tor f(c).
2*c*(c - 1)*(c + 1)/5
Factor 0 - 9/4*x**4 + 2*x - 11*x**2 + 19/2*x**3.
-x*(x - 2)**2*(9*x - 2)/4
Let p be -6*1/(-7)*168/36. Determine a, given that -4/9*a**3 + 4/9*a + 2*a**p - 2*a**2 + 0 = 0.
-1, 0, 2/9, 1
Let r = -13 - -5. Let i be r/(-6) + (-6)/6. Factor -1/3*f**2 - i - 2/3*f.
-(f + 1)**2/3
Let w(s) be the second derivative of -s**5/80 - 5*s**2/2 - 4*s. Let d(k) be the first derivative of w(k). Factor d(h).
-3*h**2/4
Let a be (-2 - (-196)/48) + -2. Let t(k) be the third derivative of 0*k**3 - 2*k**2 + 0*k - a*k**4 + 1/30*k**5 + 0. Factor t(n).
2*n*(n - 1)
Let s(u) be the third derivative of 0*u + 1/70*u**7 + 0 + 1/20*u**5 + 0*u**4 + 0*u**3 - 1/20*u**6 - 4*u**2. Factor s(t).
3*t**2*(t - 1)**2
Find i, given that -2/3*i**5 + 8/3*i**3 - 2*i + 0*i**4 - 4/3 + 4/3*i**2 = 0.
-1, 1, 2
Let f(k) be the first derivative of -k**5/5 - 5*k**4/8 - 2*k**3/3 - k**2/4 + 1. Factor f(o).
-o*(o + 1)**2*(2*o + 1)/2
Factor 0 - 5/2*i**3 - 1/2*i**4 + 0*i**2 + 0*i.
-i**3*(i + 5)/2
Let q(z) be the third derivative of z**5/140 - z**4/7 + 8*z**3/7 - 3*z**2 - 9*z. Find m such that q(m) = 0.
4
Let d(t) = 6*t**4 + 4*t**3 - 14*t**2 - 22*t - 10. Let p(m) = 13*m**4 + 8*m**3 - 29*m**2 - 45*m - 21. Let w(c) = 5*d(c) - 2*p(c). Factor w(f).
4*(f - 2)*(f + 1)**3
Let x(n) be the second derivative of -n**8/1680 + n**6/360 - n**3/6 + n. Let y(p) be the second derivative of x(p). Factor y(k).
-k**2*(k - 1)*(k + 1)
Let j = -14/5 - -122/15. Factor -j*w + 8/3 + 2*w**2.
2*(w - 2)*(3*w - 2)/3
Solve 6/7 - 3/7*j + 3/7*j**3 - 6/7*j**2 = 0 for j.
-1, 1, 2
Let g = 27/4 + -5/4. What is j in 1 + 13/2*j + g*j**2 = 0?
-1, -2/11
Let t(j) be the first derivative of 2*j**3/15 + 2*j**2/5 - 6*j/5 + 9. Factor t(n).
2*(n - 1)*(n + 3)/5
Suppose 22 = 4*a - 5*l, -3*l - 4 = -l. Let r = -194/5 + 39. Solve 1/5*x + 0 - 1/5*x**2 - r*x**a + 1/5*x**4 = 0.
-1, 0, 1
Let f be (-51)/(-55) + (-27)/135. Let -38/11*u**2 + 14/11*u**3 + f + 16/11*u = 0. What is u?
-2/7, 1, 2
Let h(q) = 13*q**3 - 24*q**2 + 30*q - 12. Let s(w) = -7*w**3 + 12*w**2 - 15*w + 6. Let f(p) = -4*h(p) - 7*s(p). What is v in f(v) = 0?
1, 2
What is z in 0*z**2 - 2/5*z**3 + 0*z**4 + 0 + 0*z + 2/5*z**5 = 0?
-1, 0, 1
Let z(a) be the second derivative of a**5/300 + a**4/15 + 8*a**3/15 + 3*a**2 + 3*a. Let c(n) be the first derivative of z(n). Factor c(i).
(i + 4)**2/5
Let h = 188 - 1314/7. Determine o so that -2/7*o**2 - h + 4/7*o = 0.
1
Let f(r) = -r**3. Let o(s) = -7*s**3 + 4*s**2 - 3*s - 3. Let x(n) = -3*f(n) + o(n). Let u(c) = -c**3 + c**2 - c - 1. Let w(h) = 3*u(h) - x(h). Factor w(v).
v**2*(v - 1)
Let v(n) be the second derivative of 0 + 0*n**3 + 2/15*n**6 + 0*n**2 + 2/21*n**7 - 1/3*n**4 - 8*n - 1/5*n**5. Factor v(k).
4*k**2*(k - 1)*(k + 1)**2
Let p(i) be the second derivative of 3*i**5/10 + 8*i**4/3 + 5*i**3 - 18*i**2 + 11*i. Let p(v) = 0. Calculate v.
