 Determine u so that 8*u + 6*u + 2*u**2 - n*u**2 + 19*u**2 - 4 = 0.
-1, 2/9
Find x, given that 4/7*x + 0 - 32/7*x**3 + 2/7*x**2 - 30/7*x**4 = 0.
-1, -2/5, 0, 1/3
Let x be (-3 + 78/27)/(2/(-2)). Let g(w) be the first derivative of -1/15*w**5 - 1/6*w**2 + 1 + x*w**3 + 1/12*w**4 + 0*w. Determine t, given that g(t) = 0.
-1, 0, 1
Suppose -1/6*y + 1/6*y**3 + 1/2*y**2 - 1/2 = 0. What is y?
-3, -1, 1
Let z(s) = 5*s**3 + 6*s**2 + s. Let u(p) be the first derivative of p**3/3 - p + 8. Let y(v) = 6*u(v) + 3*z(v). Factor y(r).
3*(r + 1)**2*(5*r - 2)
Let m(s) be the second derivative of s**8/672 - s**7/420 - s**6/240 + s**5/120 - 3*s**2/2 + 2*s. Let g(q) be the first derivative of m(q). Solve g(y) = 0 for y.
-1, 0, 1
Let j(f) = f**2 - 2*f. Let g be j(2). Suppose -3*h + 7*h = 0. Suppose 2*q + h*q**2 + 0*q**2 + 1 + q**2 + g*q = 0. What is q?
-1
Suppose 2*t - 5*i = -6, 4*t - 3*t - 3*i + 5 = 0. Let a be ((-1)/2)/(t/(-42)). Factor n**2 - 2/3*n**a + 1/6*n**4 - 2/3*n + 1/6.
(n - 1)**4/6
Let p(c) be the third derivative of 0 + 2*c**2 + 0*c**4 + 0*c**3 + 0*c**5 + 1/70*c**7 + 0*c - 1/120*c**6. Factor p(y).
y**3*(3*y - 1)
What is q in 2*q**3 + 0*q**3 - 5*q**3 + 6*q**2 - 3*q + 0*q**3 = 0?
0, 1
Let w(c) be the second derivative of -7*c**5/130 + 5*c**4/78 + 2*c**3/39 + 7*c. Factor w(r).
-2*r*(r - 1)*(7*r + 2)/13
Let l(c) be the third derivative of c**5/60 - c**4/3 + 8*c**3/3 + 6*c**2. Solve l(q) = 0 for q.
4
Let n(r) be the first derivative of 2*r**5/5 + 2*r**4 - 2*r**3/3 - 4*r**2 + 3. Solve n(k) = 0.
-4, -1, 0, 1
Let s(x) be the third derivative of x**5/270 + x**4/36 + 7*x**2. Factor s(j).
2*j*(j + 3)/9
Suppose -9*w - 11*w**3 + 12 + 19*w + 16*w**2 + 13*w**3 + 16*w = 0. What is w?
-6, -1
Let a(z) be the second derivative of 0 + 0*z**3 - 1/10*z**6 - 3*z - 1/4*z**4 + 0*z**2 - 3/10*z**5. Suppose a(q) = 0. Calculate q.
-1, 0
Let c(b) = 65*b**2 + 185*b. Let k(t) = -8*t**2 - 23*t. Let v(z) = -3*c(z) - 25*k(z). Solve v(w) = 0 for w.
-4, 0
What is v in -3*v**2 + v**3 + 0*v**2 - 3*v**2 + 9*v = 0?
0, 3
Let x = 315 + -629/2. Suppose 0 + x*t**3 + 0*t**2 + 3/2*t**4 - 2*t**5 + 0*t = 0. What is t?
-1/4, 0, 1
Let w = 43/3 - 14. Let a(p) be the first derivative of -w*p + 1/12*p**4 - 1/3*p**3 - 2 + 1/2*p**2. Find r, given that a(r) = 0.
1
Let r(a) be the first derivative of -a**4/6 - 2*a**3/3 - a**2 - a - 2. Let q(y) be the first derivative of r(y). Find z such that q(z) = 0.
-1
Let i(a) be the second derivative of -a**5/20 - a**4/12 + a**3/6 + a**2/2 - 6*a. Let i(h) = 0. What is h?
-1, 1
Suppose -4*m - 11 = -3. Let h = -2 - m. Factor -1/2*g**2 + h - 1/2*g.
-g*(g + 1)/2
Let p(l) be the first derivative of -l**3/12 + 15. Factor p(b).
-b**2/4
Let m = 6741/4 + -1685. Factor z**2 - z - m*z**3 + 0.
-z*(z - 2)**2/4
Determine k, given that 0*k**5 + 9*k**5 + 6*k**2 - 20*k**4 - 4*k**4 + 9*k**3 = 0.
