 2)*(3*z - 2)
Let d(t) be the first derivative of -t**6/180 - t**5/60 + 15*t**3 - 12. Let a(k) be the third derivative of d(k). Factor a(x).
-2*x*(x + 1)
Let p(h) = 12*h**2 - 12*h - 24. Let d(n) = -4*n**2 + 4*n + 8. Suppose -5*b + 4*f = 5, -5*f + 6 + 19 = 0. Let u(k) = b*p(k) + 10*d(k). Factor u(s).
-4*(s - 2)*(s + 1)
Let r(u) be the third derivative of -15*u**2 - 7/24*u**4 - 1/60*u**6 + 1/336*u**8 + 0*u + 0 + 1/3*u**3 - 1/105*u**7 + 2/15*u**5. Factor r(d).
(d - 1)**4*(d + 2)
Let r(q) be the first derivative of -q**3 + 8 + 3*q**2 - 3/4*q**4 + 0*q. Determine v so that r(v) = 0.
-2, 0, 1
Let u = 141/8 + -135/8. Let d = -3554 + 14231/4. What is y in -u*y**5 - 3/4 - d*y - 15/2*y**2 - 15/4*y**4 - 15/2*y**3 = 0?
-1
Let c be 1 + 546/133 + (-14)/133. Suppose 3 + 6 = 3*u. Factor 2/9*x**c + 0*x + 0 - 2/9*x**2 - 2/9*x**u + 2/9*x**4.
2*x**2*(x - 1)*(x + 1)**2/9
Let k(v) be the first derivative of -2*v**3/21 + v**2/7 + 12*v/7 + 42. Factor k(r).
-2*(r - 3)*(r + 2)/7
Let u(d) = -3*d**3 - 7*d**2 - 9*d. Let h(j) = 2*j**3 + 6*j**2 + 10*j. Let w be (-34)/6 - (-36)/(-27). Let a(n) = w*h(n) - 6*u(n). Factor a(r).
4*r*(r - 2)*(r + 2)
Let p be -4 - -66 - (2 - (0 + 0)). Let b be p/90 + -25*(-4)/66. What is h in -8/11 + 12/11*h**3 - 2/11*h**4 + b*h - 26/11*h**2 = 0?
1, 2
Let f(o) be the third derivative of 0 + 1/15*o**4 - 4*o**2 + 1/100*o**5 - 1/1050*o**7 + 0*o - 1/300*o**6 + 2/15*o**3. Suppose f(n) = 0. Calculate n.
-2, -1, 2
Let a(i) be the second derivative of i**7/3360 - i**6/720 + i**5/480 - i**3 + 6*i. Let b(z) be the second derivative of a(z). Factor b(g).
g*(g - 1)**2/4
Let c(i) be the first derivative of -i**6/24 - 21*i**5/20 - 99*i**4/16 + 121*i**3/12 - 159. Suppose c(t) = 0. Calculate t.
-11, 0, 1
Suppose -68*y**2 - 30 - 12*y**4 - 244*y**3 + 68 + 113*y + 42 - 40*y + 171*y = 0. Calculate y.
-20, -1, -1/3, 1
Let o(k) = -k**3 - k**2. Let c(n) = n**5 - 2*n**4 + 7*n**3 + 17*n**2 - 7*n + 2. Let y(s) = -4*c(s) - 36*o(s). Suppose y(l) = 0. Calculate l.
-2, 1
Suppose -8*u + 4 = -6*u. Suppose 0 = 3*a + 9, -u*a + a - 11 = -4*t. Let 2/3*w**t + 0*w**3 + 0*w + 0 - 2/3*w**4 = 0. What is w?
-1, 0, 1
Let a = -33/188 - -20/47. Suppose a - 1/2*o**3 - 3/4*o**4 + 1/2*o**2 - 1/4*o**5 + 3/4*o = 0. What is o?
-1, 1
Find i, given that 162/5 - 2/5*i**2 - 48/5*i = 0.
-27, 3
Let t(z) be the second derivative of -z**7/70 + z**6/45 + z**5/10 - z**4/3 - z**3/3 + 3*z. Let f(p) be the second derivative of t(p). Factor f(m).
-4*(m - 1)*(m + 1)*(3*m - 2)
Let w(m) be the third derivative of -m**7/1050 - 3*m**6/100 - 4*m**5/15 + 3*m**4/20 + 27*m**3/10 + 116*m**2 + 1. Solve w(z) = 0 for z.
-9, -1, 1
Let y be (0 + 1)*39/((-156)/(-20)). Factor -5/2*u**4 - 5*u**3 - 1/2*u**5 - 1/2 - 5/2*u - y*u**2.
-(u + 1)**5/2
Factor 32/5 + 2/5*y**3 + 36/5*y**2 + 66/5*y.
