hird derivative of -d**9/1008 + d**7/140 - d**5/40 - d**3/3 + 4*d**2. Let o(f) be the first derivative of j(f). Factor o(p).
-3*p*(p - 1)**2*(p + 1)**2
Suppose 0 = -6*g - 3*b + 3, -3*g + b - 1 = -10. Solve -3*o - 7/4*o**5 - 9/4*o**4 + 19/4*o**3 - 1 + 13/4*o**g = 0.
-2, -1, -2/7, 1
Let w(d) be the third derivative of -1/21*d**3 + 1/84*d**4 + 0*d + 1/210*d**5 - 1/420*d**6 - d**2 + 0. Factor w(j).
-2*(j - 1)**2*(j + 1)/7
Let d(u) be the second derivative of u**4/78 - 4*u**3/39 + 4*u**2/13 + 5*u. Factor d(h).
2*(h - 2)**2/13
Factor 0 - 2/3*r**3 - 2*r - 8/3*r**2.
-2*r*(r + 1)*(r + 3)/3
Let y(c) be the third derivative of -1/630*c**7 + 0*c + 0 - 3*c**2 + 0*c**4 - 1/18*c**3 + 1/90*c**5 + 0*c**6. Solve y(a) = 0.
-1, 1
Factor -3*s - 7 - s**2 - 6*s**2 + 10*s**2 + 4 + 3*s**3.
3*(s - 1)*(s + 1)**2
Let z = 13 - 7. Let m(h) be the third derivative of 0*h + 1/420*h**7 + 0*h**4 + 0 + 0*h**3 + 1/240*h**z + 2*h**2 + 0*h**5. Factor m(y).
y**3*(y + 1)/2
Let j = 13 - 8. Find n, given that 103*n - 103*n - n**3 + 2*n**4 + n**j - 2*n**2 = 0.
-2, -1, 0, 1
Let a = -415/3 - -139. Suppose 7/3*k**2 - 7/3*k**4 - 5/3*k**5 + a*k + k**3 + 0 = 0. What is k?
-1, -2/5, 0, 1
Suppose -2*z**3 + 7*z**2 + z**2 + 4 - 2*z - 8*z = 0. What is z?
1, 2
Let q(z) = 2*z**3 - 4*z**2 - 30*z + 3. Let y be q(-3). Factor -3/4*d**y - 36*d + 48 + 9*d**2.
-3*(d - 4)**3/4
Let u(x) be the second derivative of x**5/10 - x**3/3 + 8*x. Determine b so that u(b) = 0.
-1, 0, 1
Suppose 9 - 3 = 3*q. Suppose -2*w**q - 12*w - w**2 + 2*w**2 - 18 - w**2 = 0. Calculate w.
-3
Let l(g) = g**4 - g**3 - 8*g**2 + 6*g. Let y(p) = p**4 - p**3 - 7*p**2 + 5*p. Let r(k) = 5*l(k) - 6*y(k). Factor r(v).
-v**2*(v - 2)*(v + 1)
Let c(y) be the first derivative of -2*y + 1/80*y**5 + 1/48*y**4 - 1 + 0*y**2 + 0*y**3. Let n(j) be the first derivative of c(j). Suppose n(s) = 0. Calculate s.
-1, 0
Let c = -10 + 14. Find m, given that 12*m**3 - 23*m**4 - 25*m**c + 18*m**5 + 24*m**5 + 3*m**5 = 0.
0, 2/5, 2/3
Let l(h) = 7*h**5 - 5*h**4 - 6*h**3 + 9*h**2 + 5. Let m(w) = -6*w**5 + 4*w**4 + 6*w**3 - 8*w**2 - 4. Let r(y) = 4*l(y) + 5*m(y). What is d in r(d) = 0?
-2, 0, 1
Let s(n) be the first derivative of -1/7*n**2 + 0*n + 1 - 2/21*n**3. Factor s(p).
-2*p*(p + 1)/7
Let q = 16 - 1. Let f = 17 - q. Let -1/4*m + 1/4 - 3/2*m**f = 0. What is m?
-1/2, 1/3
Let c(o) be the second derivative of o**5/30 - o**3/3 - o**2 - 2*o. Let z(t) be the first derivative of c(t). Find s, given that z(s) = 0.
-1, 1
Let f(c) = -2*c**5 - 12*c**4 + 2*c**3 + 16*c**2 + 2. Let r(u) = 3*u**5 + 24*u**4 - 5*u**3 - 32*u**2 - 5. Let b(n) = 5*f(n) + 2*r(n). Factor b(y).
-4*y**2*(y - 1)*(y + 2)**2
Let y(k) be the second derivative of k**6/80 + k**5/20 + k**4/16 - 2*k**2 - 3*k. Let s(t) be the first derivative of y(t). Find h such that s(h) = 0.