-1/3, 0, 1, 2
Let x(o) = 72*o**2 + 412*o + 1072. Let q(b) = 13*b**2 + 75*b + 195. Let k(t) = 28*q(t) - 5*x(t). Factor k(d).
4*(d + 5)**2
Suppose -8 = r - 5*r. Find i such that 0*i + 4*i**r + 0*i - 4*i**3 = 0.
0, 1
Suppose 0 = -7*k - 92 + 120. Find d, given that 1/3*d**5 + 4/3*d + 13/3*d**3 - k*d**2 + 0 - 2*d**4 = 0.
0, 1, 2
Let c(m) be the second derivative of m**5/5 - 2*m**4 + 2*m**3 + 20*m**2 + 33*m. Factor c(v).
4*(v - 5)*(v - 2)*(v + 1)
Let l = 59806/3 - 5681386/285. Let w = l - -2/95. Factor 2/3*o**2 + 0 + w*o.
2*o*(o + 1)/3
Let t(j) be the second derivative of -5*j**6/27 - 8*j**5/9 + 38*j**4/27 - 16*j**3/27 - 20*j. Factor t(b).
-2*b*(b + 4)*(5*b - 2)**2/9
Let q(r) be the second derivative of -7*r**5/10 + 37*r**4/6 - 38*r**3/3 + 8*r**2 - 23*r. Factor q(k).
-2*(k - 4)*(k - 1)*(7*k - 2)
Let z = -113 + 115. Determine i, given that 0*i - 2/7 + 2/7*i**z = 0.
-1, 1
Factor -13*o - 3*o**3 + 14*o + 3*o**3 + o**3 - 2*o**2.
o*(o - 1)**2
Suppose 5*u + 21 = 4*b, 5*u = -5*b - 0*b + 15. Let m = u - -4. Factor 4*o**3 + 14*o**2 - 4*o - 14*o**4 - o**3 + o**m.
-2*o*(o - 1)*(o + 1)*(7*o - 2)
Solve -9/2 + 3*u - 1/2*u**2 = 0.
3
Let u(n) be the third derivative of n**8/672 - n**7/420 - n**6/60 + n**5/30 - 18*n**2. Factor u(r).
r**2*(r - 2)*(r - 1)*(r + 2)/2
Let r(k) be the first derivative of k**9/18144 + k**8/10080 - k**7/2520 + 2*k**3 - 9. Let w(s) be the third derivative of r(s). Factor w(g).
g**3*(g - 1)*(g + 2)/6
Let n(s) = 9*s**3 + 24*s**2 + 39*s - 24. Let w(k) = 2*k**3 + 5*k**2 + 8*k - 5. Let u(h) = 5*n(h) - 24*w(h). Factor u(b).
-3*b*(b - 1)*(b + 1)
Let -6*t + 52*t**3 - 2 + 8*t**5 - 6*t + 36*t**4 - 2 + 20*t**2 - 4 = 0. Calculate t.
-2, -1, 1/2
Let a(d) be the third derivative of -d**2 + 1/50*d**5 - 1/100*d**6 + 0*d**3 + 0*d + 0 + 1/525*d**7 - 1/60*d**4. Factor a(w).
2*w*(w - 1)**3/5
Let l(f) be the second derivative of -f**6/40 + f**4/8 - f**2/2 + 2*f. Let m(k) be the first derivative of l(k). Factor m(s).
-3*s*(s - 1)*(s + 1)
Factor -1/2*g**3 + 0*g + 0 + 1/2*g**2.
-g**2*(g - 1)/2
Let c(y) be the first derivative of -4*y**3/21 - 20*y**2/7 - 100*y/7 - 13. Factor c(v).
-4*(v + 5)**2/7
Let w(g) be the second derivative of g**10/60480 + g**9/30240 - g**4/12 + g. Let u(z) be the third derivative of w(z). Solve u(r) = 0.
-1, 0
Let y = 269 + -797/3. Factor -16/3*n - 2/3*n**3 + 8/3 + y*n**2.
-2*(n - 2)**2*(n - 1)/3
Let t be (-12)/(-162)*(-5)/(5/(-3)). Let y(q) be the first derivative of t*q - 2/27*q**3 - 2 + 1/3*q**2 - 1/6*q**4. Find j, given that y(j) = 0.
-1, -1/3, 1
Let h(t) = 4*t**2 - 10*t - 4. Let s(p) = -p**2 + 3*p + 1. Let m(q) = 6*h(q) + 20*s(q). Solve m(w) = 0.
-1, 1
Let d be ((-572)/8)/(2/(-4)). Let w be (-12)/(-78) - (-4)/d. Let -w + 2/11*m + 2/11*m**2 - 2/11*m**3 = 0. Calculate m.
