*3 - 1/2*u**4 - 1/2*u.
-u*(u + 1)**3/2
Let r(x) be the third derivative of -x**8/1176 + x**7/245 - x**6/140 + x**5/210 + x**2. Determine h so that r(h) = 0.
0, 1
Let u = 37/1236 - 2/927. Let d(r) be the second derivative of 0 + 1/6*r**2 - 2*r + u*r**4 - 1/9*r**3. Find z, given that d(z) = 0.
1
Let c(i) = 2 - 5*i**3 + 3*i**2 - 6*i**2 + 5*i**2. Let u(b) = -81*b**3 + 33*b**2 + 33. Let w(g) = -33*c(g) + 2*u(g). Factor w(z).
3*z**3
Let n(f) be the second derivative of -f**6/1080 + f**5/180 - f**4/72 + f**3/6 + 4*f. Let a(p) be the second derivative of n(p). Solve a(u) = 0 for u.
1
Let d be ((-18)/(-3))/(1 + 1) - 1. Find x such that 1/4*x**d + 1/4*x**3 - 1/4*x - 1/4 = 0.
-1, 1
Let z be 2/(-7) - (-2)/7. Let m = 0 + z. Factor l - l**2 - 2 + 4 + m*l**2.
-(l - 2)*(l + 1)
Let r be 8 - (-4 - -2)*1. Solve r - 6 - 33*h + 12 + 4*h**2 + 49*h = 0.
-2
Suppose 8 = -3*x - 10. Let c = x - -12. What is n in -3 + 2 + c*n**2 + 2*n - 7*n**2 = 0?
1
Let j(l) be the third derivative of l**7/1680 - l**6/160 + l**5/40 - l**4/24 - 17*l**2. Solve j(d) = 0.
0, 2
Let a be 64/24 + (-4)/6. Let k(v) be the third derivative of -4/105*v**7 - 7/60*v**5 - 1/24*v**4 + 0 - 7/60*v**6 + v**a + 0*v**3 + 0*v. What is f in k(f) = 0?
-1, -1/2, -1/4, 0
Let k be 210/200 + 1/(-4). Factor -k*c - 2/5*c**2 - 2/5.
-2*(c + 1)**2/5
Let f = 308/3 - 1516/15. Suppose f*x**3 + 8/5*x - 12/5*x**2 - 2/5 - 2/5*x**4 = 0. Calculate x.
1
Solve -5/3*f - 2/3 - 1/3*f**3 - 4/3*f**2 = 0 for f.
-2, -1
Let b(c) be the second derivative of c**7/14 - 11*c**6/30 + 11*c**5/20 - c**4/12 - c**3/3 + 4*c - 4. Let b(y) = 0. Calculate y.
-1/3, 0, 1, 2
Let t(i) be the first derivative of -1/30*i**4 + 3 - 4*i - 1/5*i**2 - 2/15*i**3. Let r(k) be the first derivative of t(k). Factor r(n).
-2*(n + 1)**2/5
Let r(g) = g**3 - g**2 - 1. Let a(i) = 2*i**3 + 16*i - 4. Let n(w) = a(w) - 4*r(w). Factor n(u).
-2*u*(u - 4)*(u + 2)
Let p be (5 + 156/(-60))/(18/20). Let i be (-2)/(-1 - 1) - -2. Factor -4/3 + p*f**2 - 2*f**i + 2/3*f.
-2*(f - 1)**2*(3*f + 2)/3
Let r(k) be the third derivative of -k**7/4200 - 2*k**3/3 - k**2. Let t(u) be the first derivative of r(u). Let t(g) = 0. Calculate g.
0
Let n be ((-1)/(-6))/(3*200/45). Let m(j) be the second derivative of -5/48*j**4 + j + 0 - 1/24*j**3 + n*j**5 + 1/4*j**2 + 1/40*j**6. Factor m(s).
(s - 1)*(s + 1)**2*(3*s - 2)/4
Let v(t) = -t - 2. Let f be v(-7). Suppose f + 1 = 2*z. Let -a**2 - a + 0*a + z*a = 0. What is a?
0, 2
What is d in 5/3*d**2 + 40/3*d + 80/3 = 0?
-4
Factor 0*y**3 - 8 + 6*y**3 - 129*y + 109*y - y**3 + 2*y**2.
(y - 2)*(y + 2)*(5*y + 2)
Let q(o) = -o**3 + 2*o**2 + o - 2. Let a(m) = -m**3 + 3*m**2 + m - 3. Let k = 3 + 1. Let x(i) = i - 9. Let c be x(k). Let v(l) = c*a(l) + 7*q(l). Factor v(s).
-(s - 1)*(s + 1)*(2*s + 1)
Let j(a) be the third derivative of a**6/180 - a**5/60 + 2*a**3/3 - 4*a**2. Let o(v) be the first derivative of j(v). Suppose o(g) = 0. Calculate g.
