u(v) be the third derivative of v**6/340 + 2*v**5/255 + v**4/204 - 8*v**2. Factor u(x).
2*x*(x + 1)*(3*x + 1)/17
Suppose -5*h = -3*w - 2, -2*w - 3 = -w - 4*h. Let q(z) = z**2 - z + 1. Let g(p) = 3*p**3 - 15*p**2 + 12*p - 9. Let a(l) = w*g(l) + 9*q(l). Factor a(d).
3*d*(d - 1)**2
Suppose -2*d = -4*d + 4. Factor 4*w + w**d - 3*w**2 + 2*w**3 - 4*w.
2*w**2*(w - 1)
Let v(t) = 10*t**4 - 36*t**3 + 54*t**2 + 94*t - 6. Let w(h) = 9*h**4 - 36*h**3 + 55*h**2 + 95*h - 5. Let x(b) = -5*v(b) + 6*w(b). Find p such that x(p) = 0.
-1, 0, 5
Let g = 0 - 5. Let o = -5 - g. Solve 2*a**4 + o*a + 0 - 1/2*a**3 - 3/2*a**5 + 0*a**2 = 0.
0, 1/3, 1
Let w(c) be the second derivative of c**4/42 + 4*c**3/21 + 3*c**2/7 + 5*c. Find l such that w(l) = 0.
-3, -1
Let c be 25/(-100) - 9/(-20). Let -c*b**3 + 2/5 + 0*b**2 + 3/5*b = 0. Calculate b.
-1, 2
Let f = 1/68 - -31/204. Let q(t) be the third derivative of -1/60*t**5 + 0*t + 0*t**4 + 0 + 4*t**2 + f*t**3. What is s in q(s) = 0?
-1, 1
Let d = 6 - 10. Let v(k) = 57*k**2 - 48*k + 24. Let w(l) = -7*l**2 + 6*l - 3. Let z(x) = d*v(x) - 33*w(x). Solve z(t) = 0.
1
Suppose a + w + 3*w = -1, 0 = 5*a - w - 16. Suppose v + 2*v = 6. Suppose -7*u**2 + 2*u**v + a*u**2 - 2*u = 0. What is u?
-1, 0
Let d = 38 + -36. Let w(l) be the second derivative of -1/45*l**6 - 1/3*l**4 - 3*l - 1/3*l**d + 0 - 2/15*l**5 - 4/9*l**3. Find q, given that w(q) = 0.
-1
Let o = 3 - 10. Let f(m) = -11*m**4 - 15*m**3 + 7*m**2 + 15*m + 11. Let c(h) = -5*h**4 - 7*h**3 + 3*h**2 + 7*h + 5. Let x(a) = o*c(a) + 3*f(a). Factor x(n).
2*(n - 1)*(n + 1)**3
Let n(s) be the third derivative of -s**7/1260 + s**6/360 + s**4/12 + 3*s**2. Let a(l) be the second derivative of n(l). Factor a(o).
-2*o*(o - 1)
Solve 4/3 - 2/3*p + 2/3*p**3 - 4/3*p**2 = 0 for p.
-1, 1, 2
Suppose 6 = d + 3. Let g(u) be the first derivative of -3 - 4/5*u - 1/15*u**d - 2/5*u**2. Factor g(q).
-(q + 2)**2/5
Let i be ((-24)/(-4))/(1 - (-1 + 0)). Suppose 12 - 33*j**4 - 15/2*j**5 - 69/2*j**i + 21*j**2 + 42*j = 0. What is j?
-2, -1, -2/5, 1
Let o be 2*-2 + (5 - -3). Suppose 4*b + 8 = b - 4*m, -o*b + 11 = m. Suppose 1/2*y**3 - 1/2*y + 1/4*y**b + 0*y**2 - 1/4 = 0. Calculate y.
-1, 1
Let d(m) be the third derivative of m**7/210 + m**6/120 - m**5/60 - m**4/24 - 9*m**2. Find k, given that d(k) = 0.
-1, 0, 1
Let p be 0 - -2 - 141/(-47). Let u(s) be the third derivative of -1/20*s**p + 0*s - 1/12*s**4 + 3*s**2 + 0 + 1/6*s**3. Factor u(t).
-(t + 1)*(3*t - 1)
Let b be 8/(-6)*(160 - -2). Let k be 114/b - (-3)/4. Find q such that 2/9 + k*q**2 + 4/9*q = 0.
-1
Let d(c) be the third derivative of 0*c**4 + 0*c**6 + 0*c + 0*c**5 + 0*c**3 + 0 + 1/420*c**7 + 2*c**2. Solve d(i) = 0 for i.
0
Let i(o) be the second derivative of -o**6/210 + o**5/140 + o**4/28 - o**3/42 - o**2/7 - 2*o - 10. Find f such that i(f) = 0.
