- 1)/4
Suppose z = 6*z + 35. Let v be -1 + (-3 - 30/z). Suppose -2/7*k**2 + 2/7*k**4 + 0 + 2/7*k**3 + 0*k - v*k**5 = 0. Calculate k.
-1, 0, 1
Let g(v) be the third derivative of 2*v**7/21 + 13*v**6/30 - 2*v**5/5 - 10*v**4/3 + 16*v**3/3 + 9*v**2. Factor g(w).
4*(w - 1)*(w + 2)**2*(5*w - 2)
Factor 0 - 18/13*s**4 + 24/13*s - 80/13*s**2 + 6*s**3.
-2*s*(s - 3)*(3*s - 2)**2/13
Let r(k) be the first derivative of -k**7/252 + k**6/180 + k**5/120 - k**4/72 + 7*k + 5. Let o(f) be the first derivative of r(f). Factor o(u).
-u**2*(u - 1)**2*(u + 1)/6
Let l(j) be the first derivative of -j**4/2 + 3*j**2 - 4*j - 9. Solve l(p) = 0 for p.
-2, 1
Let q(b) be the first derivative of -1/6*b**4 + 1/3*b + 1/6*b**2 + 1/15*b**5 - 3 + 1/18*b**6 - 2/9*b**3. Factor q(g).
(g - 1)**2*(g + 1)**3/3
Suppose 12/5 - 16/5*f**3 + 56/5*f + 28/5*f**2 = 0. Calculate f.
-1, -1/4, 3
Determine i so that 79 - 79 + 6*i**3 - 2*i + 2*i**4 - 2*i**2 - 2*i**5 - 2*i = 0.
-1, 0, 1, 2
Let b = 0 + 3. Solve -6*u**b - 5*u**3 + 7*u**3 + 2*u**5 + 2*u = 0.
-1, 0, 1
Let g(z) be the second derivative of 0 + 2/21*z**3 - 1/84*z**4 + z - z**2 - 1/210*z**5. Let c(v) be the first derivative of g(v). Let c(p) = 0. Calculate p.
-2, 1
Let g(t) be the second derivative of -1/4*t**2 + 0 + 1/6*t**3 - 3*t - 1/24*t**4. Suppose g(k) = 0. What is k?
1
Let f = 8 - 6. Suppose -f*y + 3 + 1 = 0. Determine h so that -4*h**4 + 3*h**y - 2*h**3 - h**2 - h**2 + 5*h**4 = 0.
0, 1
Factor 0*f**2 + 0 - 12/5*f**3 + 3/5*f.
-3*f*(2*f - 1)*(2*f + 1)/5
Let r(q) be the third derivative of -1/240*q**5 + 0*q**4 - 1/6*q**3 + 0 + 1/360*q**6 + 0*q - 2*q**2. Let g(z) be the first derivative of r(z). Factor g(p).
p*(2*p - 1)/2
Let a(t) be the third derivative of 0*t**4 + 0*t + 0 + 1/300*t**6 - 1/840*t**8 + 1/150*t**5 - 1/525*t**7 + 2*t**2 + 0*t**3. Factor a(c).
-2*c**2*(c - 1)*(c + 1)**2/5
Suppose 3*d - 2 = -3*x + 4, -4*d - 2*x + 14 = 0. Solve 5*a**d - 9 - 4*a**5 + 5*a**2 - 3*a**3 - a**4 + 9 - 2*a = 0.
-2, 0, 1
Let v(i) be the second derivative of -4*i**7/21 + 2*i**6/45 + 2*i**5/15 + 37*i. Factor v(w).
-4*w**3*(2*w + 1)*(3*w - 2)/3
Determine v so that 3/4 - 16*v**3 + 52*v**2 - 49/4*v = 0.
1/8, 3
Let u(z) be the second derivative of z**8/3360 + z**7/1680 - z**6/720 - z**5/240 + z**3/2 + 2*z. Let g(l) be the second derivative of u(l). Factor g(r).
r*(r - 1)*(r + 1)**2/2
Let f(c) be the third derivative of -c**11/83160 + c**9/15120 - c**5/6 - 5*c**2. Let b(i) be the third derivative of f(i). Find k such that b(k) = 0.
-1, 0, 1
Let q(p) be the third derivative of p**6/720 + p**5/60 + p**4/12 + p**3/3 + p**2. Let l(w) be the first derivative of q(w). Let l(g) = 0. What is g?
-2
Solve -16/5*z - 72/5*z**2 + 74/5*z**4 - 12/5*z**3 - 24/5*z**5 + 0 = 0.
