3*m**2*(m + 1)/4
Suppose -400/7 + 4/7*w**3 + 76/7*w**2 + 320/7*w = 0. What is w?
-10, 1
Let r(t) be the first derivative of 1/11*t**4 + 1 + 0*t - 2/55*t**5 + 0*t**3 - 1/11*t**6 + 0*t**2. Determine v so that r(v) = 0.
-1, 0, 2/3
Let f(j) be the second derivative of -7*j**6/10 + 33*j**5/20 + 3*j**4/4 - 11*j**3/2 + 6*j**2 + 10*j. Suppose f(v) = 0. Calculate v.
-1, 4/7, 1
Let f(p) = 3*p**4 + 2*p**3 - 4*p**2 + 2*p - 1. Let q(k) = 16*k**4 + 11*k**3 - 21*k**2 + 11*k - 6. Let b(s) = 11*f(s) - 2*q(s). Find y, given that b(y) = 0.
-1, 1
Let y = -10 + 3. Let h(t) = -2*t - 5. Let m be h(-4). Let r(i) = -6*i**2 + 3*i - 7. Let j(n) = -3*n**2 + n - 3. Let b(z) = m*r(z) + y*j(z). Factor b(x).
x*(3*x + 2)
Find s, given that 2/13*s**4 + 0*s + 2/13*s**3 + 0*s**2 + 0 = 0.
-1, 0
Suppose -b = -2*y + b + 14, 4*y = -4*b + 28. Let x = y + -7. Factor x*w**3 - 2/3*w - w**2 + 1/3*w**4 + 0.
w*(w - 2)*(w + 1)**2/3
Let w(c) be the third derivative of c**6/240 - c**5/40 + c**3/3 - 3*c**2. Factor w(q).
(q - 2)**2*(q + 1)/2
Factor 16/5 + 48/5*u + 52/5*u**2 + 4/5*u**4 + 24/5*u**3.
4*(u + 1)**2*(u + 2)**2/5
Factor -27*t + t**2 - 4*t**2 + 12*t + 0*t**2.
-3*t*(t + 5)
Suppose 4*b + 16 = -2*m, 0 = 3*m - 2*m - 3*b - 17. Factor -18 - 2*x + 5*x + 9*x - m*x**2.
-2*(x - 3)**2
Factor -86/3*v**3 - 78*v**2 + 36 - 10/3*v**4 - 54*v.
-2*(v + 3)**3*(5*v - 2)/3
Let g be ((-12)/(-9))/(6/9). Factor w - 2*w**g - 2*w**3 + 2*w**4 + 10 - 9 + w**5 - w**4.
(w - 1)**2*(w + 1)**3
Let s(g) be the second derivative of 0 + 0*g**2 + 1/10*g**5 - 1/3*g**3 - 1/15*g**6 + 1/6*g**4 - 3*g. Factor s(n).
-2*n*(n - 1)**2*(n + 1)
Let k(x) be the first derivative of -5*x**6/6 - 3*x**5 - 5*x**4/4 + 5*x**3 + 5*x**2 - 4. Find j such that k(j) = 0.
-2, -1, 0, 1
Let t = 10/27 + -1/27. Find k, given that -t*k**2 + 0 - 1/3*k = 0.
-1, 0
Let 15*k + 0*k**3 - 9*k**2 + 45 - 16*k**2 + 5*k**3 = 0. What is k?
-1, 3
Suppose 15*d**3 + 10*d**3 + 18*d**4 + 2*d**5 + 46*d**2 + 85 - 48*d + 29*d**3 - 157 = 0. Calculate d.
-3, -2, 1
Let g = -11 + 15. Suppose 28 = 4*v + 4*j, g*v - 15 = v - j. Solve 0*y**2 + y**2 - v*y**2 + 4*y + y**2 + 2*y**4 - 10*y**3 + 6*y**5 = 0.
-1, 0, 2/3, 1
Let 0 - 2/3*b**2 + 0*b + 2/3*b**3 = 0. What is b?
0, 1
Let o = -203/4 - -205/4. Find k such that 0 - 1/4*k**3 + o*k**2 - 1/4*k = 0.
0, 1
Let i(t) be the first derivative of t**3/5 - 9*t**2/10 + 6*t/5 - 10. Suppose i(k) = 0. Calculate k.
1, 2
Find f, given that -9*f**5 - 15*f**3 + 78*f**4 - 28*f**4 - 6*f**5 - 60*f**2 + 20*f = 0.
-1, 0, 1/3, 2
Let w(z) be the third derivative of -5*z**8/336 - 2*z**7/21 - z**6/4 - z**5/3 - 5*z**4/24 + 7*z**2. Let w(s) = 0. What is s?
-1, 0
Let u(o) be the first derivative of o**5/80 + o**4/24 + o**3/24 + 3*o + 1. Let x(t) be the first derivative of u(t). Factor x(n).
n*(n + 1)**2/4
Let g(h) be the first derivative of h**3/3 - 5*h**2 + 9*h + 6. Let f be g(9). Factor 2/5*w**2 + 0*w - 2/5*w**3 + f.
