 1)**2*(u + 1)
Let t(h) be the third derivative of h**8/1008 - h**6/180 + h**4/72 + 17*h**2. What is z in t(z) = 0?
-1, 0, 1
Factor -6*k**2 + 8*k**2 - 3*k**2.
-k**2
Let w(a) be the second derivative of -1/30*a**3 + 0 + 1/12*a**4 - 2*a - 1/10*a**2 - 3/100*a**5. Factor w(n).
-(n - 1)**2*(3*n + 1)/5
Let u = -67/12 - -19/3. Suppose u*j - 1/4 + 1/4*j**3 - 3/4*j**2 = 0. What is j?
1
Let r(y) = y**3 + 49*y**2 - 47*y + 150. Let w be r(-50). Factor 0*z**2 + 3/4*z**3 + w + 0*z + 3/2*z**4 + 3/4*z**5.
3*z**3*(z + 1)**2/4
Let i(g) be the second derivative of g**8/40320 + g**7/3780 + g**6/864 + g**5/360 + g**4/6 - 4*g. Let z(r) be the third derivative of i(r). Solve z(h) = 0.
-2, -1
Let b(d) = -3*d - 1. Let i be b(-1). Let 2/3*w**i + 2/3 + 5/3*w = 0. Calculate w.
-2, -1/2
Factor 16/9 + 44/9*b**2 + 56/9*b + 10/9*b**3.
2*(b + 2)**2*(5*b + 2)/9
Let u be (-855)/21*(-1)/6. Let s = u - 13/2. Factor 0 + 0*c**2 + 0*c**4 - 2/7*c**5 + s*c**3 + 0*c.
-2*c**3*(c - 1)*(c + 1)/7
Let k be (-26)/(-22) + 4/(-22). Let o = k - -1. Factor -d**2 + d**o + 2*d**3 - 7*d + 5*d.
2*d*(d - 1)*(d + 1)
Determine r, given that 4/5*r + 2/5*r**2 + 2/5 = 0.
-1
Let h(n) = 8*n**3 + 9*n**2 - 7*n + 4. Let o(c) = c**3 + c**2. Let r(b) = -4*h(b) + 28*o(b). Determine s, given that r(s) = 0.
-4, 1
Solve -4*a**5 + 8*a**2 - 2*a**4 + a**3 - 6*a**2 + 2*a**5 + a**5 = 0 for a.
-2, -1, 0, 1
Let p be 84/9*(-6)/4. Let u = 18 + p. Solve 0 + 0*b**u + 0*b + 0*b**2 + 1/4*b**5 - 1/4*b**3 = 0 for b.
-1, 0, 1
Let x(q) = q**3 + 6*q**2 - 1. Let d be x(-6). Let g(s) = -4*s - 1. Let p be g(d). Suppose 0*w - w**3 - w + 3*w**2 - w**p = 0. Calculate w.
0, 1/2, 1
Let h = 489 + -20537/42. Let t(k) be the second derivative of 0*k**3 + 0 - 2*k + 0*k**2 + h*k**4 + 1/70*k**5. What is p in t(p) = 0?
-1, 0
Let p(c) = c + 4. Let f be p(0). Let y(v) be the first derivative of v**2 + 0*v**3 - 1/6*v**f + 4/3*v + 2. What is k in y(k) = 0?
-1, 2
Suppose 5*q - 2*l - 12 = 0, -3*q + l + 4 = 3*l. Factor -1/4 + 0*n + 1/4*n**q.
(n - 1)*(n + 1)/4
Let f be (-44 + 44)*(-2)/8. Let v be 2/(-4)*0 + 0. Factor f*c**2 + v*c + 0 - 1/5*c**3.
-c**3/5
Factor v**4 + 2*v - 3*v**4 - 2*v**3 - 6*v**2 + 2*v**3 + 6*v**3.
-2*v*(v - 1)**3
Let i(v) be the second derivative of -v**7/63 - v**6/45 + v**5/30 + v**4/18 - 49*v. What is x in i(x) = 0?
-1, 0, 1
Let q(a) = -a**3 + 3*a**2 - 2. Let w(g) = -2*g**3 + 4*g**2 + g - 3. Let c(n) = -3*q(n) + 2*w(n). Factor c(f).
-f*(f - 1)*(f + 2)
Let a be 46*(-5)/(-200) + 4/(-10). Solve 1/2*b + a*b**2 - 1/4 = 0.
-1, 1/3
Factor -8/7*n - 2/7*n**4 + 8/7*n**2 + 0 + 2/7*n**3.
-2*n*(n - 2)*(n - 1)*(n + 2)/7
Suppose 0 = -2*p + 8, -m - 4*m + 35 = 5*p. Suppose -12 = 3*l + 4*n, l + 0 = n + m. Find b, given that l - 3/2*b**3 + 1/2*b**2 + b = 0.
