r**3 - 4*r**5.
-2*r*(r + 1)**3*(3*r + 1)
Let o(p) be the third derivative of 0 + 0*p + 3/40*p**6 + 2/3*p**3 + 5*p**2 - 1/3*p**4 - 1/20*p**5. Factor o(n).
(n + 1)*(3*n - 2)**2
Let 64/5*d + 127/5*d**3 + 9/5*d**5 - 12/5 - 57/5*d**4 - 131/5*d**2 = 0. Calculate d.
2/3, 1, 3
Let c(p) be the first derivative of -9*p - 21/2*p**2 + 5 - 5*p**3 - 3/4*p**4. Factor c(z).
-3*(z + 1)**2*(z + 3)
Let f(j) be the second derivative of -j**9/75600 + j**7/12600 - j**4/6 - 2*j. Let b(a) be the third derivative of f(a). Factor b(k).
-k**2*(k - 1)*(k + 1)/5
Let r(q) = -q**4 + q**2 + q + 1. Let n(w) = -6*w**3 - 2*w**2 + 6*w - 2. Let m(a) = n(a) + 2*r(a). Factor m(z).
-2*z*(z - 1)*(z + 2)**2
Let c(k) be the first derivative of 0*k**2 + 2 - 1/6*k**3 + 1/16*k**4 + 0*k. Factor c(m).
m**2*(m - 2)/4
Let p(u) be the second derivative of -u**7/126 + u**6/90 + u**5/20 - u**4/36 - u**3/9 + 22*u. Solve p(z) = 0 for z.
-1, 0, 1, 2
Let m(k) be the second derivative of -1/90*k**5 + 0 - 2/27*k**3 + 0*k**2 - 1/18*k**4 + 5*k. Factor m(u).
-2*u*(u + 1)*(u + 2)/9
Solve 2/9*i**5 + 16/9*i**3 - 10/9*i**4 + 0 - 8/9*i**2 + 0*i = 0.
0, 1, 2
Let m(y) = -29*y + y**2 + 0 + 12*y - 1 + 16*y. Let l(v) = 5 + 5*v - v**2 - 1 - v**2. Let b(h) = -l(h) - 3*m(h). Suppose b(q) = 0. What is q?
-1
Let m(s) be the third derivative of s**5/100 + s**4/20 - 3*s**3/10 - 13*s**2. Factor m(h).
3*(h - 1)*(h + 3)/5
Let o be ((-1)/5)/(-2 - (-56)/40). Factor o*z + 1/6*z**2 + 1/6.
(z + 1)**2/6
Suppose f - 5*g - 15 = 0, 1 + 2 = -4*f - g. Let -3*a**5 + 0*a**3 + f*a**5 + 3*a**3 = 0. Calculate a.
-1, 0, 1
Let w(q) be the second derivative of 0 - 1/15*q**6 + 0*q**3 - 1/35*q**7 - 1/25*q**5 + 0*q**4 + 0*q**2 - 3*q. Factor w(i).
-2*i**3*(i + 1)*(3*i + 2)/5
Let i(d) be the second derivative of 2197*d**5/4 - 2535*d**4/2 + 1170*d**3 - 540*d**2 + 44*d. Let i(b) = 0. What is b?
6/13
Suppose 3*l - 33*l**3 + 25*l**4 - 96*l**3 - 88*l**4 + 9*l = 0. Calculate l.
-2, -1/3, 0, 2/7
Suppose 3*k = 3*l - 6, -5*k + 0 = -4*l + 8. Let o = k - -3. Factor 0 + 4 + o*z - z**3 - 2.
-(z - 2)*(z + 1)**2
Let f(n) = -n - 10. Let y be f(0). Let t = -9 - y. Factor -1 + 3*m**2 - 6*m + t + 3*m.
3*m*(m - 1)
Suppose 9*b - b = 0. Find v such that 2/5*v**3 + b*v**2 + 0*v + 0 = 0.
0
Let l = 1/392 + 2339/5096. Suppose 0*h + 2/13*h**2 + 2/13*h**5 + l*h**3 + 0 + 6/13*h**4 = 0. What is h?
-1, 0
Suppose -n + 6 = 2*n. Determine q, given that q**3 + 6*q**2 - 6*q**n = 0.
0
Let i be ((4 + -3)/1)/(5/15). Suppose 0*z**2 - 1/3*z + 1/3*z**i + 0 = 0. Calculate z.
-1, 0, 1
Let x be (-2 + 1)*-2 + (-4)/(-2). Let k be (-1 - (-14)/6)*3. Factor 24*q**3 - k + 25*q**5 - 45*q**x + 1 - 4*q**2 + 3.
q**2*(q - 1)*(5*q - 2)**2
Let q(u) = u**2 - 7*u. Let v(c) = 6*c. Let b(a) = -4*q(a) - 6*v(a). Find x, given that b(x) = 0.
