 6*v**2 + 3*v. Determine c, given that p(c) = 0.
2
Let n be 14/(-6) + 1 + 206/103. Let u be 2/(-9)*(-8 - -2). Factor 0*k - u*k**2 + n + 2/3*k**4 + 0*k**3.
2*(k - 1)**2*(k + 1)**2/3
Let s be (-1 + -103)*(-1)/(-30). Let a = -14/5 - s. Factor 1/3*o**2 + 0 + a*o.
o*(o + 2)/3
Let m(n) be the second derivative of -n**8/224 + n**6/40 - n**4/16 - n**2 + 3*n. Let g(r) be the first derivative of m(r). Factor g(x).
-3*x*(x - 1)**2*(x + 1)**2/2
Let s = 5 + -3. Factor -6*g**2 + 0*g**2 + 4*g**s.
-2*g**2
Let w = 11/20 - -83/140. Factor w*i - 26/7*i**2 + 10/7*i**3 + 8/7.
2*(i - 2)*(i - 1)*(5*i + 2)/7
Suppose 5*n = 9*n. Let j(f) be the third derivative of -1/120*f**6 - 1/24*f**4 + 1/30*f**5 - f**2 + 0 + n*f**3 + 0*f. Factor j(v).
-v*(v - 1)**2
Suppose 0 = -3*o + o + 3*j + 14, -3*o + 4 = 4*j. Let z be (-12)/42*o/(-1). Determine d so that -2/7 + 2/7*d**2 + 8/7*d**3 - z*d = 0.
-1, -1/4, 1
Let c(d) be the second derivative of -1/70*d**5 - 9/7*d**2 - 1/7*d**3 + 2*d + 5/42*d**4 + 0. Factor c(a).
-2*(a - 3)**2*(a + 1)/7
Let p = 11 - 14. Let r be -1*(-3)/p*0. Find a such that -1/3*a**2 + 0 + r*a = 0.
0
Let m(q) be the second derivative of -q**7/63 + q**6/45 + q**5/10 - q**4/18 - 2*q**3/9 + 5*q. Determine j, given that m(j) = 0.
-1, 0, 1, 2
Let v(w) be the first derivative of -w**5 + 25*w**4/4 - 10*w**3 - 10*w**2 + 40*w - 27. Suppose v(x) = 0. What is x?
-1, 2
Let a(u) = 17*u**3 + 22*u**2 + 16*u + 5. Let c(t) = 18*t**3 + 21*t**2 + 17*t + 6. Let h be 3 - (-2)/(4/2). Let v(b) = h*a(b) - 3*c(b). Factor v(f).
(f + 1)*(2*f + 1)*(7*f + 2)
Let l(q) be the first derivative of q**6/1980 + q**5/165 + q**4/33 - 4*q**3/3 - 4. Let z(k) be the third derivative of l(k). Find g, given that z(g) = 0.
-2
Let o be ((-8)/(-6))/((-7)/(-3)). Let j be ((-72)/588)/((-3)/7). Determine q so that -6/7*q + j*q**2 + o = 0.
1, 2
Let d(j) = -j**4 - 8*j**3 - 4*j - 5. Let h(u) = u**3 - 5*u**2 + u + 6. Let v(c) = -c**2 + 1. Let f(o) = h(o) - 5*v(o). Let a(m) = -d(m) - 6*f(m). Factor a(b).
(b - 1)*(b + 1)**3
Suppose -4*v = -2*v + 2. Let f = v + 1. Determine z, given that 0*z + 0*z**2 + 0*z**3 + f + 1/2*z**4 = 0.
0
Suppose 6 = 2*g, 2*w = -3*w + 2*g - 6. Suppose 0 = 5*h - w*h. Find m, given that 1/5*m**2 - 1/5*m**3 + h + 1/5*m**5 - 1/5*m**4 + 0*m = 0.
-1, 0, 1
Solve -14/11*s**3 + 0 + 2/11*s**5 - 12/11*s**2 + 0*s + 0*s**4 = 0 for s.
-2, -1, 0, 3
Determine n, given that 0 + 2/7*n**3 + 0*n - 2/7*n**2 = 0.
0, 1
Let m = 17/4 + -4. Factor 0 - 1/4*v**5 + 0*v**2 + m*v**3 + 0*v + 0*v**4.
-v**3*(v - 1)*(v + 1)/4
Let m(t) = t**2. Let h(r) be the third derivative of -r**5/20 + r**2. Let d(g) = -3*h(g) - 8*m(g). Determine f so that d(f) = 0.
0
Let m = 17/81 - -1/81. Solve -8/9*c - 8/9 - m*c**2 = 0 for c.
-2
Factor 3/2*w**4 + 3/2*w - w**3 - w**2 - 1/2 - 1/2*w**5.