2*(y + 1)**2*(y + 16)/5
Let a be (5 + (-2 - -1))*((-1407)/140)/(-67). Find x, given that 0 + 3/5*x**2 + a*x = 0.
-1, 0
Let q(b) be the second derivative of 1/18*b**3 + 6*b + 0 + 0*b**2 + 1/252*b**7 - 1/36*b**6 + 3/40*b**5 - 7/72*b**4. Factor q(x).
x*(x - 2)*(x - 1)**3/6
Let l(n) = n**3 - 5*n**2 - 6*n + 3. Let p be l(6). Determine t so that -2*t**2 + 2*t**4 + 4*t - 19*t**3 + 2*t**5 + 0*t**5 + 13*t**p = 0.
-2, -1, 0, 1
Let t(p) be the third derivative of p**8/336 - p**7/42 + 7*p**6/120 + p**5/60 - p**4/3 + 2*p**3/3 - p**2 - 18*p. Factor t(b).
(b - 2)**2*(b - 1)**2*(b + 1)
Solve -16/5 - 12/5*j + 4/5*j**2 = 0 for j.
-1, 4
Factor -5*c**4 + 17*c**2 + 104*c**5 + 10*c + 21*c**3 - 18*c**3 - 105*c**5.
-c*(c - 2)*(c + 1)**2*(c + 5)
Let o(d) be the third derivative of 7/6*d**4 + 0*d + 8/15*d**5 - 1/84*d**8 - 4/105*d**7 + 1/15*d**6 + 25*d**2 + 4/3*d**3 + 0. Determine s, given that o(s) = 0.
-1, 2
Let l(i) be the third derivative of -i**5/30 - i**4/4 + 4*i**3/3 - 144*i**2 - i. Factor l(x).
-2*(x - 1)*(x + 4)
Let l(u) = u**3 - 2*u**2 - 7*u + 6. Let o be l(4). Factor -o*a + 4*a**2 - 1 - 14 + a**2.
5*(a - 3)*(a + 1)
Let 4/3*q - 2/3*q**2 + 2/3*q**4 - 4/3*q**3 + 0 = 0. Calculate q.
-1, 0, 1, 2
Suppose -2*x - 3*x + 37 = 3*f, x - 4*f + 11 = 0. Factor -4*t - 4*t**2 + x*t + 7*t - 4.
-4*(t - 1)**2
Let k(s) = -s**3 + s. Let t(f) = 3*f**2 + 3*f**3 + f**2 + 2 - 9*f**3. Let w(i) = 5*k(i) - t(i). Factor w(p).
(p - 2)*(p - 1)**2
Let q(g) be the first derivative of -2*g**3/9 + 7*g**2/3 - 4*g - 105. Factor q(d).
-2*(d - 6)*(d - 1)/3
Let g(a) be the second derivative of -a**4/84 - a**3/42 + 3*a**2/7 + 90*a. Factor g(y).
-(y - 2)*(y + 3)/7
Let g = -46/229 - -1054/687. Solve g*d**4 - 40/3*d - 8*d**3 + 16*d**2 + 4 = 0.
1, 3
Let i = -9 + 41. Suppose -2*k - i*k**2 + 57*k**2 - 23*k**2 = 0. Calculate k.
0, 1
Let x = -49 + 57. Suppose -2*z = 0, -4*l + 3*z = -0*z - x. Solve 1/4*f**3 + 0 + 1/2*f**l + 1/4*f = 0 for f.
-1, 0
Let c = 44/139 - -197/695. Let c + 3/5*l - 3/5*l**3 - 3/5*l**2 = 0. Calculate l.
-1, 1
Let y(q) be the first derivative of -1/26*q**4 + 25 + 14/39*q**3 - 16/13*q**2 + 24/13*q. What is g in y(g) = 0?
2, 3
Let m(f) be the first derivative of -f**6/3 + 38*f**5/5 - 49*f**4/2 + 26*f**3/3 + 50*f**2 - 64*f - 276. Suppose m(s) = 0. What is s?
-1, 1, 2, 16
Suppose -25*i = 11 - 11. Let m(b) be the first derivative of 0*b**5 + 0*b + 0*b**3 + 4 + i*b**2 - 1/10*b**6 + 3/20*b**4. Factor m(k).
-3*k**3*(k - 1)*(k + 1)/5
Let w = -21 - -14. Let b = w + 9. Factor -4*k**b + 6 + 6 - k + 0 - 7*k.
-4*(k - 1)*(k + 3)
Let s(i) = 2*i + 2. Let b be s(8). Let r be 27/b + (-2)/(-4). Suppose -3 - 25*j**2 + 13*j**3 + 21*j - 8*j**2 + r*j**3 = 0. What is j?