-3, 2/3
Let p(f) = -2*f**2 - 17*f - 33. Let b be p(-3). Solve -1/3*x**2 + 1/3*x + b = 0.
0, 1
Let c = 1 - -12. Let b = c - 3. Factor -23/2*x**2 - b*x - 2 - 7/2*x**3.
-(x + 1)*(x + 2)*(7*x + 2)/2
Let k(g) be the third derivative of -g**8/280 + g**7/525 + 3*g**6/100 - 3*g**5/50 + g**4/30 + 20*g**2. Find h such that k(h) = 0.
-2, 0, 1/3, 1
Factor 80*w**2 + 82*w**2 - 5*w**3 - 177*w**2.
-5*w**2*(w + 3)
Let f = -3 - 2. Let w be f/12 + 4/6. Solve 1/4*k**5 - 1/4*k**2 + 0 + 1/4*k**4 - w*k**3 + 0*k = 0 for k.
-1, 0, 1
Let a be 8/((-2)/((-10)/25)). Suppose 2*k + 5*z - 24 = 0, -k + 4*z - 2 = 12. Let -8/5*v - a - 2/5*v**k = 0. What is v?
-2
Let n = -23 + 28. Suppose -2*v - n*v = -14. Let 0 + 1/3*b**v - 1/3*b = 0. Calculate b.
0, 1
Let q = 5 - 2. Determine r so that r**3 + 3*r**2 + 0*r**4 + r**4 - 4*r**q - r = 0.
0, 1
Let t(j) = -2*j**3 + 4*j**2 + 8*j - 4. Let z(s) = -3*s. Let l be z(-2). Let o(f) = -2*f**3 + 4*f**2 + 9*f - 4. Let w(p) = l*o(p) - 7*t(p). Factor w(u).
2*(u - 2)*(u - 1)*(u + 1)
Let o(s) be the first derivative of s**8/840 - s**7/525 + s**2/2 + 2. Let d(m) be the second derivative of o(m). Factor d(p).
2*p**4*(p - 1)/5
Let o be (-1 - -2)/(5/20). Let i(h) be the first derivative of -2/3*h - 20/9*h**3 + 1 - 2/3*h**5 - 5/3*h**o - 5/3*h**2 - 1/9*h**6. Factor i(t).
-2*(t + 1)**5/3
Solve 10/13*u**3 - 8/13 + 32/13*u - 34/13*u**2 = 0 for u.
2/5, 1, 2
Let v(p) = p**3 + 4*p**2 - p. Let n(t) = 2*t**3 + 9*t**2 - 3*t. Let z(b) = 2*n(b) - 5*v(b). Determine j, given that z(j) = 0.
-1, 0
Suppose -2*i = 4*y + i + 6, 2*i + 4 = y. Let 2/7*t**3 + 4/7*t**4 + 0 + y*t**2 + 2/7*t**5 + 0*t = 0. Calculate t.
-1, 0
Let i(m) be the third derivative of 0*m**3 - 1/24*m**4 + 0*m + 0 - 1/120*m**5 - 4*m**2. Determine a, given that i(a) = 0.
-2, 0
Let m(s) be the third derivative of 1/210*s**5 + 0*s + 16/21*s**3 + 2*s**2 - 2/21*s**4 + 0. Solve m(c) = 0 for c.
4
Let a(t) be the first derivative of -1/30*t**5 - 2 + 0*t**3 - 1/60*t**6 - 1/2*t**2 + 0*t**4 + 0*t. Let w(y) be the second derivative of a(y). Factor w(d).
-2*d**2*(d + 1)
Let b = -9 + 8. Let h(j) = -j + 1. Let n be h(b). Solve -2 - 1/2*u**n + 2*u = 0 for u.
2
Solve 17/7*k**3 + 1/7*k**4 + 90/7*k**2 + 108/7*k - 216/7 = 0 for k.
-6, 1
Let t(u) = u + 1. Let j(h) = 6*h**2 + 16*h - 10. Let i(a) = -a**2 - 3*a + 2. Let l(o) = 11*i(o) + 2*j(o). Let w(p) = l(p) - t(p). Factor w(y).
(y - 1)**2
Suppose -432/5*w**2 + 192/5*w - 162/5*w**4 - 32/5 + 432/5*w**3 = 0. Calculate w.
2/3
Let t(r) be the first derivative of 5*r**6/18 + 6*r**5/5 + 11*r**4/6 + 8*r**3/9 - r**2/2 - 2*r/3 + 4. Suppose t(j) = 0. What is j?
-1, 2/5
Let p(m) = 13*m. Let l be p(-2). Let i = l - -80/3. Factor 0 + i*q + 2/3*q**2.
2*q*(q + 1)/3
Factor -29*z + 69 - 5*z**2 - 194 - 21*z.