-(w - 1)**4*(w + 1)/2
Determine x so that 42*x**3 - 8 - 8*x**2 - 27/2*x**4 - 40*x = 0.
-2/3, -2/9, 2
Let k(t) be the first derivative of t**7/5040 - t**5/720 - 5*t**3/3 - 4. Let x(r) be the third derivative of k(r). Solve x(y) = 0.
-1, 0, 1
Suppose -5*p + 3*s = -1, 4*p = 4*s - 2 - 2. Suppose 3*b = p*x + 10, -2*b - 15 = 5*x + 10. Factor 2/5*j**2 + 0*j + b.
2*j**2/5
Factor -83*w + 67*w + 0*w**2 - 4*w**2.
-4*w*(w + 4)
Let h(a) be the third derivative of a**7/1260 - a**6/180 + a**5/60 - a**4/36 - 2*a**3/3 - 2*a**2. Let k(r) be the first derivative of h(r). Factor k(u).
2*(u - 1)**3/3
Let x(i) be the second derivative of -i**4/3 - 8*i**3 - 72*i**2 - 10*i. Factor x(v).
-4*(v + 6)**2
Factor -59*i**5 + 4*i**2 - 4*i**4 - 4*i**2 + 63*i**5.
4*i**4*(i - 1)
Let -1/9*f**5 - 2/9*f**4 + 0 + 0*f + 0*f**2 - 1/9*f**3 = 0. Calculate f.
-1, 0
Factor 2*o**5 - 23*o**3 + 25*o**3 - 4*o**4 - o**4 + o**4.
2*o**3*(o - 1)**2
Let n(b) be the third derivative of -b**7/105 - b**6/12 - 4*b**5/15 - b**4/3 + 45*b**2. Determine t so that n(t) = 0.
-2, -1, 0
Suppose 5*d - 16 = -3*d. Factor 0 + 0*k - 1/3*k**3 - 1/3*k**d.
-k**2*(k + 1)/3
Let c(b) = -b - 4. Let j be c(-12). Factor 13*f + 0*f**2 - j*f**3 + 4 - 5*f - 4*f**4 + 0*f**2.
-4*(f - 1)*(f + 1)**3
Let y = 7 + -3. Suppose -2*t + y*t = 4. Factor -i + 0*i**2 + 2*i**4 + 3*i - 2*i**3 - 2*i**t.
2*i*(i - 1)**2*(i + 1)
Let g = 0 + 36. Let n = g + -106/3. Solve n*x**2 + 0 + 2/3*x = 0.
-1, 0
Factor 36/7*q**2 - 12/7*q + 1/7.
(6*q - 1)**2/7
Suppose 3*z = n + 4*z - 7, -n - 2*z + 10 = 0. Let b be 45/10 - 2/n. Factor -8*v + 3 - v + v**3 + 12*v**b - 15*v**2 + 8*v**3.
3*(v - 1)*(v + 1)**2*(4*v - 1)
Let z = 2 + -2. Suppose -2 = -l + 3*i + 8, 5*l + 3*i - 14 = z. Factor 3*f**2 - 3*f**3 + f**4 + 0*f**3 - f + 0*f**l.
f*(f - 1)**3
Factor -1/3 - f**3 + f + 1/3*f**2.
-(f - 1)*(f + 1)*(3*f - 1)/3
Let -t**2 + 1/2*t**3 + 0 + 0*t = 0. What is t?
0, 2
Let t(n) be the second derivative of 0*n**5 + 1/15*n**4 - n + 0 - 1/105*n**7 + 0*n**2 - 2/75*n**6 + 1/15*n**3. Factor t(p).
-2*p*(p - 1)*(p + 1)**3/5
Let s(w) be the second derivative of w**6/80 + 3*w**5/40 + 5*w**4/32 + w**3/8 + 8*w. Factor s(v).
3*v*(v + 1)**2*(v + 2)/8
Let j be (3/4)/(6/4). Let u be 11/(-4) + -2 + (95 - 90). Suppose u*r**2 - 3/4*r + j = 0. What is r?
1, 2
Suppose -3*j - 3*n = n - 9, -3*j + 9 = n. Find u, given that 2/7*u - 2/7*u**2 + 2/7 - 2/7*u**j = 0.
-1, 1
Let s(n) be the third derivative of -n**7/840 + n**6/480 + n**5/40 - n**4/24 - n**3/3 + 4*n**2. Solve s(g) = 0.
-2, -1, 2
Let 24/5*a - 3/5*a**3 - 57/5*a**4 - 21/5*a**5 + 69/5*a**2 - 12/5 = 0. Calculate a.
-2, -1, 2/7, 1
Let u(o) = -o**2 + 3*o. Let t be u(2). Solve -2*v**t + 4*v + v**2 - v**2 = 0.
0, 2
Find r such that 3/7*r**2 + 0*r**3 + 0 + 0*r - 3/7*r**4 = 0.
