derivative of m**8/784 - m**7/490 - m**2/2 + 7. Let f(n) be the second derivative of a(n). Solve f(k) = 0 for k.
0, 1
Let b(w) be the third derivative of w**8/1008 + 2*w**7/315 + w**6/60 + w**5/45 + w**4/72 + 11*w**2. Factor b(n).
n*(n + 1)**4/3
Suppose 10*d**3 - 4*d + 4*d**2 - 4*d**5 - 2*d**3 - 4*d**2 = 0. Calculate d.
-1, 0, 1
Suppose 4*w + 5 = 25. Suppose -w*s + 9*s = 0. Factor 0 + s*m**2 - 1/3*m**3 + 0*m.
-m**3/3
Let n(w) be the second derivative of -w**6/90 + w**5/12 - w**4/4 + 7*w**3/18 - w**2/3 - 5*w. Solve n(v) = 0.
1, 2
Let q(w) be the third derivative of w**8/112 - w**7/35 + w**6/40 + 16*w**2. Let q(h) = 0. Calculate h.
0, 1
Let r(w) be the third derivative of w**6/900 - w**5/50 + 3*w**4/20 - 3*w**3/5 - 29*w**2. Factor r(i).
2*(i - 3)**3/15
Factor -1/3*p - 1/3*p**3 + 2/3*p**2 + 0.
-p*(p - 1)**2/3
Let k(n) = -n**5 + 2*n**4 - n. Let f(q) = q**4 - q**3. Suppose 0 = 3*a - a + 4. Let s(w) = a*k(w) + 4*f(w). Factor s(p).
2*p*(p - 1)**2*(p + 1)**2
Let a(g) be the second derivative of 3/2*g**2 + 1/48*g**4 + 0 + 0*g**3 + 7/240*g**5 - 3*g + 1/96*g**6. Let f(k) be the first derivative of a(k). Factor f(p).
p*(p + 1)*(5*p + 2)/4
Determine v, given that -3/7*v - 3/7*v**2 - 1/7*v**3 - 1/7 = 0.
-1
Solve 8/13*z - 2/13*z**4 - 4/13*z**3 + 6/13*z**2 - 8/13 = 0 for z.
-2, 1
Suppose 4/11*q**2 + 2/11 - 6/11*q = 0. Calculate q.
1/2, 1
Let a = 103 - 58. Suppose q - 6*q + 5*i + a = 0, 25 = -5*i. What is v in -2*v**3 + 8/3*v**q + 0*v - 2/3*v**2 + 0 = 0?
-1/4, 0, 1
Let g be (284/(-320) + 1)/(30/8). Let t(p) be the second derivative of -p - 3/10*p**2 - 3/20*p**4 - g*p**5 + 0 - 3/10*p**3. Factor t(l).
-3*(l + 1)**3/5
Let h = -16 + 26. Suppose h = -4*y + 9*y. Find n, given that -2*n**2 + y*n - 15 + 15 = 0.
0, 1
Solve -1/3*m**2 - m - 2/3 = 0 for m.
-2, -1
Let o(u) be the first derivative of 2/39*u**3 + 2/13*u**2 + 0*u - 3. Factor o(d).
2*d*(d + 2)/13
Let f be 8/44 - (-75)/11. Suppose 0 = -3*j + f*j - 24. Factor -p**5 - 3*p**5 - 2*p**3 - p**5 + j*p**5 + p.
p*(p - 1)**2*(p + 1)**2
Suppose -5*i - 4*m + 74 = 0, 3*i + 5*m + 56 = 5*i. Suppose -5*y - i = -3*n - n, -2*n + 8 = -2*y. Factor -2*b**2 - 2*b**3 + 4*b + 3 - 1 - n*b.
-2*(b - 1)*(b + 1)**2
Let a(p) be the third derivative of p**6/300 - p**5/150 - p**4/12 - p**3/5 - 10*p**2. Factor a(l).
2*(l - 3)*(l + 1)**2/5
Let t(w) = 7*w**4 - 7*w**3 - w**2 + 7*w + 9. Let g(i) = 4*i**4 - 4*i**3 + 4*i + 5. Let q(y) = -5*g(y) + 3*t(y). Solve q(b) = 0 for b.
-1, 1, 2
Let d = -16 - -9. Let b(z) = -8*z**3 + z**2 + 2*z - 7. Let a(n) = 8*n**3 - 2*n + 6. Let l(v) = d*a(v) - 6*b(v). Factor l(u).
-2*u*(u + 1)*(4*u - 1)
Let b(c) be the third derivative of -3*c**5/20 - 25*c**4/24 + c**3 + 12*c**2. Solve b(l) = 0.
-3, 2/9
Factor -14*g**3 - g + 0 + 15/2*g**2.
