1/840*a**7. Find r, given that s(r) = 0.
-1, 0, 1
Let o = 109/876 + -3/73. Let q(z) be the third derivative of 0*z + 0*z**3 + 1/105*z**7 - o*z**4 + 0 - 2*z**2 + 1/60*z**6 - 1/30*z**5. Factor q(f).
2*f*(f - 1)*(f + 1)**2
Let c be 5*6/15*20/8. Find i, given that 0 - 1/4*i**2 - 3/4*i**3 + 3/4*i**c + 1/4*i**4 + 0*i = 0.
-1, -1/3, 0, 1
Let n be (6 - -10) + (2 - -2). Let c be (48/n - 4) + 2. Factor 4/5*j + 0 + c*j**2.
2*j*(j + 2)/5
Let n(y) be the third derivative of 1/60*y**4 - 1/75*y**5 + 0*y + 2/15*y**3 - 6*y**2 - 1/300*y**6 + 0. Factor n(z).
-2*(z - 1)*(z + 1)*(z + 2)/5
Let r(s) be the third derivative of 1/30*s**5 - 5*s**2 - 1/36*s**4 + 0 + 0*s**3 + 0*s. Factor r(k).
2*k*(3*k - 1)/3
Let g(u) = 5*u**2 - 1. Let c be g(1). Factor -3*l**4 + 3*l**4 + l**2 - l**c.
-l**2*(l - 1)*(l + 1)
Let h(w) = -w - 18. Let v be h(-22). Let l(r) be the second derivative of -3*r + 0*r**2 - 1/6*r**3 + 1/24*r**v + 0. Determine s so that l(s) = 0.
0, 2
Let z(d) = -2*d**2 + d + 1. Let v(j) = -10*j**2 + 4*j - 6. Let u(o) = 2*v(o) - 12*z(o). Factor u(y).
4*(y - 3)*(y + 2)
Determine l, given that -3*l**5 - 6*l**4 - l**2 + 3*l + l**2 + 4*l**2 + 2*l**2 = 0.
-1, 0, 1
Let a = 28/153 + 2/51. Let m(w) = w - 4. Let u be m(6). Determine r so that -a*r**u + 0 - 2/9*r = 0.
-1, 0
Let p(o) be the first derivative of -o**6/200 - o**2/2 + 3. Let s(t) be the second derivative of p(t). Factor s(i).
-3*i**3/5
Let c(j) = -2*j**2 - 55*j - 75. Let k be c(-26). Factor 2/7*p**k - 2/7*p + 0 + 0*p**2.
2*p*(p - 1)*(p + 1)/7
Let g(j) be the second derivative of -j**4/16 + j**3/8 - 13*j. Find u, given that g(u) = 0.
0, 1
Let a(d) be the second derivative of -d**6/180 - d**5/60 + d**4/6 + d**3/3 + 4*d. Let h(s) be the second derivative of a(s). Factor h(m).
-2*(m - 1)*(m + 2)
Let o(b) be the third derivative of 1/108*b**4 - 1/540*b**6 - 1/90*b**5 + 1/945*b**7 + 0 + 0*b + 2/27*b**3 - 4*b**2. Find a such that o(a) = 0.
-1, 1, 2
Suppose w + 15 = 4*w. Let t(i) be the third derivative of 1/420*i**6 + 0*i + 1/70*i**w + i**2 + 1/21*i**3 + 1/28*i**4 + 0. Factor t(d).
2*(d + 1)**3/7
Let g(b) = -3*b**4 + 3*b**3 + 8*b**2 + 8*b - 8. Let j(n) = 2*n**4 - 2*n**3 - 5*n**2 - 5*n + 5. Let i(z) = -5*g(z) - 8*j(z). Find u, given that i(u) = 0.
0, 1
Let j(o) be the second derivative of -2*o**7/7 - 2*o**6/15 + 11*o**5/5 - o**4 - 16*o**3/3 + 8*o**2 - 9*o. What is p in j(p) = 0?
-2, -1, 2/3, 1
Let h(u) be the second derivative of 1/8*u**4 - 3/4*u**2 + 0 - 3*u - 3/40*u**5 + 1/4*u**3. Factor h(g).
-3*(g - 1)**2*(g + 1)/2
Let z(a) be the second derivative of 3*a**5/40 + 16*a. Factor z(c).
3*c**3/2
Let n(u) = 5*u**3 + u**2 - 31*u - 21. Let j(t) = 5*t**3 + 2*t**2 - 32*t - 22. Let q(l) = 6*j(l) - 7*n(l). Let q(h) = 0. What is h?
-1, 3
Let c(w) be the third derivative of 0 - 1/15*w**3 + 0*w + 0*w**4 + 1/150*w**5 + 5*w**2. Determine i so that c(i) = 0.