-2/3, 0, 1
Suppose 5*r - 73 = 7. Let g be (4/r)/((-9)/(-48)). Factor g*q**3 + 0*q**2 + 0*q**4 - 2/3*q + 0 - 2/3*q**5.
-2*q*(q - 1)**2*(q + 1)**2/3
Let p be 2/3 + (-16)/(-120)*25. Suppose 0*q + 0 + 2/3*q**p + 0*q**2 + 4/3*q**3 = 0. Calculate q.
-2, 0
Let m(x) = x**5 + x**4 + x**3 - x**2 + x - 1. Let q(j) = -4*j**5 + 12*j**4 + 7*j**3 - 5*j**2 + 5*j - 5. Let h(s) = -5*m(s) + q(s). Find i, given that h(i) = 0.
-2/9, 0, 1
Find w such that 0 + 6/11*w**3 + 16/11*w**2 - 6/11*w = 0.
-3, 0, 1/3
Factor -10/13*n**3 - 16/13 - 46/13*n + 2/13*n**4 - 42/13*n**2.
2*(n - 8)*(n + 1)**3/13
Factor -6*t - 105*t**3 + 2*t**2 + 53*t**3 + 2*t**4 - 4*t**4 + 58*t**3.
-2*t*(t - 3)*(t - 1)*(t + 1)
Let l(t) be the third derivative of t**5/9 - t**4/9 + 36*t**2. Determine n so that l(n) = 0.
0, 2/5
Let r = -3 + 3. Suppose 3*t - 6 - 21 = r. Factor q + 2*q**4 - t*q - 1 + 3 + 12*q**2 - 8*q**3.
2*(q - 1)**4
Suppose 0*m = m - 2*u - 5, -5*m + 15 = -5*u. Let w(k) = -4*k**3 + 2*k**2 - 4*k. Let s(f) = f**3 + f. Let h(l) = m*w(l) + 3*s(l). What is q in h(q) = 0?
0, 1
Factor -4/9*j**3 + 0 - 16/9*j - 20/9*j**2.
-4*j*(j + 1)*(j + 4)/9
Suppose -2*l = 4*b - 8, 5*b - 24 = 2*l - l. Factor 2*g**2 + b*g**3 + 0*g**2 - 2*g**3.
2*g**2*(g + 1)
Let x(b) be the third derivative of b**6/180 - b**5/30 + b**4/12 + b**3/3 - b**2. Let n(w) be the first derivative of x(w). Factor n(c).
2*(c - 1)**2
Let z(s) be the second derivative of 4/3*s**3 + s**4 + 1/15*s**6 + s**2 + 0 - 8*s + 2/5*s**5. Solve z(j) = 0 for j.
-1
Let r(z) = -15*z**2 - 25*z + 10. Let u(n) = -n**2 - n - 1. Let v(w) = r(w) - 10*u(w). Suppose v(l) = 0. Calculate l.
-4, 1
Let g = 5 - 2. Let f be 1/(-21) - (-13)/39. Factor f*o**g - 2/7*o**4 + 0 + 0*o**2 + 0*o.
-2*o**3*(o - 1)/7
Let s be (-2)/((2/(-9))/(6/18)). Let a(b) be the first derivative of 0*b**2 + 2/5*b - 2/15*b**s - 3. Factor a(t).
-2*(t - 1)*(t + 1)/5
Let h = 5 - 3. Suppose -g + 2*u = 8, 4*g - 2*u - h*u = -12. Find o, given that 8 + o**g + 12*o**2 - 24*o - 3*o**2 = 0.
2/5, 2
Let s be (-14)/18 - 8/36. Let k be s/(-2) - (-3)/2. Determine q so that 4*q + 9*q**2 + 2*q**4 - 3*q**k - 6*q - 6*q**3 = 0.
0, 1
Let q(d) be the third derivative of 6*d**5/5 + d**4 + d**3/3 + 23*d**2. Factor q(p).
2*(6*p + 1)**2
Let y = 17 - -19. Let o = -106/3 + y. Determine k so that 2/3*k - 2/3*k**3 - 2/3*k**2 + o = 0.
-1, 1
Solve 30 - 1 + 27*g**2 + 19 + 33 - 3*g**3 - 81*g = 0.
3
Let m = 3868/3 + -1241. Let j = m - 48. Factor -1/3*c**3 + 0 - j*c - 2/3*c**2.
-c*(c + 1)**2/3
Let a = -225 - -451/2. Let -a - 1/2*n**2 - n = 0. What is n?
-1
Suppose 3*d = -3 + 18. Factor -3*i**d - 6*i**3 - 14*i + 6*i**5 + 17*i.
3*i*(i - 1)**2*(i + 1)**2
Factor 3*g**3 + g**4 - 3*g**2 + 46*g - 48*g + g**4.
g*(g - 1)*(g + 2)*(2*g + 1)
Factor 64/5 + 1/5*j**2 + 16/5*j.