-2/3, -1/4, 0, 2
Let j(d) be the third derivative of -d**8/1680 + d**7/252 - d**6/90 + d**5/60 + d**4/24 - 2*d**2. Let v(r) be the second derivative of j(r). Factor v(s).
-2*(s - 1)**2*(2*s - 1)
Let l(d) = 3*d**2 - 1. Suppose -5*k - 6 = -1. Let c be l(k). Find n, given that n - 4*n**3 + 2*n - n + c*n**5 = 0.
-1, 0, 1
Let w(u) be the third derivative of -u**8/1680 - u**7/840 + u**3/6 - u**2. Let h(v) be the first derivative of w(v). Factor h(x).
-x**3*(x + 1)
Suppose -a = -5*a + 12. Suppose -x + a = -0. Factor -1/3*b**x - 1/3*b**2 + 1/3 + 1/3*b.
-(b - 1)*(b + 1)**2/3
Factor -1/2*b**3 - 5/2*b**2 - 2 - 4*b.
-(b + 1)*(b + 2)**2/2
Let f(y) = 9*y**3 + y**2 - 5*y + 5. Let m(z) = -4*z**3 + 2*z - 2. Let o(d) = -2*f(d) - 5*m(d). Suppose o(h) = 0. What is h?
0, 1
Let u(j) be the third derivative of j**7/10 + 9*j**6/40 - j**5/4 - 9*j**4/8 - j**3 + 2*j**2. Factor u(p).
3*(p - 1)*(p + 1)**2*(7*p + 2)
Let a = -4 - -4. Suppose -n - 2*n + 6 = a. Factor 1 - 1 + 4*f + n*f**2.
2*f*(f + 2)
Factor 3/2 - 5/4*g + 1/4*g**2.
(g - 3)*(g - 2)/4
Let o(x) be the second derivative of -x**10/30240 - x**9/7560 + x**7/1260 + x**6/720 + x**4/12 + 3*x. Let p(m) be the third derivative of o(m). Factor p(g).
-g*(g - 1)*(g + 1)**3
Let s = -21 + 23. Let x(i) be the first derivative of 0*i + 4/21*i**3 + 1/2*i**4 + 0*i**2 - s + 2/7*i**5. Factor x(r).
2*r**2*(r + 1)*(5*r + 2)/7
Let y(x) be the third derivative of -x**9/5040 + x**7/280 - x**6/120 - x**4/6 - x**2. Let v(t) be the second derivative of y(t). Factor v(l).
-3*l*(l - 1)**2*(l + 2)
Let l(n) be the second derivative of -1/3*n**3 + 1/10*n**5 + n**2 - 3*n - 1/6*n**4 + 0. Find x, given that l(x) = 0.
-1, 1
Let j(i) = 176*i**3 - 19*i**2 + 11*i. Let p(q) = 35*q**3 - 4*q**2 + 2*q. Let a(w) = 2*j(w) - 11*p(w). Factor a(h).
-3*h**2*(11*h - 2)
Let h(q) be the third derivative of -q**8/112 - 3*q**7/70 - 3*q**6/40 - q**5/20 - 2*q**2. Let h(j) = 0. What is j?
-1, 0
Let p be (-369)/(-180) + 2*-1. Let u(q) be the second derivative of -3*q + 0 + 0*q**3 + p*q**5 + 1/60*q**6 + 0*q**2 + 1/24*q**4. Determine x so that u(x) = 0.
-1, 0
Let o(p) = -16*p**3 + 16*p. Let r(d) = -3*d**3 + 3*d. Let h(q) = 5*o(q) - 28*r(q). Suppose h(z) = 0. What is z?
-1, 0, 1
Let k(g) be the third derivative of g**7/3360 - 7*g**3/6 + 5*g**2. Let n(i) be the first derivative of k(i). Suppose n(d) = 0. Calculate d.
0
Let a(j) be the second derivative of -j**6/120 - j**5/30 - j**4/24 + 2*j**2 - 2*j. Let m(w) be the first derivative of a(w). Factor m(p).
-p*(p + 1)**2
Let j(k) be the first derivative of k**4/3 - 2*k**2/3 + 11. Suppose j(n) = 0. Calculate n.
-1, 0, 1
Let m(l) be the second derivative of 0*l**3 + 2/3*l**4 + 0*l**2 + 1/5*l**5 + 0 + 5*l - 2/15*l**6. Suppose m(c) = 0. What is c?
-1, 0, 2
Solve 0*l + 0 - 1/3*l**2 + 5/9*l**3 = 0.