-1, 1
Let b(k) = -168*k**3 - 90*k**2 + 70*k - 14. Let n(z) be the second derivative of z**5/20 - z**3/6 + z**2/2 - 2*z. Let c(i) = b(i) + 6*n(i). Factor c(g).
-2*(g + 1)*(9*g - 2)**2
Let a be 8 - (-7 - 917/(-63)). Determine w so that 0*w**2 - 2/9*w**4 + 2/9 + a*w - 4/9*w**3 = 0.
-1, 1
Let x(m) be the first derivative of -m**3/3 - m**2/2 + 7. Factor x(f).
-f*(f + 1)
Let b(x) be the first derivative of 3*x**4/16 + 7*x**3/4 + 45*x**2/8 + 27*x/4 - 36. Factor b(i).
3*(i + 1)*(i + 3)**2/4
Let o(q) be the third derivative of q**10/42000 - q**9/21600 - q**8/25200 - q**5/20 + 3*q**2. Let w(r) be the third derivative of o(r). Solve w(c) = 0 for c.
-2/9, 0, 1
Let u be 5 + -6 + (-5)/(-3). Solve -5/3*p**3 - u + 7/3*p**4 - 2/3*p**5 + 7/3*p - 5/3*p**2 = 0 for p.
-1, 1/2, 1, 2
Let a be 42/24*(8/(-28))/(-2). Factor -a*u + 1/4*u**2 - 1/2.
(u - 2)*(u + 1)/4
Suppose -5*c - 3 = -2*n, 3*n + 4 = 5*c + 1. Let p be (4/n)/(7/(-42)). Factor 1/4*y**5 - y**p + 0 - y + y**2 + 3/4*y**3.
y*(y - 2)**2*(y - 1)*(y + 1)/4
Let n(x) be the second derivative of 2/3*x**3 + 0 + 3*x + 1/6*x**4 + x**2. Factor n(l).
2*(l + 1)**2
Let w be (6 - 114/18)*(-6)/10. Factor -1/5*z**3 - w + 1/5*z + 1/5*z**2.
-(z - 1)**2*(z + 1)/5
Let f(d) be the first derivative of -d**5/35 + d**3/21 - 9. Factor f(y).
-y**2*(y - 1)*(y + 1)/7
Factor -4*j + 2/17*j**2 + 34.
2*(j - 17)**2/17
Let d(f) be the first derivative of 5*f**4/22 - 2*f**3/33 - 5*f**2/11 + 2*f/11 - 6. Find l such that d(l) = 0.
-1, 1/5, 1
Let j(m) be the third derivative of 0*m - 1/3*m**3 - 1/8*m**4 + 0 - 2*m**2 - 1/60*m**5. Solve j(p) = 0.
-2, -1
Factor 15/8*m**3 + 7/8*m**4 + 0 + 13/8*m**2 + 1/2*m + 1/8*m**5.
m*(m + 1)**3*(m + 4)/8
Suppose -4*t + 3*t + 4*f - 3 = 0, 0 = -4*t + 4*f + 12. What is g in -15*g**t - 11*g**4 - 28*g**4 - 27*g**3 + 3*g**2 + 0*g**2 + 6*g = 0?
-1, 0, 2/5
Let z be (-4)/14 + 36/28 + -1. Let w(n) be the third derivative of 3*n**2 + 1/90*n**5 + 0 + 0*n**3 + z*n - 1/36*n**4. Factor w(r).
2*r*(r - 1)/3
Suppose 4*p - b = 4, -2 = 5*p - b - 2*b. Factor -f + 15*f + 2*f - 2*f**p - 32.
-2*(f - 4)**2
Let h(x) be the third derivative of x**7/945 + x**6/180 + x**5/270 - x**4/36 - 2*x**3/27 + 10*x**2. Let h(j) = 0. What is j?
-2, -1, 1
Let y = 4/57 - -322/285. Factor 3/5*o - 3/5*o**2 + y.
-3*(o - 2)*(o + 1)/5
Find w such that -735/4*w**3 + 455/2*w**2 - 85*w + 10 = 0.
2/7, 2/3
Let m(a) be the first derivative of 8/3*a**3 + 2/3*a**6 + 8 - 2*a**2 + 0*a**4 + 0*a - 8/5*a**5. Factor m(q).
4*q*(q - 1)**3*(q + 1)
Let x = 173/12 - 57/4. Let g(o) be the first derivative of 0*o - 4/9*o**3 - x*o**4 - 1/3*o**2 - 1. Solve g(w) = 0.
-1, 0
Let t(k) be the second derivative of -k**6/1800 - k**5/300 - 3*k**3/2 - 4*k. Let h(v) be the seco