0, 1
Let b(f) = -6*f**2 - 36*f - 25. Let s(l) = -3*l**2 - 18*l - 13. Let o(k) = -2*b(k) + 5*s(k). Factor o(x).
-3*(x + 1)*(x + 5)
Let y(n) be the second derivative of 0*n**2 + 1/10*n**5 - 1/3*n**3 + 1/15*n**6 + 0 - 1/6*n**4 + 2*n. Factor y(u).
2*u*(u - 1)*(u + 1)**2
Let h(q) be the first derivative of -q**2 + 4 + 0*q**3 + 3*q + 1/6*q**4. Let f(m) be the first derivative of h(m). Suppose f(x) = 0. Calculate x.
-1, 1
Let b(c) be the second derivative of -c**4/24 - c**3/3 - c**2 - 3*c. Factor b(i).
-(i + 2)**2/2
Let l = 462/5 - 92. Factor l*k**2 + 0 + 4/5*k.
2*k*(k + 2)/5
Suppose -2*p - 4 = 0, -w - 2 + 0 = 4*p. Let k = 10 - w. Factor 5 + 2*b**k + 2*b**3 - 5.
2*b**3*(b + 1)
Let j = -5 + 9. Factor j*q**2 + 3*q**2 + q**2 + 6*q**3 + 2*q + 0*q.
2*q*(q + 1)*(3*q + 1)
Let m(d) be the first derivative of d**3 - 6*d - 3 + 3/2*d**2. What is w in m(w) = 0?
-2, 1
Find m such that 28*m**2 + 38/3*m + 4/3 = 0.
-2/7, -1/6
Let x(k) be the first derivative of k**7/2520 - k**6/360 + k**5/180 + k**3/3 - 3. Let s(p) be the third derivative of x(p). Determine f so that s(f) = 0.
0, 1, 2
Let h = -13 - -16. Factor -3*a + 2 - 3*a**2 + 1 + h*a.
-3*(a - 1)*(a + 1)
Suppose -4*j + 6 = -3*j. Let t(f) = -f**2 + 9*f - 8. Let p be t(j). Factor 2*k**2 + 3 - p*k + 1 + 2*k**2.
2*(k - 2)*(2*k - 1)
Suppose -d - 3*d = -20. Suppose d*i - 21 = -6. Suppose 1/5*l + 1/5*l**i + 2/5*l**2 + 0 = 0. Calculate l.
-1, 0
Let w(v) be the third derivative of -v**5/270 + v**3/27 - 2*v**2. Factor w(d).
-2*(d - 1)*(d + 1)/9
Let q(v) be the second derivative of v**5/2 + v**3/3 + 2*v. Let d(p) = -21*p**3 + p**2 - 5*p. Let t(w) = 2*d(w) + 5*q(w). What is f in t(f) = 0?
-1/4, 0
Let n be ((-165)/(-850))/(2/(-12)). Let s = 3/85 - n. Factor -8/5*q**2 + 0 - s*q**3 - 2/5*q.
-2*q*(q + 1)*(3*q + 1)/5
Let h be 256/35 + (-20)/(-70). Solve h*j + 96/5*j**3 - 112/5*j**2 - 4/5 = 0 for j.
1/4, 2/3
Let x(o) be the third derivative of -o**6/1080 - o**5/120 - o**4/36 + o**3/2 - 3*o**2. Let u(z) be the first derivative of x(z). Let u(q) = 0. What is q?
-2, -1
Let o(a) = 2*a**2 - 11*a + 3. Let w(d) = 6*d**2 - 34*d + 8. Let x(f) = 20*o(f) - 6*w(f). Factor x(q).
4*(q - 3)*(q - 1)
Let a(u) = -u**2 - 16*u + 195. Let i be a(8). Factor 15/4*d**i + 0 + 75/4*d**4 - 12*d**2 + 3*d.
3*d*(d + 1)*(5*d - 2)**2/4
Let u = -1321/7 - -189. Factor -2/7*t**5 - 6/7*t**4 - 6/7*t**3 + 0 + 0*t - u*t**2.
-2*t**2*(t + 1)**3/7
Let c(h) be the first derivative of -h**5/90 - h**4/9 - 4*h**3/9 - 9*h**2/2 - 8. Let i(p) be the second derivative of c(p). Let i(x) = 0. Calculate x.
-2
Suppose 0 - 2/5*j**3 + 2/5*j**2 + 12/5*j = 0. Calculate j.
-2, 0, 3
Let x be 0 - (1 + (-15)/6). Let s be (-8)/(-6) + 4/6. Factor -x*d**3 - d**s + 1 + 3/2*d.