-1, 1
Let t(h) be the second derivative of 2/15*h**6 + 7/5*h**5 + 0 - 1/3*h**7 - 7*h - 2/3*h**4 - 7/3*h**3 + 2*h**2. Suppose t(p) = 0. What is p?
-1, 2/7, 1
Let n(c) = 34*c**4 - 204*c**3 + 206*c**2 - 36*c - 14. Let y(d) = -11*d**4 + 68*d**3 - 69*d**2 + 12*d + 5. Let i(m) = 5*n(m) + 14*y(m). Factor i(w).
4*w*(w - 3)*(w - 1)*(4*w - 1)
Let p(o) be the second derivative of o**7/42 + 2*o**6/15 + o**5/20 - 7*o**4/6 - 10*o**3/3 - 4*o**2 + 2*o - 3. Solve p(k) = 0 for k.
-2, -1, 2
Let r(a) be the first derivative of -3 + 0*a**5 - 1/10*a**4 + 1/15*a**6 + 0*a**3 + 0*a + 0*a**2. Determine l, given that r(l) = 0.
-1, 0, 1
Suppose -3*j + 6/5 + 6/5*j**2 = 0. What is j?
1/2, 2
Let k(q) be the first derivative of 4*q**3/3 + 6*q**2 + 8*q + 9. Factor k(g).
4*(g + 1)*(g + 2)
Let j be 5 - 1 - 428752/(-20). Let v = -21368 + j. Factor -192/5*p - 48*p**3 + 32/5 + v*p**2 + 10*p**4.
2*(p - 2)**2*(5*p - 2)**2/5
Let i(p) be the first derivative of 4*p - 1/2*p**3 + 0*p**4 + 1/5*p**5 + 2 - 1/2*p**2. Let g(n) be the first derivative of i(n). Factor g(s).
(s - 1)*(2*s + 1)**2
Let o be 2/12 + (-34)/(-12). Let t = o - -1. Factor -2*m**3 - 5*m**4 + 4*m**4 - t*m**3 + 4*m**3.
-m**3*(m + 2)
Let f = -70 - -141/2. Factor -f - 5/2*o**4 - 5*o**2 - 5*o**3 - 5/2*o - 1/2*o**5.
-(o + 1)**5/2
Let o(r) = 5*r**2 - 11*r - 14. Let c(j) = 2*j**2 - 4*j - 5. Let g(t) = 8*c(t) - 3*o(t). Let h be g(0). Factor 0 + 0*m - 4/3*m**2 - h*m**3.
-2*m**2*(3*m + 2)/3
Let d(q) = 144*q. Let o be d(1). Let s be o/27*(-6)/(-20). Find a, given that s*a + 12/5*a**2 + 2/5 + 2/5*a**4 + 8/5*a**3 = 0.
-1
Suppose -2/3 - 8/9*i - 2/9*i**2 = 0. Calculate i.
-3, -1
Let r = 466/595 + 2/119. Factor -r*l - 2*l**2 + 2/5*l**4 - 6/5*l**3 + 0 + 2/5*l**5.
2*l*(l - 2)*(l + 1)**3/5
Suppose -7*m - 4 = -3*m. Let u be m/(1*3/(-9)). What is t in 7 - 7 + 6*t**u - 6*t**4 - 2*t**2 + 2*t**5 = 0?
0, 1
Suppose 2*c + 1 - 7 = 0, -2*j - 3*c + 69 = 0. Let p be j/14 - 2 - -1. Factor 2/7*d**2 + 8/7*d + p.
2*(d + 2)**2/7
Let g be 3/(54/4)*1. Let k be 336/432 - 2/18*3. Factor -2/3*z - g*z**2 - k.
-2*(z + 1)*(z + 2)/9
Let i(w) be the third derivative of w**5/330 - 4*w**4/33 + 64*w**3/33 + 2*w**2. Let i(v) = 0. What is v?
8
Suppose 9/5*h**3 + 3/5*h**2 + 0 + 0*h = 0. Calculate h.
-1/3, 0
Suppose -3*h + 28 = 5*m, 0*m + 17 = 4*m - 3*h. Factor -10*o**3 + 10*o**2 + m*o + 9*o + 12*o**3 + 6.
2*(o + 1)**2*(o + 3)
What is v in 2/13 - 2/13*v**2 + 0*v = 0?
-1, 1
Let l(r) be the first derivative of -1/3*r**2 + 2/9*r**3 + 0*r + 5. Determine b, given that l(b) = 0.
0, 1
Let y = -5 - -7. Suppose y = m - 4. Let g(q) = q**3 - q**2 - q + 1. Let l(p) = 4*p**3 - 12*p + 8. Let o(b) = m*g(b) - l(b). Factor o(x).