0, 3/5
Let x(z) be the first derivative of z**4/14 + 2*z**3/21 - z**2/7 - 2*z/7 + 24. Determine v so that x(v) = 0.
-1, 1
Let k(p) = p**3 + 5*p**2 + 3*p - 4. Let z be k(-2). Let w(x) be the second derivative of 0 - 49/10*x**5 + x + 8*x**3 + 4*x**z + 7/2*x**4. Solve w(i) = 0 for i.
-2/7, 1
Let g(h) = h + 10. Let m be g(-6). Find f such that 0 + 1/2*f**5 + f**m - f**2 - 1/2*f + 0*f**3 = 0.
-1, 0, 1
Let y(r) = r**2 + 24*r - 50. Let f be y(-26). Solve -2/7*o**f + 6/7*o + 0 = 0 for o.
0, 3
Let u(v) be the second derivative of v**6/165 + 4*v**5/55 + 23*v**4/66 + 28*v**3/33 + 12*v**2/11 - v + 4. Suppose u(n) = 0. Calculate n.
-3, -2, -1
Let g(r) be the first derivative of -12*r - 21*r**3 + 3 - 3/2*r**4 + 30*r**2 + 21/5*r**5. Factor g(n).
3*(n - 1)**2*(n + 2)*(7*n - 2)
Let s(t) be the first derivative of 11/16*t**4 + 7/24*t**6 - 4/5*t**5 - 6 - 1/6*t**3 + 0*t**2 + 0*t. Factor s(o).
o**2*(o - 1)**2*(7*o - 2)/4
Let i(f) = -5*f**5 + f**4 - 3*f**3 - 5*f**2 - 4*f + 4. Let x(w) = -w**5 - w**3 - w**2 - w + 1. Let h(c) = -3*i(c) + 12*x(c). Factor h(v).
3*v**2*(v - 1)**2*(v + 1)
Let l(n) be the first derivative of -n**9/1008 - n**8/280 - n**7/280 - 4*n**3/3 + 1. Let g(y) be the third derivative of l(y). Factor g(k).
-3*k**3*(k + 1)**2
Let b(p) be the second derivative of p**7/23940 + p**6/3420 - 2*p**4/3 + 10*p. Let o(r) be the third derivative of b(r). Factor o(f).
2*f*(f + 2)/19
Let y(o) be the first derivative of 16/5*o**5 - 6 - 2/3*o**6 - 2*o**2 + 16/3*o**3 - 6*o**4 + 0*o. Find c such that y(c) = 0.
0, 1
Let b(m) be the first derivative of -m**7/210 + m**6/120 - m**2 + 1. Let d(j) be the second derivative of b(j). Suppose d(g) = 0. Calculate g.
0, 1
Let c = 53/98 + -2/49. Let r = 59/2 + -29. Factor c*l**2 - l + r.
(l - 1)**2/2
Let z be 6 + (0 - 3/3). Determine r, given that -r**z + 3*r**5 - r**4 + r**3 + r**2 - 3*r**3 = 0.
-1, 0, 1/2, 1
Let f(z) = 16*z**3 + 10*z**2 - 16*z - 10. Let m(u) = 3*u - 2*u - u**3 - 2 + 3 - u**2. Let w(k) = -f(k) - 6*m(k). Determine n so that w(n) = 0.
-1, -2/5, 1
Let d(w) = -w - 7. Let m be d(-9). Factor -2*l**3 + 2*l**2 - 4*l**2 - m*l**4 + l**4 + 3*l**4 + 2*l**5.
2*l**2*(l - 1)*(l + 1)**2
Let o(u) be the second derivative of u**5/40 - u**4/8 + u**3/6 + 4*u. Find b, given that o(b) = 0.
0, 1, 2
What is n in 19*n - 6*n**2 + 4*n**2 + n - 4*n - 32 = 0?
4
Let u be 8/28 - (-1728)/(-70). Let i = -24 - u. Factor 2/5*d**2 - i + 2/5*d - 2/5*d**3.
-2*(d - 1)**2*(d + 1)/5
Let o(c) be the first derivative of -5*c**3/3 - 25*c**2/2 + 35. Suppose o(m) = 0. What is m?
-5, 0
Suppose -3*q + 8*q + 2*n - 138 = 0, 0 = -q - n + 30. Let h = 53/2 - q. Factor -h*a + 0 + 1/2*a**2.
a*(a - 1)/2
Suppose 3*l = 2*l - 11. Let c(p) = -p**3 - 11*p**2 - p - 9. Let b be c(l). Let 1/3 - 2/3*d**b - 1/3*d = 0. What is d?
