)/(3/(-18)). Solve -3/4*n**3 + 3/4*n**2 + r*n + 0 - 3/4*n**4 = 0 for n.
-1, 0, 1
Let r(s) = -s**3 + s - 1. Let w(b) = -b**4 + 12*b**3 - 12*b**2 + 4*b + 3. Let z(a) = 6*r(a) + w(a). Solve z(o) = 0.
1, 3
Suppose 2*r - k - 2*k = 52, -84 = -4*r + k. Let z = r - 20. Determine s, given that 1/4*s + z*s**2 - 1/4*s**3 + 0 = 0.
-1, 0, 1
Let 0*s**2 + 3/4*s**4 + 0 + 0*s + 0*s**3 = 0. Calculate s.
0
Let p(y) be the third derivative of y**7/280 - 3*y**6/160 + y**5/40 + 10*y**2. Factor p(s).
3*s**2*(s - 2)*(s - 1)