-2, 0
Let h(m) = m + 8. Let g be h(-7). Suppose 0 = -c + g + 1. Factor 22*s**4 - 2*s**4 - 14*s**5 + 12*s**4 - 22*s**3 + 4*s**c.
-2*s**2*(s - 1)**2*(7*s - 2)
Let m = 2 - 0. Suppose 4 = 2*x - 4. Factor m*g**3 + 10*g + x*g + 2*g - 8 - 10*g**2.
2*(g - 2)**2*(g - 1)
Let z = 3 - 3. Let 2*f + f - 2*f**2 + z*f - 7*f - 2 = 0. Calculate f.
-1
Let d(p) be the second derivative of p**5/80 - 11*p**4/48 + 35*p**3/24 - 25*p**2/8 + 3*p. Determine i so that d(i) = 0.
1, 5
Let v(n) = 4*n**3 - 9*n**2 + 2. Let d(z) = 9*z**3 - 19*z**2 + z + 4. Let a(r) = 3*d(r) - 5*v(r). Factor a(h).
(h - 1)**2*(7*h + 2)
Suppose -2*p - 3*b - 15 = 2*b, 4*p = 2*b + 6. Suppose p*o**4 + o**2 - 2*o**3 - 2*o**4 - 2*o**2 + o**4 = 0. Calculate o.
-1, 0
Suppose -2*b = 3*a - 10, -2*b + 4 = a + 2. Find y such that 0*y**2 + 0*y**2 + a*y - 4*y**3 + 2 + 32*y**4 - 34*y**4 = 0.
-1, 1
Let -88/3*y**2 - 16/3 - 3*y**4 - 64/3*y - 16*y**3 = 0. Calculate y.
-2, -2/3
Let l(w) be the first derivative of -w**7/3780 - w**6/810 + 4*w**3/3 + 4. Let c(f) be the third derivative of l(f). Factor c(k).
-2*k**2*(k + 2)/9
Determine t, given that 16/7*t**2 + 12/7*t + 0 = 0.
-3/4, 0
Solve 41 + 12*t**3 - 2*t**4 + t**3 - 18*t**2 + 67 - 54*t + t**3 = 0 for t.
-2, 3
Suppose 0 = -31*b + 32*b. Let y(v) be the second derivative of 1/40*v**5 + 0*v**2 + b + 3*v - 1/24*v**4 + 0*v**3. Suppose y(w) = 0. Calculate w.
0, 1
Let k(l) be the third derivative of -l**8/5880 - l**7/980 - l**6/420 - l**5/420 + 2*l**3/3 + l**2. Let j(h) be the first derivative of k(h). Factor j(s).
-2*s*(s + 1)**3/7
Let j(i) be the first derivative of 0*i + 0*i**2 + 0*i**3 - 2 - 1/12*i**4. Suppose j(r) = 0. What is r?
0
Solve -2*a + 4*a**4 + 4 + 0*a**5 + a**2 + 4*a**3 - 2*a**5 - 9*a**2 = 0 for a.
-1, 1, 2
Let j(k) = 5*k**4 - 4*k**3 - 9*k**2 - 6. Let f(b) = -6*b**4 + 4*b**3 + 10*b**2 + 7. Let l(u) = -6*f(u) - 7*j(u). What is z in l(z) = 0?
-3, -1, 0
Solve 1/5*x**3 + 9/5*x + 6/5*x**2 + 0 = 0 for x.
-3, 0
Suppose -4*w**2 + 5*w**2 - 5*w**2 + 0*w**2 - 120*w - 900 = 0. Calculate w.
-15
Let x(y) be the second derivative of y**10/151200 - y**9/75600 - y**8/16800 + y**4/2 - 3*y. Let k(w) be the third derivative of x(w). Factor k(z).
z**3*(z - 2)*(z + 1)/5
Suppose -i - 12 = -5*i. Let 1 - i*g**2 + 4*g**3 + 7*g**2 + g**4 + 4*g + 2*g**2 + 0 = 0. What is g?
-1
Let i(q) be the second derivative of -2/45*q**6 + 0*q**2 - q + 0 - 1/9*q**4 + 1/18*q**3 + 1/10*q**5 + 1/126*q**7. Factor i(d).
d*(d - 1)**4/3
Let o(v) be the second derivative of -175*v**7/9 + 21*v**6 + 272*v**5/15 - 116*v**4/9 - 16*v**3/3 + 16*v**2/3 + 3*v. Let o(d) = 0. Calculate d.
-2/5, 2/7, 1
Let v = 73 - 71. Let o(z) be the second derivative of -1/5*z**2 + 1/15*z**4 + v*z - 1/15*z**3 - 1/105*z**7 - 1/75*z**6 + 0 + 1/25*z**5. Factor o(y).