-(d - 1)*(d + 1)*(3*d + 2)/2
Let j(g) be the third derivative of g**10/252000 - g**8/33600 + g**5/30 + 2*g**2. Let y(x) be the third derivative of j(x). Determine c so that y(c) = 0.
-1, 0, 1
Let -16*k**3 + 5*k - 3*k + 6*k + 19*k**2 + 9*k**2 = 0. What is k?
-1/4, 0, 2
Let x(p) be the second derivative of p**7/252 - p**6/45 + p**5/120 + 5*p**4/36 - p**3/9 - 2*p**2/3 + 22*p. Factor x(u).
(u - 2)**3*(u + 1)**2/6
Factor 0 + 4/11*y**2 + 2/11*y + 2/11*y**3.
2*y*(y + 1)**2/11
Find a such that -1/3 + 0*a + 1/3*a**2 = 0.
-1, 1
Factor 3/5 + 1/5*z**2 + 4/5*z.
(z + 1)*(z + 3)/5
Let o(h) be the first derivative of -2*h**3/15 + h**2/5 - 10. Factor o(i).
-2*i*(i - 1)/5
Determine f, given that 8/7*f + 2/7*f**4 + 2/7 + 12/7*f**2 + 8/7*f**3 = 0.
-1
Let p(j) be the third derivative of j**8/84 + j**7/105 - 12*j**2. Determine q, given that p(q) = 0.
-1/2, 0
Let k = 12 + -1. Let f be k/11*2/7. Factor f - 2/7*m**2 + 0*m.
-2*(m - 1)*(m + 1)/7
Suppose -2*u + 3 + 3 = 0. Suppose 6*b**2 - 6*b**4 - 7*b**5 + 2*b**5 + 8*b**5 - u*b + 0*b**5 = 0. Calculate b.
-1, 0, 1
Suppose 4 = 2*i - 0. Solve 3*u**2 - i*u**2 + 1 - 2*u**2 = 0.
-1, 1
Let v(h) = -4*h**5 + 48*h**4 - 60*h**3 + 16*h**2 + 8. Let r(l) = l**5 - 16*l**4 + 20*l**3 - 5*l**2 - 3. Let g(j) = -8*r(j) - 3*v(j). Factor g(m).
4*m**2*(m - 2)*(m - 1)**2
Let c = 1059/7 - 151. Factor c*g**2 + 2/7 - 4/7*g.
2*(g - 1)**2/7
Factor 9/4*p + 9/4*p**2 + 3/4 + 3/4*p**3.
3*(p + 1)**3/4
Let y = 1339/20 + -255/4. Factor 6/5*v**3 + 6/5*v - 4/5 + y*v**2.
2*(v + 1)*(v + 2)*(3*v - 1)/5
Suppose 5*n + 7 = -3*k + 22, -5*k - 4*n + 12 = 0. Suppose k*o = -o. Determine f, given that o - 4*f**3 + 3*f + 3*f**2 - 2 + 2*f**3 = 0.
-1, 1/2, 2
Suppose 6 = 22*r - 19*r. Let z(o) be the first derivative of 1/3*o**4 + 14/27*o**3 + 2/9*o - r - 2/3*o**2 - 16/45*o**5. Find a, given that z(a) = 0.
-1, 1/4, 1/2, 1
Let t(u) be the first derivative of 1/2*u**6 - 4 + 0*u**5 + 0*u + 2*u**3 - 9/4*u**4 + 0*u**2. What is m in t(m) = 0?
-2, 0, 1
Let p be (1 - 6)*12/(-10). Let p - 2*m**2 + m**2 + 3*m - 2*m**2 = 0. Calculate m.
-1, 2
Find j, given that -21*j + 4*j**3 + 5*j**2 + 3*j**2 - 48 + 5*j + 16 = 0.
-2, 2
Let k = -1 - -4. Suppose -s - k*s + 8 = 0. Find v such that 4/7*v**s + 0 - 2/7*v**5 + 2/7*v - 4/7*v**4 + 0*v**3 = 0.
-1, 0, 1
Let b(t) be the third derivative of 49*t**6/180 + 7*t**5/15 + t**4/3 + 5*t**3/6 + 8*t**2. Let d(s) be the first derivative of b(s). Let d(u) = 0. What is u?
-2/7
Let f(z) = 3*z**3 + 9*z**2 + 8*z - 2. Let x(k) = 3*k**3 + 9*k**2 + 9*k - 3. Let r(l) = -3*f(l) + 2*x(l). Factor r(d).
-3*d*(d + 1)*(d + 2)
Factor 12/5 - 12/5*s**2 + 4/5*s - 4/5*s**3.
-4*(s - 1)*(s + 1)*(s + 3)/5
Let w(d) = -2*d**3 + 5*d**2 + 