-1, 1, 2
Let c(m) be the first derivative of -m**6/1620 - m**5/135 - m**4/27 + 2*m**3/3 - 2. Let z(h) be the third derivative of c(h). Factor z(i).
-2*(i + 2)**2/9
Suppose -2*r = t + 3, -1 = -r - t - 4. Let p(v) be the third derivative of -1/12*v**4 - 3*v**2 + r - 1/40*v**5 - 1/12*v**3 + 0*v. Find k, given that p(k) = 0.
-1, -1/3
Let y(o) = -4*o**2 + 11*o. Let n(h) = -h. Let a(z) = 5*z - 1. Let c(r) = a(r) + 6*n(r). Let g(s) = 2*c(s) + y(s). Factor g(l).
-(l - 2)*(4*l - 1)
Let r(z) = 4*z**5 + 5*z**4 + 3*z**3 - 3*z**2 + 5. Let b(x) = x**5 + x**4 - x**2 + 1. Let k(f) = 15*b(f) - 3*r(f). Factor k(l).
3*l**2*(l - 2)*(l + 1)**2
Solve -10*m**4 - 7*m**4 + 2*m**5 - 24*m**2 + 5*m**4 + 4*m + 26*m**3 + 4*m = 0.
0, 1, 2
Factor 2/3 + 0*w**4 + 4/3*w**3 - 2/3*w**2 - 1/3*w**5 - w.
-(w - 1)**3*(w + 1)*(w + 2)/3
Let v(k) be the second derivative of -k**4/4 - k**3/2 + 9*k**2 - 6*k. Factor v(h).
-3*(h - 2)*(h + 3)
Let c = -119519/120 + 996. Let z(q) be the third derivative of 1/24*q**4 - 1/12*q**3 + 0*q - 2*q**2 - c*q**5 + 0. Factor z(m).
-(m - 1)**2/2
Let j(p) be the first derivative of 3/4*p**4 + 0*p**2 + 6/5*p**5 + 0*p**3 + 0*p + 1/2*p**6 + 1. What is n in j(n) = 0?
-1, 0
Let b = 5 - 3. Factor 0*h - 3*h**b + 4*h**2 + h.
h*(h + 1)
Let t(c) be the third derivative of -c**7/1050 + c**6/150 - c**5/60 + c**4/60 - 35*c**2. Factor t(y).
-y*(y - 2)*(y - 1)**2/5
Let y(p) be the third derivative of p**6/1020 + 2*p**5/255 - p**4/204 - 4*p**3/51 + 40*p**2. Factor y(k).
2*(k - 1)*(k + 1)*(k + 4)/17
Factor -1/3*z**5 + 0*z**3 + 0*z**2 + 0 - 1/3*z**4 + 0*z.
-z**4*(z + 1)/3
Let f(o) be the second derivative of o**7/2940 - o**5/420 - 5*o**3/6 - 5*o. Let m(w) be the second derivative of f(w). Determine z, given that m(z) = 0.
-1, 0, 1
Let q(s) = -2*s**4 + 3*s**3 + 5*s**2 + 3*s - 3. Let g(n) = 2*n**4 - 2*n**3 - 4*n**2 - 2*n + 2. Let t(k) = 3*g(k) + 2*q(k). Find y such that t(y) = 0.
-1, 0, 1
Suppose 7*i = i - i. Let g(s) be the second derivative of -1/4*s**3 + 1/16*s**4 + i + 3/8*s**2 + 2*s. Let g(a) = 0. Calculate a.
1
Let l(a) = -4*a**2 + 12*a + 14. Let i(s) = -s**2 + s - 1. Let k(q) = 2*i(q) + l(q). Suppose k(g) = 0. Calculate g.
-2/3, 3
Suppose 2*f = 5*m + f + 2, 5*m - 3*f = -6. Determine k so that 0*k**3 - 2/9*k**2 + 2/9*k**4 + 0*k + m = 0.
-1, 0, 1
Let k(y) be the third derivative of y**5/60 + 5*y**4/24 + y**3 - 18*y**2. Factor k(f).
(f + 2)*(f + 3)
Let h = 8 + -5. Suppose 3*x = -h*c + 30, 2*x + 4*c = -c + 29. Solve -1 + 15*z**4 + 9*z**4 + 10*z**5 - 23*z**2 - 9*z + 6*z**5 - x*z**3 = 0.
-1, -1/4, 1
Let q = -22 - -22. Factor q*k - 1/2*k**2 + 1/2.
-(k - 1)*(k + 1)/2
Solve 0 + 7/4*s**5 - 11/4*s**3 - 3*s**4 + 3*s**2 + s = 0.
-1, -2/7, 0, 1, 2
Let q(v) be the third derivative of v**8/10080 - v**5/15 - 4*v**2. Let m(c) be the third derivative of q(c). Solve m(x) = 0.