-g*(4*g - 1)*(7*g - 2)/2
Let w = 151 - 452/3. Factor -l**2 - 1/3*l**3 - l - w.
-(l + 1)**3/3
Suppose -2/5 + 11/5*y - 13/5*y**2 + 4/5*y**3 = 0. Calculate y.
1/4, 1, 2
Let k be (-1)/(-2 - 15/(-9)). Let z(o) = -o + 7. Let v be z(k). Factor -2*i + 1 + 4*i + 5*i**2 - v*i**2.
(i + 1)**2
Suppose 26*v + 9*v = 0. Factor 0*c - 1/6*c**5 + v*c**3 + 0*c**4 + 0 + 0*c**2.
-c**5/6
Let b = -85/4 + 275/12. What is q in 16/3*q - 17/3*q**2 - 4/3 + b*q**3 = 0?
2/5, 1, 2
Let m = -15 + 33. Let g be (-60)/m*(-1)/15. Factor 8/9 + g*n**2 - 8/9*n.
2*(n - 2)**2/9
Let h(y) = -y**3 + 3*y**2 - 2*y - 3. Let k(n) = -3*n**3 + 9*n**2 - 6*n - 8. Let i(u) = -8*h(u) + 3*k(u). Factor i(l).
-l*(l - 2)*(l - 1)
Let z = -91 - -95. Factor 0*p**2 + 3/5*p**z + 3/5*p**5 + 0 + 0*p + 0*p**3.
3*p**4*(p + 1)/5
Factor -1/5*i**2 - 121/5 + 22/5*i.
-(i - 11)**2/5
Let o(u) be the third derivative of -u**8/13440 + u**6/1440 + u**4/8 - 2*u**2. Let d(g) be the second derivative of o(g). Factor d(c).
-c*(c - 1)*(c + 1)/2
Let y(n) be the second derivative of n**5/160 - n**3/48 + 22*n - 2. Factor y(z).
z*(z - 1)*(z + 1)/8
Suppose -2/15*i**4 - 8/15*i**3 + 8/15*i - 2/5*i**2 + 8/15 = 0. Calculate i.
-2, -1, 1
Factor -2*l - 55*l**4 - 3*l**3 + 5*l**2 + 1 - 1 + 54*l**4 + l**5.
l*(l - 1)**3*(l + 2)
Let u(y) = -6*y**2 - 9*y + 9. Let a(t) = -t**2 - 2*t + 2. Let j(m) = -33*a(m) + 6*u(m). Suppose j(k) = 0. What is k?
2
Factor 65 - 65 + 4*t**3 - 2*t**3 - 4*t**2.
2*t**2*(t - 2)
Suppose 4*d = 2*r - 5*r - 9, 2*d = 0. Let i be 1/r + (-6 - -7). Determine h, given that 0 + 0*h**2 - 2/3*h**5 - 4/3*h**4 + 0*h - i*h**3 = 0.
-1, 0
Determine v so that -3*v**2 - 36*v**3 - 2*v**2 + 31*v**3 = 0.
-1, 0
Factor 4/7*r**4 - 2/7*r**5 - 4/7*r**2 + 2/7*r + 0 + 0*r**3.
-2*r*(r - 1)**3*(r + 1)/7
Factor -42*j + 39/2*j**2 + 6.
3*(j - 2)*(13*j - 2)/2
Let d(a) be the second derivative of -a**6/15 + a**5/5 + 7*a**4/6 + 4*a**3/3 - 6*a. Solve d(x) = 0 for x.
-1, 0, 4
Suppose -1 = -k - 7. Let q be 2/(-3) - 8/k. Let 2/3*u**3 + q*u**2 + 0*u + 0 = 0. Calculate u.
-1, 0
Let z(y) = y**4 - y**2 - y + 1. Let t(s) = s**5 + 12*s**4 + 7*s**3 - 4*s**2 - 7*s + 7. Let m(i) = 4*t(i) - 28*z(i). Factor m(d).
4*d**2*(d + 1)**2*(d + 3)
Let j be (-1 - (-4)/8)*-18. Solve 14 + j*k**2 - 7 - 6*k - 3*k**4 - 7 = 0 for k.
-2, 0, 1
Let b be (3 - 19)/(8/(-68)). Let r be b/264 - 4/22. Determine w so that -2/3 + 5/3*w + r*w**4 - 1/3*w**3 - w**2 = 0.
-2, 1
Let y(w) be the second derivative of w**7/280 - w**6/160 - 3*w**5/80 + w**4/32 + w**3/4 + w**2 - 4*w. Let a(i) be the first derivative of y(i). Factor a(b).
3*(b - 2)*(b - 1)*(b + 1)**2/4
Factor -1/5*h**2 - 2/5*h - 1/5.
