**4 + 6*q = 0. What is q?
-1, -2/3, -2/5
Let c(x) be the first derivative of 5*x**4/4 - 5*x**3 + 5*x**2 - 1. Find j, given that c(j) = 0.
0, 1, 2
Let t(n) be the third derivative of 0*n**4 - 1/420*n**7 - 1/60*n**6 + 0 + 0*n**3 + 8*n**2 - 1/90*n**5 + 0*n + 5/2016*n**8. Suppose t(w) = 0. What is w?
-1, -2/5, 0, 2
Let g(q) be the second derivative of q**4/42 - q**2/7 + 12*q + 1. Factor g(y).
2*(y - 1)*(y + 1)/7
Let r(u) be the second derivative of -u**4/84 + 2*u**2/7 + u. Determine s so that r(s) = 0.
-2, 2
Let d(b) be the second derivative of 0*b**3 - 4*b + 0 + 0*b**4 + 1/90*b**5 + 0*b**2. Factor d(t).
2*t**3/9
Suppose 140 - 5*w - 140 + 5*w**3 = 0. Calculate w.
-1, 0, 1
Let n(c) = -2*c**5 - 4*c**3 - 4*c**2 - 2*c. Let l(w) = -w**5 - 4*w**3 - 3*w**2 - w. Let i(h) = -4*l(h) + 3*n(h). Factor i(g).
-2*g*(g - 1)**2*(g + 1)**2
Let f(z) be the first derivative of 8/3*z + 10*z**3 + 14/3*z**4 - 98/15*z**5 - 28/3*z**2 - 2. Solve f(a) = 0 for a.
-1, 2/7, 1
Suppose 42 = -2*n - 4*y, 2*n + 4*y - 77 = 7*n. Let g = n - -17. Factor g + 2/3*v**3 - 2/3*v**2 - 2/3*v + 2/3*v**4.
2*v*(v - 1)*(v + 1)**2/3
Let n(a) be the first derivative of a**6/300 + a**5/150 - a**4/30 - 2*a**2 - 1. Let i(y) be the second derivative of n(y). Factor i(u).
2*u*(u - 1)*(u + 2)/5
Let x(d) be the second derivative of -d**5/10 - 2*d. Suppose x(k) = 0. Calculate k.
0
Find a such that 1/8 + 0*a - 1/8*a**2 = 0.
-1, 1
Let c(j) = -3*j**3 - 2*j**2 + 11*j - 8. Let l(d) = 7*d**3 + 3*d**2 - 22*d + 17. Let x(s) = 10*c(s) + 4*l(s). Solve x(v) = 0.
-6, 1
Suppose -11*i**4 - 4*i**3 + 11*i**2 - i**4 + 8*i + 8*i**5 - 12*i**5 + i**2 = 0. What is i?
-2, -1, 0, 1
Let w(t) = -t**2 + 7*t. Let c be w(5). Solve -5*o**2 + 25*o**3 - c*o - 3 + 8*o - 14*o - 1 = 0 for o.
-2/5, 1
Let v(o) = -15*o**3 + 7*o**2 + 5*o + 5. Let l(i) = -4*i**3 + 2*i**2 + i + 1. Let w(j) = -22*l(j) + 6*v(j). Find t, given that w(t) = 0.
-2, -1, 2
Let h(u) be the first derivative of 1/7*u**2 + 4/7*u - 6 - 2/21*u**3. Determine n so that h(n) = 0.
-1, 2
Let b(q) be the third derivative of q**8/40320 + q**7/5040 + q**6/1440 - q**5/15 - 3*q**2. Let v(t) be the third derivative of b(t). Factor v(g).
(g + 1)**2/2
Let 7/2*k**3 + 0*k + 0 - k**2 = 0. What is k?
0, 2/7
Let u = 14 - 10. Suppose -3*b = -u*b. What is l in 17*l**2 + 2 - 17*l**3 + 10*l**2 + b + 4*l**4 - 3*l**2 - 13*l = 0?
1/4, 1, 2
Let a(g) be the third derivative of g**7/735 + g**6/140 - 13*g**2. Determine l, given that a(l) = 0.
-3, 0
Let w(n) be the first derivative of -3/4*n - 1/12*n**3 - 1/2*n**2 - 1. Determine h so that w(h) = 0.
-3, -1
Suppose 27/7*i**3 + 99/7*i**2 + 57/7*i + 9/7 = 0. Calculate i.
-3, -1/3
Let c(x) be the third derivative of -x**7/420 - x**6/80 - x**5/120 + x**4/16 + x**3/6 + 11*x**2. Factor c(v).
-(v - 1)*(v + 1)**2*(v + 2)/2
Let h(v) be the second derivative of 4/15*v**6 + 1/3*v**3 + 3/5*v**5 + 6*v + 2/3*v**4 + 0 + 1/21*v**7 + 0*v**2. Factor h(m).