1/5, 1
Let y = 503 + -12071/24. Let j(b) be the second derivative of -5/48*b**4 - 7/80*b**5 + 0*b**2 - 2*b - 1/40*b**6 + 0 - y*b**3. Factor j(o).
-o*(o + 1)**2*(3*o + 1)/4
Suppose 0 = -4*q + 4*i + 15716, 4*q - 4598 = 3*i + 11120. Suppose 2*s**2 + q*s - 3931*s = 0. What is s?
0
Let s(n) = -3*n**2 + 102*n - 870. Let i(r) = -3*r**2 + 102*r - 869. Let x(b) = 3*i(b) - 2*s(b). Solve x(o) = 0 for o.
17
Factor -5*j**2 + 2258*j + 2558*j + 260 - 5071*j.
-5*(j - 1)*(j + 52)
Factor -16*g - 68*g - 4*g**2 - 1184 + 1104.
-4*(g + 1)*(g + 20)
Suppose 2*x - 3 = 5*x. Let w = x + 7. Factor w*p**3 - 4*p**5 - p**5 + 2*p**5 - 3*p.
-3*p*(p - 1)**2*(p + 1)**2
Let w(l) be the second derivative of 9/10*l**5 + 0*l**2 + 0*l**4 - 5*l + 0*l**3 + 0 - 1/15*l**6. Factor w(y).
-2*y**3*(y - 9)
Factor 10/3*c**2 - 4/3*c - 4/3*c**3 + 0.
-2*c*(c - 2)*(2*c - 1)/3
Let r(q) = 4*q + 6. Let u be r(0). Let b(v) = 4*v**3 + 3*v**2 + 9*v - 3. Let y(z) = -23*z**3 - 19*z**2 - 54*z + 17. Let x(d) = u*y(d) + 34*b(d). Factor x(j).
-2*j*(j + 3)**2
Let o(x) be the first derivative of -x**5/270 + 7*x**4/108 - 22*x**2 - 23. Let c(j) be the second derivative of o(j). Factor c(s).
-2*s*(s - 7)/9
Let b = -917/94140 - -8/523. Let h(j) be the third derivative of 0*j + 7/180*j**4 + b*j**6 + 0 + 1/50*j**5 + 1/1575*j**7 + 2/45*j**3 - 3*j**2. Factor h(q).
2*(q + 1)**3*(q + 2)/15
Let l = -202337/55 + 3679. Let k(m) be the first derivative of -8/33*m**3 - 1/11*m**4 + 1/11*m**6 + 0*m + l*m**5 - 11 - 1/11*m**2. Let k(w) = 0. What is w?
-1, -1/3, 0, 1
Let y(q) be the third derivative of 18/11*q**3 - 4*q**2 + 0*q - 1/165*q**7 + 45/44*q**4 + 0 + 61/660*q**6 - 57/110*q**5. Solve y(v) = 0.
-2/7, 3
Let t = 1178/805 - 4/115. Let w = 157/21 + -19/3. Factor 16/7*d + t*d**2 - w.
2*(d + 2)*(5*d - 2)/7
Let b(h) be the second derivative of h**7/1260 - 3*h**6/200 + h**5/30 - 13*h**4/4 - 29*h. Let d(s) be the third derivative of b(s). Solve d(t) = 0.
2/5, 5
Let a = 3 - -3. Factor -6*w**4 - 20*w + 4 - 3*w**3 + a*w + 18*w**2 + 8*w**4 - 7*w**3.
2*(w - 2)*(w - 1)**3
Suppose 6*m**2 + 0*m**2 + 152 + 8*m**2 + 156*m - 10*m**2 = 0. Calculate m.
-38, -1
Let i(f) be the first derivative of f**5/5 - f**4/2 - f**3 - 52. Factor i(x).
x**2*(x - 3)*(x + 1)
Let i(t) be the first derivative of 1/6*t**6 + 0*t - 1/4*t**4 + 4 + 0*t**2 - 1/3*t**3 + 1/5*t**5. Factor i(w).
w**2*(w - 1)*(w + 1)**2
Let m(z) be the second derivative of -z**3 + 1/3*z**6 + 0 - 10*z - 13/10*z**5 + 0*z**2 + 11/6*z**4. Suppose m(d) = 0. What is d?
0, 3/5, 1
Let s = -11 + 14. Let h(x) = 1 + 0 + 6*x**s - 3*x**2 - 3 - 2*x**3 - x**4. Let g(b) = b**3 - b**2 - 1. Let f(z) = 6*g(z) - 3*h(z). Factor f(y).
3*y**2*(y - 1)**2
Let h = -82 + 68. Let o be (12/h)/6*-4. Determine u, given that -18/7*u**4 - o*u**3 + 0 + 4/7*u + 18/7*u**2 = 0.
-1, -2/9, 0, 1
Factor 3*m + 3*m**3 - 3/4*m**4 - 9/2