(j + 8)**2/5
Let v(n) be the first derivative of -5*n**8/168 - n**7/6 - 11*n**6/45 - 2*n**5/15 + n**3/3 - 2. Let m(a) be the third derivative of v(a). Factor m(q).
-2*q*(q + 2)*(5*q + 2)**2
Let s = -49/124 + 20/31. Let -1/2 - v**2 - 5/4*v - s*v**3 = 0. Calculate v.
-2, -1
Let p(z) be the second derivative of z**6/90 + z**5/60 - z**4/12 - z**3/18 + z**2/3 + 6*z. Factor p(i).
(i - 1)**2*(i + 1)*(i + 2)/3
Let w(z) be the first derivative of -5*z**6/2 - z**5 + 15*z**4/4 + 5*z**3/3 + 2. Solve w(b) = 0 for b.
-1, -1/3, 0, 1
Suppose -4*g**5 - 11*g**5 + 9*g**2 - 6*g - 9*g**4 + g**3 + 20*g**3 = 0. What is g?
-1, 0, 2/5, 1
Let i(p) be the second derivative of p**5/20 - p**4/6 + p**3/6 - 14*p. Factor i(b).
b*(b - 1)**2
Let n(h) be the first derivative of -h**4 + 8*h**3/3 + 2*h**2 - 8*h - 1. Factor n(m).
-4*(m - 2)*(m - 1)*(m + 1)
Let i(h) be the first derivative of -h**6/210 - h**5/105 + 4*h**2 - 5. Let o(d) be the second derivative of i(d). Factor o(l).
-4*l**2*(l + 1)/7
Solve 0*p + 0 - 1/2*p**2 = 0 for p.
0
Let t(f) be the second derivative of f**6/900 - f**4/60 + f**3/3 + 2*f. Let i(u) be the second derivative of t(u). Factor i(y).
2*(y - 1)*(y + 1)/5
Suppose -635*a = -641*a + 12. Let u be (2/(-20))/(4/(-30)). Factor 3/4 - 3/4*o**a - 3/4*o + u*o**3.
3*(o - 1)**2*(o + 1)/4
Let g(x) be the third derivative of -x**8/896 + x**7/560 + x**6/160 - x**5/80 - x**4/64 + x**3/16 + 18*x**2. Solve g(w) = 0 for w.
-1, 1
Let q(b) be the third derivative of 1/100*b**6 + 4/15*b**3 + 0 - 2*b**2 + 0*b + 1/150*b**5 - 2/15*b**4. Factor q(x).
2*(x - 1)*(x + 2)*(3*x - 2)/5
Let k(s) = -s**2 + 5*s - 2. Let a be k(3). Suppose b - 16 = 4*d, 0*d - a*d - 16 = b. What is z in -2*z**3 + 3*z**2 + 1 + b + 8*z + 3*z**3 - 5*z = 0?
-1
Suppose 2*c + 17 = 5*f, -4*f + 0*f - 2*c + 28 = 0. Suppose 1/3*l**4 + 1/3*l**f - 1/3*l**2 + 0*l + 0 - 1/3*l**3 = 0. Calculate l.
-1, 0, 1
Let c(x) be the second derivative of 5*x - 3/40*x**5 - 1/20*x**6 + 0*x**3 - 1/24*x**4 + 0 - 1/84*x**7 + 0*x**2. What is v in c(v) = 0?
-1, 0
Let v be (-4)/14 - 816/(-504). Let 2/3*n**2 + 2/3*n**4 - 2*n - v + 2*n**3 = 0. What is n?
-2, -1, 1
Let w be (-1)/((-12)/(16/4)). Let d = 5 + -3. Factor 1/3*v**d + 0*v - w.
(v - 1)*(v + 1)/3
Suppose -4*w - 4 = -3*c, 0 = 4*w + w - 5*c + 10. Factor 8 - a - 2*a - 5*a + w*a**2.
2*(a - 2)**2
Suppose 2*w**3 - 3/2*w**2 - 2*w - 1/2*w**4 + 2 = 0. What is w?
-1, 1, 2
Let m be 12/(-9)*3/(-2). Determine d, given that -2 + 10*d**4 + 20*d**3 + 4 + 2*d**5 + 32*d**2 - 12*d**m + 10*d = 0.
-1
Suppose k + 3*o - 3 = 2*k, o = k - 3. Let y = k - 4. Find z, given that -18 - 3*z - z**y + 9*z + 9 = 0.
3
Let c(h) be the second derivative of 3*h**5/20 + h**4/4 - 3*h**3 + 3*h. Let w(y) = y**3 + y**2 - 5*y. Let s(z) = -5*c(z) + 18*w(z). Factor s(u).
3*u**2*(u + 1)
Let b(i) be the first derivativ