-(h + 1)**2/5
Let n(o) be the second derivative of 2*o**7/3 + 32*o**6/15 + 4*o**5/5 - 14*o**4/3 - 22*o**3/3 - 4*o**2 - 8*o. What is t in n(t) = 0?
-1, -2/7, 1
Suppose -14 + 20 = 5*q - l, 0 = -q - 4*l + 18. Factor -1/2*f**3 + 0 - 3/2*f**q - f.
-f*(f + 1)*(f + 2)/2
Let t be (54/(-72))/(6/(-16)). Let z(l) be the third derivative of 0*l**3 - 2*l**t - 1/240*l**5 + 1/96*l**4 + 0 + 0*l. Find s such that z(s) = 0.
0, 1
Let m(r) be the third derivative of -r**8/13440 - r**7/3360 - r**5/15 + r**2. Let u(j) be the third derivative of m(j). Suppose u(s) = 0. Calculate s.
-1, 0
Suppose 2*w = 5*n + w - 11, 2*n = 2*w + 6. Let y be (36/(-8) - -3)*-2. Determine a, given that 0 + 2/3*a**n - 2/3*a**y + 4/3*a = 0.
-1, 0, 2
Suppose 4*z = 5*t - 2*t + 1101, 2*z - 5*t = 561. Find a, given that -3*a + 81*a**3 - z*a**3 - a**2 + 13*a**2 + 36*a**2 = 0.
0, 1/8
Let q(j) be the third derivative of -j**6/160 + 3*j**5/160 - 3*j**2. Factor q(s).
-3*s**2*(2*s - 3)/8
Let n = 3 - 1. Let w(x) be the second derivative of x + 1/4*x**3 - 1/24*x**4 + 0 - 1/2*x**n. Factor w(o).
-(o - 2)*(o - 1)/2
Let g(s) = s + 7. Let j be g(-5). Let a(f) be the third derivative of 0*f**3 - 1/540*f**6 + f**j + 0 + 0*f**4 + 0*f - 1/270*f**5. Factor a(c).
-2*c**2*(c + 1)/9
Let l(z) = z + 5. Let r be l(0). Let g be 20/(-2)*(-2)/r. Factor 2/7*p**g + 0*p**2 - 4/7*p**3 - 2/7 + 4/7*p.
2*(p - 1)**3*(p + 1)/7
Factor -9/5*h**2 + 0 + 12/5*h - 3/5*h**3.
-3*h*(h - 1)*(h + 4)/5
Factor 9*m + 99*m**2 - 12 + 3*m - 102*m**2.
-3*(m - 2)**2
Let h = 19 - -3. Let s(q) = -16*q**2 + 11*q - 6. Let l(t) = -3*t**2 + 3 - 2*t - 2 + 6*t**2. Let k(v) = h*l(v) + 4*s(v). Factor k(n).
2*(n - 1)*(n + 1)
Let q(p) be the third derivative of -p**6/180 - p**5/15 + 7*p**4/36 - 6*p**2. Suppose q(h) = 0. Calculate h.
-7, 0, 1
Let n(s) = -s**2 + s + 6. Let u be n(-2). Let w(k) = k**2 + k. Let h be w(u). Determine o, given that -1/4*o**4 + 0 + h*o**2 - 1/4*o**3 + 0*o = 0.
-1, 0
Factor 34*y**2 + 2 - 47*y**2 + 28*y**2 - 11*y.
(3*y - 1)*(5*y - 2)
Suppose 4*a + u = a + 12, -5*a + 3*u + 6 = 0. Determine m, given that 16/5 - 12/5*m**2 + 8/5*m - 2*m**a - 2/5*m**4 = 0.
-2, 1
Let n(p) be the second derivative of 0*p**2 + 0 - 1/12*p**4 + p - 1/3*p**3. What is y in n(y) = 0?
-2, 0
Let k(g) be the third derivative of g**7/1680 + g**6/720 - g**5/120 - 2*g**3/3 + 4*g**2. Let a(f) be the first derivative of k(f). Factor a(n).
n*(n - 1)*(n + 2)/2
Let a(v) be the second derivative of v**7/14 - 3*v**5/20 - 8*v. Factor a(t).
3*t**3*(t - 1)*(t + 1)
Let q(d) be the first derivative of d**5/5 + d**4 + 5*d**3/3 + d**2 + 1. Factor q(y).
y*(y + 1)**2*(y + 2)
Let k(y) be the first derivative of -y**8/2520 + y**7/630 - y**6/540 + y**3 + 4. Let h(m) be the third derivative of k(m). Determine j, given that h(j) = 0.
0, 1
Let r(q) be the second derivative of -q**6/10 + q**4/4 + 15*q. Factor r(j).
-3*j**2*(j - 1)*(j + 1)
Suppose -1 = d - 5. Let v(l) = -3*l - 10. Let w be v(-4). Fac