-2*w**2*(w - 1)/5
Suppose -8*o - 154 + 170 = 0. Factor -2/3*j + 0 - 2/3*j**o.
-2*j*(j + 1)/3
What is m in -5*m**5 + 7*m**3 - 2*m**3 + 77*m**4 - 87*m**4 + 10*m**2 = 0?
-2, -1, 0, 1
Let g(l) be the second derivative of -5*l - 1/8*l**2 + 0*l**3 + 0 + 1/48*l**4. What is d in g(d) = 0?
-1, 1
Let y(j) = -j**2 + 1. Let f(i) be the first derivative of 5*i**3/3 - 3*i**2/2 - 2*i + 6. Let u(b) = f(b) + 2*y(b). Factor u(p).
3*p*(p - 1)
Solve 0*s + 0 + 1/4*s**2 + 0*s**3 - 1/4*s**4 = 0 for s.
-1, 0, 1
Let a = -634/35 - -92/5. Factor 2/7*y**2 + 0*y + 0 + 4/7*y**3 + a*y**4.
2*y**2*(y + 1)**2/7
Suppose -3*x + 8 = -115. Suppose z - x = 5*i, 41 - 8 = z - i. Determine p so that 3*p**3 + 3*p**5 + z - 31 + 6*p**4 = 0.
-1, 0
Let z(m) be the first derivative of 16*m**5/5 + 14*m**4 + 17*m**3/3 - 10*m**2 + 3*m - 9. Factor z(r).
(r + 1)*(r + 3)*(4*r - 1)**2
Factor 1/2*d**2 - 1/4*d + 1/2*d**3 - 1/4*d**4 - 1/4 - 1/4*d**5.
-(d - 1)**2*(d + 1)**3/4
Let g be 27/6*(-100)/(-15). Let r = g + -27. Factor 2/9*f**5 - 4/9*f**r + 2/9*f + 0 + 0*f**2 + 0*f**4.
2*f*(f - 1)**2*(f + 1)**2/9
Let m(z) = 8*z**2 + 4*z + 7. Suppose 5*s = 2*s + 21. Let w(t) = 7*t**2 + 3*t + 6. Let p(o) = s*w(o) - 6*m(o). Factor p(f).
f*(f - 3)
Let w(p) = -p**5 + p**3 - p**2 + p - 1. Let l(s) = -108*s**5 + 180*s**4 - 88*s**3 + 8*s**2 + 8*s - 8. Let h(y) = -l(y) + 8*w(y). Solve h(n) = 0.
0, 2/5, 1
Let u(l) be the first derivative of -10*l**6/9 + 7*l**5/15 + 11*l**4/12 + 2*l**3/9 - 12. Find y, given that u(y) = 0.
-2/5, -1/4, 0, 1
Let x be (-4)/(-2)*(-2)/(-20). Let i(o) be the first derivative of -o**4 + x*o**5 + 1 + o + 2*o**3 - 2*o**2. Determine u, given that i(u) = 0.
1
Find a, given that 8*a - 6*a**5 - 3*a - 10*a**3 + 11*a**5 = 0.
-1, 0, 1
Suppose -14 - 1 = -3*c. Let p(h) be the third derivative of 0 - 1/480*h**6 + 1/96*h**4 - 1/240*h**c + 0*h**3 + 2*h**2 + 0*h + 1/840*h**7. Solve p(k) = 0.
-1, 0, 1
Let b be 1*1/(19 - 4). Let s(r) be the second derivative of -1/75*r**6 - 1/10*r**4 + b*r**3 + 0*r**2 - 2*r + 0 + 3/50*r**5. Find u such that s(u) = 0.
0, 1
Let y(z) = 3*z**2 + 2*z - 5. Let u(j) = 2*j**2 + j - 3. Let d(i) = 8*u(i) - 5*y(i). Factor d(s).
(s - 1)**2
Let o(g) be the third derivative of -g**8/128 + 33*g**7/560 - 11*g**6/320 - 69*g**5/160 - 9*g**4/32 - 40*g**2. Find q, given that o(q) = 0.
-1, -2/7, 0, 3
Let h(j) be the second derivative of j**5/150 - j**4/18 + 4*j**3/45 - 8*j. Factor h(k).
2*k*(k - 4)*(k - 1)/15
Let y(g) be the second derivative of 6*g**5/5 - 13*g**4/3 + 8*g**2 - 9*g. Factor y(f).
4*(f - 2)*(2*f + 1)*(3*f - 2)
Let 0*d**2 - 2/3*d**4 - 1/6*d**5 + 0*d + 0 - 1/2*d**3 = 0. What is d?
-3, -1, 0
Factor 15*k + 8 + 11 - 4 + 5*k**2 + 5*k.