-1, 0
Factor 0*b**2 + 1/4*b - 1/4*b**3 + 1/8*b**4 - 1/8.
(b - 1)**3*(b + 1)/8
Let d(j) be the first derivative of 0*j**2 + 10 + 2/45*j**5 + 1/18*j**4 + 0*j**3 + 0*j. Factor d(v).
2*v**3*(v + 1)/9
Let k = 0 + 3. Factor 2*y**k - 10 + 10 + 3*y**4 - 5*y**5.
-y**3*(y - 1)*(5*y + 2)
Let w(g) be the first derivative of -1 - 1/8*g**4 + 1/2*g**3 + 0*g**2 - 2*g. Factor w(h).
-(h - 2)**2*(h + 1)/2
Let d(q) be the third derivative of -q**7/210 + q**6/24 + 7*q**5/20 + 23*q**4/24 + 4*q**3/3 - 3*q**2. Factor d(g).
-(g - 8)*(g + 1)**3
Let o(p) be the first derivative of 1 + 5*p**3 - 1/2*p**2 - 19/4*p**4 - 2*p + 7/5*p**5. Determine m, given that o(m) = 0.
-2/7, 1
Let g(i) = i**4 + 7*i**3 + 3*i**2 - 7*i - 8. Let m(h) = -h**4 - 1 - 12*h**3 + 7*h**3 + 4*h**3 + h. Let j(a) = g(a) - 2*m(a). Solve j(b) = 0.
-2, -1, 1
Factor 3/4*u - 3/4*u**3 + 0 + 3/4*u**4 - 3/4*u**2.
3*u*(u - 1)**2*(u + 1)/4
Let n be (-2)/7 + 250/140. Factor -7/2*u + n*u**2 + 1.
(u - 2)*(3*u - 1)/2
Let k be 0/(-4*2/(-8)). Factor 5 + k - 2*x - 1 + 0*x - 2*x**2.
-2*(x - 1)*(x + 2)
Let l(i) = 15*i**4 + 33*i**3 - 129*i**2 + 33*i + 48. Let b(j) = j**4 + 2*j**3 - 8*j**2 + 2*j + 3. Let p = 5 - 7. Let m(o) = p*l(o) + 33*b(o). Factor m(q).
3*(q - 1)**2*(q + 1)**2
Suppose -6/5*i**2 - 3/5*i**5 + 9/5*i**4 - 3/5 + 9/5*i - 6/5*i**3 = 0. Calculate i.
-1, 1
Let m = -1 - -4. Solve 4 - m*y**2 - 4*y**2 - 2*y**5 + 8*y**3 + 3*y**2 - 6*y = 0.
-2, -1, 1
Let a(y) be the first derivative of -y**5/25 + 3*y**4/20 - 2*y**3/15 + 7. What is k in a(k) = 0?
0, 1, 2
Let l(p) be the first derivative of -p**4/16 - p**3/6 - p**2/8 + 13. Factor l(r).
-r*(r + 1)**2/4
Let v(j) be the second derivative of j**7/147 - 2*j**6/105 + j**4/21 - j**3/21 - 9*j. Determine q, given that v(q) = 0.
-1, 0, 1
Let f = 143 + -569/4. Solve -3/4*p**2 + 3/4 - 3/4*p + f*p**3 = 0.
-1, 1
Let h(c) be the third derivative of c**9/241920 + c**8/40320 + c**7/20160 - c**5/30 - 2*c**2. Let m(p) be the third derivative of h(p). Factor m(l).
l*(l + 1)**2/4
Suppose -s + 3*s - 3*r - 21 = 0, -4*s + 47 = -r. Solve -s*l**2 - 4*l**3 - 8 - 16*l - 1/2*l**4 = 0.
-2
Let i(l) = l**3 - 12*l**2 + 4. Let f be i(12). Let h be f/14 + 36/21. Factor 1/4*s**h - 1/4 + 0*s.
(s - 1)*(s + 1)/4
Let q = 46 - 229/5. Let i(s) be the first derivative of 1 + 0*s**3 + s + s**2 - q*s**5 - 1/2*s**4. Factor i(r).
-(r - 1)*(r + 1)**3
Let c be (1/15)/((-256)/(-400)). Let r(x) be the third derivative of x**2 + 0*x + 0 - 1/30*x**5 + c*x**4 - 1/12*x**3. Factor r(d).
-(d - 1)*(4*d - 1)/2
Let y(z) be the second derivative of -z**7/420 - z**6/240 + z**5/120 + z**4/48 - z**2 + z. Let l(i) be the first derivative of y(i). Factor l(a).
-a*(a - 1)*(a + 1)**2/2
Let w = 308003/21 + -14663. Let c = w + -22/7. Let -c*z + z**2 + 0 = 0. Calculate z.