2*m*(m + 1)**4
Let 1/6*o**2 + 3/2 - 5/3*o = 0. What is o?
1, 9
Let l(p) be the first derivative of 2*p**3/3 + 12*p**2 + 72*p + 11. Factor l(a).
2*(a + 6)**2
Let s = 3 - 9/4. What is f in -3/8*f**2 + s*f - 3/8 = 0?
1
Let r(o) be the third derivative of -1/80*o**5 + o**2 + 1/8*o**3 + 0*o + 0 + 0*o**4. Solve r(z) = 0.
-1, 1
Let a(n) be the third derivative of n**7/210 - n**6/20 + n**5/60 + n**4 + 8*n**3/3 - 25*n**2. Find h, given that a(h) = 0.
-1, 4
Suppose 1 + 1 = v. Solve -2*b + 3 + 2*b - b**v - 2 = 0 for b.
-1, 1
Let t(m) be the third derivative of -1/720*m**6 + 0*m**4 - 1/2016*m**8 + 0*m**5 + 0 - 6*m**2 + 0*m**3 + 1/630*m**7 + 0*m. Factor t(f).
-f**3*(f - 1)**2/6
Let o(u) be the second derivative of 1/3*u**3 - 1/12*u**4 + 0*u**2 - u + 1/30*u**5 - 1/180*u**6 + 0. Let k(b) be the second derivative of o(b). Factor k(n).
-2*(n - 1)**2
Determine n so that 167*n + 28*n**3 - 3*n**3 + 30 + 110*n**2 - 52*n = 0.
-3, -1, -2/5
Let m(p) = -p**2 - 7*p - 8. Let q be m(-6). Let v = q + 4. Factor -w**3 - 6*w + v*w + 3*w**2 + w**2.
-w*(w - 2)**2
Let s(l) be the second derivative of -l**4/28 + 5*l**3/7 - 75*l**2/14 + l. What is g in s(g) = 0?
5
Let c be (-86)/(-48) + 8/(-12). Let h = c + -13/40. Suppose 2/5*k + 0 + h*k**2 - 2/5*k**5 + 0*k**3 - 4/5*k**4 = 0. What is k?
-1, 0, 1
Let a(k) be the third derivative of -3*k**2 - 1/42*k**4 + 0 + 0*k + 0*k**3 + 3/70*k**5. Factor a(z).
2*z*(9*z - 2)/7
Let k(c) be the second derivative of 1/2*c**4 - 6*c - 1/2*c**5 + 0 + 2/3*c**3 + 0*c**2. Find t such that k(t) = 0.
-2/5, 0, 1
Let u(v) be the third derivative of v**4/24 + 4*v**3/3 - v**2. Let m be u(-6). Determine h so that -2*h**2 - 2*h**3 + 5*h**4 + m*h**5 + h**4 - 4*h**4 = 0.
-1, 0, 1
Let x(a) = 10*a**4 - 4*a**3 + 12*a**2 + 12*a - 12. Let y(v) = -v**4 - v**2 - v + 1. Suppose 0 = -5*o - 19 - 41. Let d(w) = o*y(w) - x(w). Factor d(l).
2*l**3*(l + 2)
Let q = -46 - -31. Let v(s) = s**3 + 15*s**2 - 2*s - 25. Let i be v(q). Factor 0 - 2*n + 2*n**2 - n**4 - 1/2*n**i + 3/2*n**3.
-n*(n - 1)**2*(n + 2)**2/2
Let m(h) = h**3 + 4*h**2 + 4*h + 3. Let o be m(-2). Find j, given that -j**o + j**2 - j + 4*j**3 - 1 - 2*j**3 = 0.
-1, 1
Let g(q) = -4*q**3 - 12*q**2 + 15*q + 1. Let o(h) = -7*h**3 - 25*h**2 + 31*h + 1. Let v(m) = 14*g(m) - 6*o(m). Let v(s) = 0. Calculate s.
-2, -2/7, 1
Let t(x) = -7*x**5 - 10*x**4 + 5*x**3 + 4*x**2 - 4*x. Let u(k) = 6*k**5 + 9*k**4 - 6*k**3 - 3*k**2 + 3*k. Let v(n) = 3*t(n) + 4*u(n). Let v(z) = 0. Calculate z.
-3, 0, 1
Let -3/5*v**2 + 0 + 3/5*v = 0. Calculate v.
0, 1
Let o be (5 - 40)/(-5) + -3. Let m(i) be the third derivative of 0*i + 1/24*i**5 - 2*i**2 + 1/6*i**3 - 7/48*i**o + 0. Find q such that m(q) = 0.