5*(k + 1)*(k + 3)
Let r = 18/5 - 116/35. Factor -r + 0*p + 2/7*p**2.
2*(p - 1)*(p + 1)/7
Let p(a) = -208*a**3 - 978*a**2 - 1144*a - 176. Let f(t) = 19*t**3 + 89*t**2 + 104*t + 16. Let g(s) = -68*f(s) - 6*p(s). Find o, given that g(o) = 0.
-2, -2/11
Solve a**2 + 3*a**2 + 4*a**4 - 5*a - 6*a**2 + a**5 + 3 - 5 + 4*a**3 = 0.
-2, -1, 1
Let u be (-1)/2*(-4 + 14). Let q(n) = n**2 + 5*n + 5. Let f be q(u). Factor 1/2*y**3 + 0*y - 1/2*y**f + 1/2*y**4 + 0 - 1/2*y**2.
-y**2*(y - 1)**2*(y + 1)/2
Let z(y) = -3*y**3 + 5*y**2 - 4. Let t(u) be the first derivative of u**5/5 + 3*u**4/4 - 4*u**3/3 + 3*u + 3. Let p(c) = 4*t(c) + 3*z(c). Solve p(h) = 0 for h.
-1, 0, 1/4
Factor -1 + 0*n**2 - 3/2*n + 1/2*n**3.
(n - 2)*(n + 1)**2/2
Suppose -12/5*d - 2/5 + 64/5*d**3 + 0*d**2 = 0. Calculate d.
-1/4, 1/2
Let q(v) = -v**4 + 2*v**3 - 2*v**2 - 4*v + 1. Let s(f) = 3*f**4 - 4*f**3 + 3*f**2 + 9*f - 1. Let i(m) = -5*q(m) - 2*s(m). Factor i(k).
-(k - 1)**2*(k + 1)*(k + 3)
Let i be -1 - (0/(-2) + -1). Suppose i*y + 8 = 2*y. Solve -7*r**3 - 2*r + y*r**2 - r**3 + 6*r**3 = 0 for r.
0, 1
Let m(n) = -n**3 - n**2 + n + 2. Let b be m(-2). Let 3*i**4 + 9*i**3 - 6*i**b - 17*i + 5*i = 0. Calculate i.
-1, 0, 2
Let n(c) = c**3 - 9*c**2 + 4. Let w(g) = 9*g**3 - 72*g**2 + 33. Let v(p) = -33*n(p) + 4*w(p). Determine b, given that v(b) = 0.
-3, 0
Suppose 4*x = x - 6, 3*v = x + 14. What is z in 0*z**3 + 1/2*z**2 + 0*z + 0 - 1/2*z**v = 0?
-1, 0, 1
Let y(a) be the second derivative of a**5/15 + 2*a**4/9 + 5*a**3/18 + a**2/6 + 2*a + 2. Let y(s) = 0. Calculate s.
-1, -1/2
Let g(f) = f - 3. Let n be g(3). Let h(t) be the second derivative of n*t**3 + 0*t**2 + 2*t + 0 - 1/30*t**5 - 1/18*t**4. Solve h(d) = 0 for d.
-1, 0
Let d(v) = -v**2. Let p(z) = -5*z**2 + 5*z + 6. Let n(w) = 4*d(w) - p(w). Let r be n(6). Factor r + 1/6*j**4 - 1/6*j**3 + 0*j + 0*j**2.
j**3*(j - 1)/6
Let s(v) be the second derivative of -3*v + 1/21*v**3 + 1/147*v**7 + 2/21*v**4 + 0 + 3/35*v**5 + 4/105*v**6 + 0*v**2. Factor s(n).
2*n*(n + 1)**4/7
Let w be (5/16)/((-3)/(-12)) + -1. Solve w*k - 15/4*k**2 - 7/4*k**4 + 19/4*k**3 + 1/2 = 0 for k.
-2/7, 1
Let a(k) = 14*k**5 + 16*k**4 - 8*k**3 - 14*k**2 - 7*k - 3. Let j(b) = -13*b**5 - 16*b**4 + 8*b**3 + 13*b**2 + 7*b + 4. Let o(p) = -3*a(p) - 2*j(p). Factor o(s).
-(s - 1)*(2*s + 1)**4
Let j = 25 + -26. Let q be (2/(-18))/(j/2). What is v in -10/9*v**3 + 0 + 0*v + 8/9*v**4 + 4/9*v**2 - q*v**5 = 0?
0, 1, 2
Let m(u) be the third derivative of -u**9/30240 - u**8/10080 + u**7/2520 + u**6/360 - u**5/30 - 2*u**2. Let r(a) be the third derivative of m(a). Factor r(o).
-2*(o - 1)*(o + 1)**2
Let v(y) be the second derivative of -4*y + 0 + 2*y**3 + 1/3*y**4 + 0*y**2. Factor v(q).
4*q*(q + 3)
Let k(p) be the third deriv