-1, 0, 1
Let z(d) be the third derivative of -d**5/75 - 3*d**4/5 - 54*d**3/5 + 30*d**2. Solve z(o) = 0.
-9
Let f = 157/4 + -39. Let k = -2/219 + 227/876. Factor 0 + 0*w + 0*w**2 + k*w**3 - f*w**4.
-w**3*(w - 1)/4
Let z(p) = p**5 + 9*p**4 - 13*p**3 + 7*p**2 + 4. Let o(y) = -y**5 + y**3 - y**2 - 1. Let v(d) = -4*o(d) - z(d). Determine q, given that v(q) = 0.
0, 1
Factor 29*g**2 - g - 27*g**2 + 3*g.
2*g*(g + 1)
Suppose 3 = 2*v - 3. Let k(r) be the first derivative of 8 - 9 - r**3 - v*r - 2*r**2 - r**2. Factor k(f).
-3*(f + 1)**2
Let h(q) = q**5 + q**3 - q**2 + q. Let c(r) = 8*r**5 - 8*r**4 + 4*r**3 + 4*r**2. Let u(x) = c(x) - 4*h(x). Factor u(m).
4*m*(m - 1)**3*(m + 1)
Let l(g) be the first derivative of 2*g**3/27 + g**2/3 - 29. Factor l(k).
2*k*(k + 3)/9
Suppose 10 = 5*m - 0. Let 14/3*c + 4/3*c**m - 14/3*c**3 - 4/3 = 0. Calculate c.
-1, 2/7, 1
Suppose 40*l - 45*l = -10. Let j(r) be the first derivative of 1/15*r**3 + 3/5*r**l + 3 + 9/5*r. What is x in j(x) = 0?
-3
Factor -39*m**3 + 36*m**2 + 64*m**3 - 37*m**3 + m**4.
m**2*(m - 6)**2
Let i(d) be the second derivative of -d**6/75 + d**4/10 - 2*d**3/15 + 6*d. Solve i(k) = 0.
-2, 0, 1
Let i(y) be the first derivative of 0*y**3 + 1/78*y**4 + 1 + 0*y + 1/390*y**5 - y**2. Let k(h) be the second derivative of i(h). Let k(x) = 0. Calculate x.
-2, 0
Let t(w) be the first derivative of 2*w**5/35 - 3*w**4/14 + 2*w**3/21 + 3*w**2/7 - 4*w/7 - 22. Factor t(s).
2*(s - 2)*(s - 1)**2*(s + 1)/7
Let i(l) be the second derivative of -l**4/36 + l**2/6 - 13*l. Solve i(s) = 0 for s.
-1, 1
Suppose -3*v + 4*d = 4, -4*v + v + 5*d = 8. Suppose -g = a - 1 - 5, -g = -v*a + 34. Factor -6*r**3 + a*r**4 - 5*r**3 - 4*r**3 + 2*r**2 + 5*r**3.
2*r**2*(r - 1)*(4*r - 1)
Let d be (0 - 3) + 0 + 6. Factor -9*g - 6 - 9*g**3 - 8*g**3 + 24*g**2 + 8*g**d.
-3*(g - 2)*(g - 1)*(3*g + 1)
Suppose 5*r + 24 = -2*z, -2*z + 21 = -5*r - 5*z. Let m = -4 - r. Factor -8*u**2 + 0*u**2 + u**3 + 6*u**m.
u**2*(u - 2)
Let c(i) be the second derivative of 1/18*i**3 - 3*i + 0*i**2 - 1/72*i**4 + 0. Suppose c(x) = 0. What is x?
0, 2
Let f = -2363/4 + 591. Find a, given that f*a**2 + 4 + 2*a = 0.
-4
Let d(q) = -12*q**4 + 45*q**3 - 108*q**2 + 84*q - 9. Let x(g) = 3*g**4 - 11*g**3 + 27*g**2 - 21*g + 2. Let u(r) = 4*d(r) + 15*x(r). Factor u(j).
-3*(j - 2)*(j - 1)**3
Let g(k) = -4*k**3 + 4*k + 3. Let h(s) = 17*s**3 - 17*s - 13. Let o(l) = 26*g(l) + 6*h(l). Factor o(q).
-2*q*(q - 1)*(q + 1)
Factor -k**3 + 0*k + 3*k**2 + 0*k + 9 - 13.
-(k - 2)**2*(k + 1)
Suppose 11 = 2*a + 1. Let o = a + 1. Determine u so that -u**3 - 6*u**2 - 9*u - 2*u**3 + o*u = 0.
-1, 0
Find v such that 7*v**2 + 27*v**5 - v**2 + 60*v**4 + 41*v**3 - 2*v**3 = 0.
-1, -2/9, 0
Let j(d) = 3*d**2 - 11*d. Let t be j(4). Factor -2/3*g**t + 0 + 4/3*g**3 +