2/5, 1
Let y(b) be the first derivative of -b**3/3 + 2*b + 2. Let o be y(0). Factor -s**4 - s + s**5 - s**4 + 3*s**2 - s**o.
s*(s - 1)**3*(s + 1)
Let 24*i - 4 + 29*i**2 - 4*i**3 - 9*i**2 + 4 = 0. Calculate i.
-1, 0, 6
Let k(n) be the third derivative of 0 + 1/130*n**5 + 0*n - 1/78*n**4 + 0*n**3 + 6*n**2 - 1/780*n**6. Solve k(d) = 0.
0, 1, 2
Let g(z) = -3*z**4 - 21*z**3 - 8*z**2 + 5*z + 5. Let h(y) = -16*y**4 - 116*y**3 - 44*y**2 + 28*y + 28. Let c(s) = -28*g(s) + 5*h(s). Solve c(v) = 0.
-1, 0
Factor -14/3*u**2 - 16/3*u + 32/3 - 2/3*u**3.
-2*(u - 1)*(u + 4)**2/3
Let x(u) = 6*u**2 + 7*u + 1. Let z(i) = 3*i**2 + 3*i. Suppose 5*f = -8 - 7. Let g(k) = f*x(k) + 7*z(k). Factor g(v).
3*(v - 1)*(v + 1)
Let x(u) be the second derivative of -u**4/54 + 2*u**3/27 - u**2/9 + 2*u. Find n such that x(n) = 0.
1
Suppose 54 = 3*n + 45. Let p(t) be the second derivative of 0 + n*t - 1/2*t**5 - 1/15*t**6 - 7/3*t**3 - 3/2*t**4 - 2*t**2. Factor p(b).
-2*(b + 1)**3*(b + 2)
Let u = 1/76 + 73/228. Factor 1/3*j**5 - j + 2/3*j**3 + j**4 - 2/3*j**2 - u.
(j - 1)*(j + 1)**4/3
Suppose 2*s - s - 3 = 0. Factor -4*b + 3*b**2 - 4*b**2 + s - 1 + 3*b**2.
2*(b - 1)**2
Factor 185*b - 507*b + 226*b - 36*b**2 - 4*b**3 - 64.
-4*(b + 1)*(b + 4)**2
Let t = 19 + -16. Let d(f) be the first derivative of 1 + 1/8*f**4 - 1/6*f**t + 1/2*f - 1/4*f**2. Factor d(q).
(q - 1)**2*(q + 1)/2
Let s(k) = k + 7. Let g be s(-7). Let j(b) be the third derivative of 0*b**3 + 1/300*b**5 + 0*b + 0*b**4 + 1/120*b**6 + 2/525*b**7 + g - 4*b**2. Factor j(m).
m**2*(m + 1)*(4*m + 1)/5
Let j(m) be the second derivative of -1/84*m**4 - 2*m - 1/210*m**5 + 0 + m**2 + 0*m**3. Let z(o) be the first derivative of j(o). Factor z(r).
-2*r*(r + 1)/7
Determine l, given that -2 + 4*l**2 - 5 + 11*l + 4 = 0.
-3, 1/4
Suppose 0*f + 8 = 2*q + f, -4*q + 4 = 5*f. Let r(n) be the second derivative of 1/18*n**3 + 1/90*n**q - 1/60*n**5 + n - 1/36*n**4 + 0 + 0*n**2. Factor r(p).
p*(p - 1)**2*(p + 1)/3
Let a(h) be the third derivative of -h**8/168 + h**7/70 + h**6/60 - h**5/15 + h**3/6 + h**2. Factor a(x).
-(x - 1)**3*(x + 1)*(2*x + 1)
Let h be (-22)/(-8) + 3/12. Suppose -h*i - 3*w - 9 = -4*i, 0 = 4*i - 3*w - 9. Factor 2/5*k**4 - 2/5*k**2 + 0 + 0*k**3 + i*k.
2*k**2*(k - 1)*(k + 1)/5
Let x = -25 - -21. Let m be 7/(245/x)*-10. Solve 0 + 2/7*p - m*p**2 = 0 for p.
0, 1/4
Let t(p) = p**2 - 7*p - 15. Let z be t(9). Suppose -5*n + i = -21, z*n + 2*n = 2*i + 22. Solve -4/7 - 2*b**3 - 6/7*b**2 + 2*b + 10/7*b**n = 0.
-1, 2/5, 1
Factor -4*t**3 + 3*t - 2*t + 3*t**3.
-t*(t - 1)*(t + 1)
Let b(o) = 2*o**2 + 2*o - 1. Let w(m) = 2*m**2 + 2*m. Let j(v) = 4*b(v) - 3*w(v). Suppose j(k) = 0. What is k?
-2, 1
Factor 0*a + 0 - 1/4*a**3 + 3/4*a**