-2*(y - 1)**2*(y + 1)**3/5
Let d(x) be the second derivative of -1/33*x**4 + 1/110*x**5 + 1/33*x**3 - x + 0*x**2 + 0. Solve d(m) = 0 for m.
0, 1
Let d(q) be the first derivative of 0*q - 10/21*q**3 + 4/35*q**5 + 9/28*q**4 + 1 - 3/14*q**2. Suppose d(s) = 0. What is s?
-3, -1/4, 0, 1
Let p(c) be the second derivative of c**6/1260 - c**5/210 - c**3/6 + 4*c. Let d(u) be the second derivative of p(u). Factor d(o).
2*o*(o - 2)/7
Let l be 46/12 - (-3)/18. Let x = 7 - l. Solve 0*h**3 - 3*h**2 + 4 + h**x + 6*h + 2*h + 8*h**2 = 0 for h.
-2, -1
Let z = 68 + -66. Let x(c) be the first derivative of 6*c**3 - 7/2*c**4 + 2 - z*c**2 + 0*c. Factor x(u).
-2*u*(u - 1)*(7*u - 2)
Let i = 1/4 + 13/4. Let a be (-36)/126 + (-221)/(-14) + -4. Factor a*y**3 + i*y**4 + 1 + 13/2*y + 27/2*y**2.
(y + 1)**3*(7*y + 2)/2
Let y = -5/24 + 73/120. Factor -2/5*s**2 + 4/5 - y*s.
-2*(s - 1)*(s + 2)/5
Let g(y) be the first derivative of -y**5/10 + y**3/3 - 7*y - 8. Let k(t) be the first derivative of g(t). What is z in k(z) = 0?
-1, 0, 1
Find k, given that -3/2*k**2 + 0 + 3/2*k**4 + 9/2*k**3 - 9/2*k = 0.
-3, -1, 0, 1
Let a = 23/1032 + -3/215. Let g(k) be the second derivative of -1/48*k**4 - a*k**6 + 0*k**3 - k + 0 + 0*k**2 + 1/40*k**5. Factor g(m).
-m**2*(m - 1)**2/4
Let f(x) be the second derivative of -x + 1/24*x**4 + 0*x**2 + 0*x**3 + 0. Factor f(c).
c**2/2
Suppose 0 = -3*p + 4*p - 3. Let a be (-4)/(-26) - 36/(-104). What is x in 3*x**2 + x**p - 7/2*x**4 + 3/2*x**5 - 5/2*x + a = 0?
-1, 1/3, 1
Find t such that -6*t**4 - 3*t**3 - 2*t**4 + 6*t**5 - 2*t**5 + 7*t**3 = 0.
0, 1
Let p(a) be the third derivative of 0*a + 0 + 1/15*a**3 + 1/150*a**5 + 2*a**2 + 1/30*a**4. Factor p(x).
2*(x + 1)**2/5
Let h(z) be the first derivative of 5*z**3/3 + 10*z**2 + 15*z + 1. Factor h(w).
5*(w + 1)*(w + 3)
Let z(u) = u**3 + 9*u**2 + 10*u + 10. Let p be z(-8). Let s be (7/35)/(p/(-20)). Factor -j + 0*j**2 + 1/3*j**3 + s.
(j - 1)**2*(j + 2)/3
Suppose 3*s - 1 = -2*s - 3*p, 4*p = -4*s - 4. Factor 0 - 9 + 3 + 12*l**s + 3*l - 8*l**3 - l**3.
-3*(l - 1)**2*(3*l + 2)
Factor 3*f + 0 + 3/4*f**3 + 3*f**2.
3*f*(f + 2)**2/4
Let o(b) = 6*b - 52. Let m be o(9). Suppose 0*i + 2/3*i**m - 2/3 = 0. Calculate i.
-1, 1
Let z(p) be the second derivative of -7/18*p**3 + 1/3*p**2 - 1/18*p**7 + 1/45*p**6 - 3*p + 0 - 1/9*p**4 + 7/30*p**5. Determine x so that z(x) = 0.
-1, 2/7, 1
Let j(c) be the third derivative of 1/6*c**4 - 2*c**2 + 1/30*c**5 + 0 + 1/3*c**3 + 0*c. Factor j(o).
2*(o + 1)**2
Let w be (10/(-6))/(25/(-10)). Let y = 6 - 16/3. Solve -y*q**3 + w*q**5 + 0*q + 0 + 4/3*q**4 - 4/3*q**2 = 0 for q.
-2, -1, 0, 1
Factor 4*g**2 - 72*g + 3*g**2 + 4*g**2 + 324 - 7*g**2.
4*(g - 9)**2
Let m(p) be the third derivative of -p**8/1344 + p**7/420 + p**6/60 + p**5/120 - 7*p**4/96 - p**3/6 - 