-5*(z + 5)**2
Suppose -9 = 4*m + 7. Let k be 2 - (m - (-87)/15). Suppose 0 + k*a**2 + 0*a - 1/5*a**3 = 0. What is a?
0, 1
Let y be 1 - -7 - (-6)/(-2). Determine f so that 5*f**2 - 4*f**3 - 16*f**2 - y*f**2 = 0.
-4, 0
Let q(n) be the third derivative of -n**8/112 - n**7/10 - 19*n**6/40 - 5*n**5/4 - 2*n**4 - 2*n**3 + 30*n**2 - n. Let q(y) = 0. Calculate y.
-2, -1
Let h = 55/21 + -7/3. Factor 2/7 - 2/7*x + h*x**3 - 2/7*x**2.
2*(x - 1)**2*(x + 1)/7
Let c = 2/391 + 3122/1173. Factor -2/3*n**2 - c*n + 8/3*n**3 + 2/3.
2*(n - 1)*(n + 1)*(4*n - 1)/3
Let c(r) = -r**3 + 2*r**2 + 3*r + 2. Suppose -5*y + 31 = 4*k - 0*k, -3*k + 9 = -y. Let f be c(y). What is w in f + 2*w - 2*w - 2*w**2 = 0?
-1, 1
Let h(s) be the second derivative of s**6/15 + s**5/2 + 3*s**4/2 + 7*s**3/3 + 2*s**2 + 13*s. Find o such that h(o) = 0.
-2, -1
Let h(y) = 3*y - 5*y**4 - y**5 + 0*y**5 + y. Suppose 2*d + 0*d + 8 = 0. Let m(n) = -2*n**5 - 11*n**4 + 9*n. Let k(r) = d*m(r) + 9*h(r). Factor k(t).
-t**4*(t + 1)
Let 0 + 1/3*g**3 - 1/3*g**5 + 0*g - 1/3*g**2 + 1/3*g**4 = 0. What is g?
-1, 0, 1
Let d = -1255 + 2511/2. Find x such that 1/4*x**2 - 3/4*x + d = 0.
1, 2
Let c(g) be the second derivative of -3*g**5/80 - g**4/8 + 19*g. Determine l so that c(l) = 0.
-2, 0
Let t(c) = -c + 9. Let k be t(13). Let x be k/40*(2 + -4). Factor -x*f**5 + 2/5*f**3 - 1/5*f + 0 + 0*f**4 + 0*f**2.
-f*(f - 1)**2*(f + 1)**2/5
Suppose 7*c + o - 17 = 2*c, -5*c - 4*o = -8. Let a be 2/(-2 + c) - -2. Factor 1 - 3/2*k - k**2 + 3/2*k**a.
(k - 1)*(k + 1)*(3*k - 2)/2
Factor 0 - 14/19*r**2 - 10/19*r**4 - 4/19*r - 2/19*r**5 - 18/19*r**3.
-2*r*(r + 1)**3*(r + 2)/19
Suppose -10/3*w + 4 - 8/3*w**2 = 0. What is w?
-2, 3/4
Solve 15*s**3 + 5*s**2 - 5*s**4 + 5*s**5 + 6*s**4 + 14*s**4 = 0.
-1, 0
Suppose 0 = 3*g + 2*g - 175. Let n be ((-42)/g)/(4/(-10)). Factor 28/5*r**2 + 8*r + 6/5*r**n + 16/5.
2*(r + 2)**2*(3*r + 2)/5
Let -4/7 - 10/7*n + 4/7*n**2 + 10/7*n**3 = 0. Calculate n.
-1, -2/5, 1
Let p(z) be the first derivative of z**6/2 - 27*z**5/5 + 24*z**4 - 56*z**3 + 72*z**2 - 48*z - 15. Factor p(i).
3*(i - 2)**4*(i - 1)
Let u(l) be the third derivative of l**5/60 - l**4/12 - l**3/2 + 8*l**2. Determine n, given that u(n) = 0.
-1, 3
Let h(p) be the third derivative of p**5/12 - 5*p**4/12 + 47*p**2. Factor h(l).
5*l*(l - 2)
Solve 4*p - 5304*p**3 + 0*p + 5303*p**3 = 0.
-2, 0, 2
Let 1/5*j**2 - 1/5*j + 0 = 0. What is j?
0, 1
Let k be (-5 + 7)/(1 + 1). Let s be (0 + -12)/(-3) - k. Factor s - 3*h**2 + 0 + 6*h - 3.
-3*h*(h - 2)
Let x be 6/8 + 90/40. Factor -3*i + 4*i**x + 0*i**4 - i**3 - 6*i**2 + 6*i**4.
3*i*(i - 1)*(i + 1)*(2*i + 1)
Suppose -r + 12 = -0. Let k be ((-1)/2)/((-2)/r). Factor 1 + 0*z**3 - 3*z + 2*z**2 + 3*z**k + 2*z**2 