0
Suppose 2 = 2*m, -2*x + 5*m + 2 + 1 = 0. Factor 168/5*l**3 + 686/5*l**5 - 16/5*l**2 + 0 - 588/5*l**x + 0*l.
2*l**2*(7*l - 2)**3/5
Let n(k) = 5*k**4 - 16*k**3 + 4*k - 5. Let o(p) = 5*p**4 - 15*p**3 + 5*p - 5. Let q(v) = 5*n(v) - 6*o(v). Find t such that q(t) = 0.
-1, 1
Let w(n) = -3*n**2 + 2. Let f(y) = -10*y**2 + 7. Let v(t) = -t**2 + 5*t - 2. Let p be v(4). Suppose -p*m + m + 14 = 0. Let x(l) = m*w(l) - 4*f(l). Factor x(g).
-2*g**2
Suppose 4*z + 10 = -2*c, 3*z - 3*c = 4*z + 15. Let q = -30 + 33. What is t in -6/11*t**4 - 2/11*t**2 + 10/11*t**q + z - 2/11*t = 0?
-1/3, 0, 1
Suppose 6*w**3 + w + 5/2*w**4 + 0 + 9/2*w**2 = 0. What is w?
-1, -2/5, 0
Let k = 9 - 7. Suppose 2*y - 8 = -2*y. Factor -3*p**2 + 0*p**y - 2*p**3 + k*p + 3*p**4 + 0*p**2.
p*(p - 1)*(p + 1)*(3*p - 2)
Let i = 2/417 - -824/2085. Let i*m - 1/5 - 1/5*m**2 = 0. Calculate m.
1
Let u(p) be the second derivative of p**10/10080 - p**9/3024 + p**8/6720 + p**7/2520 + p**4/4 - 6*p. Let d(h) be the third derivative of u(h). Solve d(f) = 0.
-1/3, 0, 1
Let r(o) = o**3 + 5*o**2 - 9*o - 14. Let c be r(-6). Factor 2*t**4 - 3*t + t - t**2 - c*t**4 + 3*t**2 + 2*t**3.
-2*t*(t - 1)**2*(t + 1)
Let r(x) = 5*x**2 + 13*x + 20. Let v(i) = -4*i**2 - 12*i - 18. Let q(f) = 5*r(f) + 6*v(f). Factor q(u).
(u - 8)*(u + 1)
Let c = -1 - -1. Suppose -v - 3*p + 2 = c, 0 = 4*v - 0*p - 2*p - 8. Factor i - i**3 + 0*i**v + 0*i**2.
-i*(i - 1)*(i + 1)
Let h(v) = -20*v**3 - 8*v**2 - 9*v + 20. Let d(m) be the first derivative of -7*m**4/4 - m**3 - 3*m**2/2 + 7*m + 1. Let p(x) = 17*d(x) - 6*h(x). Factor p(q).
(q - 1)**3
Let 0 - 3/4*t**5 - 39/4*t**3 - 9*t**2 - 3*t - 9/2*t**4 = 0. What is t?
-2, -1, 0
Suppose 6*w = 5*w + 5. Suppose -2*r = -3*r - w*j - 17, -r = -5*j - 23. Solve 0*i**2 + 3/4*i**4 + 1/2*i**r + 0*i + 0 = 0 for i.
-2/3, 0
Let k = 58/3 - 77/4. Let d(x) be the third derivative of 0 + 1/12*x**3 + 1/60*x**6 + k*x**4 + 1/420*x**7 + 0*x + 1/20*x**5 + 2*x**2. Factor d(m).
(m + 1)**4/2
Let l(r) be the second derivative of r**6/30 + r**5/20 - r**4/12 - r**3/6 - 9*r. Factor l(j).
j*(j - 1)*(j + 1)**2
Let k(j) be the third derivative of j**5/180 - j**4/72 + 28*j**2. Find t such that k(t) = 0.
0, 1
Let x(v) = 20*v**4 - 24*v**3 + 20*v**2 - 16*v. Let a(l) = -l**4 + l**3 - l**2 + l. Let r(b) = 16*a(b) + x(b). Factor r(j).
4*j**2*(j - 1)**2
Let r(b) be the second derivative of b**4/3 - 16*b**3/3 + 32*b**2 - 7*b. Factor r(c).
4*(c - 4)**2
Let d(g) be the third derivative of 0*g**4 + 0*g - 1/420*g**6 - 4/21*g**3 - 3*g**2 + 1/70*g**5 + 0. Find y such that d(y) = 0.
-1, 2
Let g(p) be the third derivative of 1/12*p**4 + 0*p**3 + 0*p + 0 + 1/60*p**5 - 2*p**2. Suppose g(w) = 0. What