2*(x - 1)**3
Let x be (-1 + 1)/3 - -2. Let v = 138/5 - 231/10. Factor -3/2*a**3 + 6 + 0*a - v*a**x.
-3*(a - 1)*(a + 2)**2/2
Determine o, given that -5/2*o + 1/2*o**2 - 3 = 0.
-1, 6
Let x(w) be the third derivative of w**7/6300 - w**6/300 + 3*w**5/100 + w**4/24 + 7*w**2. Let v(t) be the second derivative of x(t). Factor v(z).
2*(z - 3)**2/5
Let t(p) be the third derivative of 3*p**2 + 0 - 1/30*p**6 - 1/3*p**3 + 0*p**5 + 1/6*p**4 + 1/105*p**7 + 0*p. Factor t(k).
2*(k - 1)**3*(k + 1)
Let i = -12 - -17. Suppose 0*g + i*g - 15 = 0. Factor 2*o**5 + 3 - 3*o + 2*o**2 - g*o**4 - 2 - o**5 + 2*o**3.
(o - 1)**4*(o + 1)
Let p(s) = 27*s**3 + 56*s**2 - 11*s + 5. Let f(i) = 13*i**3 + 28*i**2 - 5*i + 3. Let k(c) = -5*f(c) + 3*p(c). What is x in k(x) = 0?
-2, 0, 1/4
Let c(m) = -m**3 + 8*m**2 - 10*m + 7. Let o be c(6). Factor -o*g - g**2 - 2 + 3 + 2*g**2 + 21*g.
(g + 1)**2
Let u(m) be the first derivative of m**3/12 - 5*m**2/8 + m - 7. Factor u(c).
(c - 4)*(c - 1)/4
Let g(a) be the first derivative of 2*a**3/33 + 4*a**2/11 + 8*a/11 + 15. Factor g(d).
2*(d + 2)**2/11
Let w be 95/25 - 40/50. Factor -5*o**2 + o + 23/4*o**w - 7/4*o**4 + 0.
-o*(o - 2)*(o - 1)*(7*o - 2)/4
Let q(t) be the third derivative of t**8/840 + t**7/420 - t**6/180 - t**5/60 - t**3/3 - 2*t**2. Let i(o) be the first derivative of q(o). Factor i(h).
2*h*(h - 1)*(h + 1)**2
Let s(z) = -6*z**4 - 12*z**3 + 3*z**2 + 12*z. Let t(i) = 13*i**4 + 25*i**3 - 7*i**2 - 24*i. Let q(j) = -7*s(j) - 3*t(j). Let q(u) = 0. What is u?
-2, 0, 1
Let v be 4/2 + 32/(-24). Factor -8/3*i + v*i**2 + 8/3.
2*(i - 2)**2/3
Let m be 6/21 + 3183/(-42). Let y = 77 + m. Determine u so that 1 + 1/2*u**2 + y*u = 0.
-2, -1
Let y(t) = t**3 - 2*t**2 - 3*t + 6. Let d be y(2). Factor 2/5*c**3 + 0 - 2/5*c**5 + d*c - 2/5*c**4 + 2/5*c**2.
-2*c**2*(c - 1)*(c + 1)**2/5
Let c(j) be the first derivative of j**3/3 + j**2 + 2*j + 2. Let g be c(-2). Determine h, given that 0*h**4 + 0*h**3 + g*h**4 + h**2 - 4*h**3 + h**2 = 0.
0, 1
Let n(w) be the third derivative of w**6/540 + w**5/54 + 7*w**4/108 + w**3/9 + 15*w**2. Factor n(v).
2*(v + 1)**2*(v + 3)/9
Factor -4/7*p**2 + 0*p + 0.
-4*p**2/7
Let l(g) = -g + 16. Let n be l(14). Suppose 0 = -5*s + n*s. Let 0*a**2 - 2/5*a + s*a**4 + 0 + 4/5*a**3 - 2/5*a**5 = 0. What is a?
-1, 0, 1
Let j(v) be the third derivative of v**7/420 - v**6/120 - v**5/120 + v**4/24 + 2*v**2. Find i such that j(i) = 0.
-1, 0, 1, 2
Determine s so that -2/7*s**4 + 0 - 1/7*s + 2/7*s**2 + 1/7*s**5 + 0*s**3 = 0.
-1, 0, 1
Determine m so that 19*m - 3*m**2 - 33 - 17*m + 16*m + 6 = 0.
3
Let x(d) be the second derivative of d**4/36 - 5*d**3/9 + 25*d**2/6 + 16*d. Factor x(f).
(f - 5)**2/3
Factor -87*s**2 - 96*s - 2*s**3 - 3*s**4 - 36 + 8*s**3 - 36*s**3.
-3*(s + 1)**2*(s + 2)*(s + 6)
Suppose 0 + 1/2