0, 2/3
Suppose 4*m = -2*y + 132, -2*m + 45 = 3*y - 133. Suppose -j - y = -5*j. Factor -4 - 14*p + j*p + 3*p**2 - p**3.
-(p - 2)**2*(p + 1)
Let l(q) be the third derivative of -3*q**7/280 + 7*q**5/120 - q**4/12 - q**3/6 + 2*q**2. Let y(d) be the first derivative of l(d). Solve y(o) = 0.
-1, 1/3, 2/3
Let g = -6 + 15. Let i be (-1)/3*(0 - g). Let 0 + 4/13*w**2 - 2/13*w + 2/13*w**5 - 4/13*w**4 + 0*w**i = 0. What is w?
-1, 0, 1
Let x(m) be the first derivative of -4 - 4/3*m**3 + 2/5*m**5 + m**6 + 2*m + 3*m**2 - 3*m**4. Let x(v) = 0. What is v?
-1, -1/3, 1
Let n = -4 - -4. Solve 3*i**2 - i**3 - i**4 + i + n*i**3 - 2*i**2 = 0 for i.
-1, 0, 1
Factor 4*v**4 - 12*v**3 - 7*v**3 + 11*v**3 + v**5 - 16*v**2 + v**5.
2*v**2*(v - 2)*(v + 2)**2
What is x in -5*x**3 + 6*x + 10*x**3 - 7*x**3 - 2 - 2 = 0?
-2, 1
Find y, given that 7/2*y**4 + 3/2*y**3 - 5/2*y**5 + y + 0 - 7/2*y**2 = 0.
-1, 0, 2/5, 1
Suppose -3*n + 7*t + 6 = 5*t, -4*n = 2*t + 6. Factor -1/2*d**3 + n*d**2 + 2*d + 0.
-d*(d - 2)*(d + 2)/2
Let g(v) be the second derivative of 0*v**3 + 6*v**2 + 0 - 3*v - 1/4*v**4. Factor g(p).
-3*(p - 2)*(p + 2)
Let o be (-4)/(12/3) + 3. Let g(k) = -17*k**3 + 17*k**2 + 7*k. Let q(w) = 4*w**3 - 4*w**2 - 2*w. Let t(a) = o*g(a) + 9*q(a). Factor t(z).
2*z*(z - 2)*(z + 1)
Factor 0*y**2 - 1/3*y**3 + 0*y**4 + 0 + 1/3*y**5 + 0*y.
y**3*(y - 1)*(y + 1)/3
Suppose -4*j = -2*t + 38, 4*t - 2*t = -5*j - 7. Determine o, given that t*o**5 + o**2 + 13*o**3 + 0*o**5 + o**2 + 20*o**4 = 0.
-1, -2/9, 0
Find p such that -2/13*p**4 + 4/13*p**2 + 2/13*p**5 - 4/13*p**3 + 2/13*p - 2/13 = 0.
-1, 1
Let f(a) be the first derivative of 5*a**6/18 + 7*a**5/15 + a**4/6 - 13. Factor f(l).
l**3*(l + 1)*(5*l + 2)/3
Let h(y) = -2*y**3 + 5*y**2 - y - 2. Let s be h(2). Factor 1/4*l + 0*l**3 + 1/2*l**2 - 1/4*l**5 - 1/2*l**4 + s.
-l*(l - 1)*(l + 1)**3/4
Let d be (1/(-6))/((-7)/28)*6. Let y(o) be the second derivative of 3/40*o**5 + 0 + 3/8*o**d + 1/2*o**3 + 0*o**2 - 3*o. Factor y(q).
3*q*(q + 1)*(q + 2)/2
Find z such that -2/5*z**5 + 0 + 2/5*z**3 + 0*z - 2/5*z**2 + 2/5*z**4 = 0.
-1, 0, 1
Let p(q) be the third derivative of q**8/90720 - q**7/11340 + q**6/3240 + q**5/15 - q**2. Let y(f) be the third derivative of p(f). Find a, given that y(a) = 0.
1
Let b(i) be the first derivative of 0*i + 0*i**3 + 0*i**2 + 3 - 1/18*i**4. Factor b(s).
-2*s**3/9
Let s(t) = 25*t**3 + 41*t**2 + 17*t - 15. Let x(p) = -3*p**3 - 5*p**2 - 2*p + 2. Let g(q) = 6*s(q) + 51*x(q). Suppose g(m) = 0. What is m?
-2, 1
Let n(r) be the second derivative of -r**7/21 + r**5/5 - r**3/3 - 19*r. Suppose n(l) = 0. What is l?
-1, 0, 1
Let t be (-4)/(-8) - 2/(-12). Let o(y) be the first derivative of -t*y**3 + 0*y - 1/8*y**4 - 1 - y**2. Factor o(c).
-c*(c + 2)**2/2
Let n(z)