Let p(t) = 2*t**4 + 4*t**3 + 3*t**2 - 4*t - 5. Let s be -2 + 1 - (-5 - -7). Let z(n) = s*d(n) - p(n). Factor z(x).
-2*(x - 1)*(x + 1)**3
Let g(y) be the second derivative of -y**7/98 - 3*y**6/70 - 3*y**5/70 + y**4/14 + 3*y**3/14 + 3*y**2/14 + 7*y. What is u in g(u) = 0?
-1, 1
Let m(t) be the third derivative of 0*t**3 + 1/21*t**4 + t**2 + 4/105*t**5 - 1/20*t**6 + 0 + 0*t + 1/168*t**8 + 2/735*t**7. Solve m(q) = 0 for q.
-2, -2/7, 0, 1
Let h(k) = -7*k**4 + 19*k**3 - 20*k**2 + 8*k + 3. Let p(b) = -8*b**4 + 20*b**3 - 20*b**2 + 8*b + 4. Let u(a) = 4*h(a) - 3*p(a). Factor u(x).
-4*x*(x - 2)*(x - 1)**2
Let d(o) = 4*o**2. Let s be d(1). Let q be 1 + 0 + -1 + 32. Determine c, given that -80*c**3 - 151*c**s + 16 + 112*c + 6*c**5 + 184*c**2 + 43*c**5 + q*c**4 = 0.
-1, -2/7, 2
Let z(d) be the first derivative of 3*d**5 + 21*d**4/4 - 3*d**3 - 21*d**2/2 - 6*d - 20. Factor z(w).
3*(w - 1)*(w + 1)**2*(5*w + 2)
Solve 0*h**4 - 1/4*h + 0 + 0*h**2 - 1/4*h**5 + 1/2*h**3 = 0 for h.
-1, 0, 1
Let o be (-8)/32 + (-42)/(-8). Find i such that -9*i**2 + 15*i - o*i**3 + 3*i**3 - 6 - i**3 + 3*i**4 = 0.
-2, 1
Let y be (-308)/(-21)*2/(-8) - -5. Suppose -4*z - 11/3*z**2 - z**3 - y = 0. What is z?
-2, -1, -2/3
Let q(a) = -a**3 - a - 1. Let y(u) = -4*u**3 + 6*u**2 - 12*u - 5. Let x(f) = -5*q(f) + y(f). Solve x(h) = 0 for h.
-7, 0, 1
Let z be 2 + -8 + 2 + 58/11. Let y be 8/33*(-3)/(-2). Suppose -y*n**2 - z*n - 4/11 + 6/11*n**3 = 0. What is n?
-1, -1/3, 2
Let g = -112 - -225/2. Solve m + 0 - g*m**2 = 0 for m.
0, 2
Let u(w) = -w**2 - 5*w + 3 + 1 + 0*w**2. Let x(n) = -2*n**2 - 6*n + 5. Let j(b) = 6*u(b) - 4*x(b). Factor j(l).
2*(l - 2)*(l - 1)
Let o(k) be the first derivative of k**6/2 - 15*k**4/4 + 6*k**2 + 39. Solve o(q) = 0 for q.
-2, -1, 0, 1, 2
Let r(j) = -j**4 - j**3 + j. Let i(q) = -q**4 - 2*q**3 + 3*q. Let k = 2 + -8. Let g be 50/(-15) + (-2)/k. Let t(u) = g*r(u) + i(u). Factor t(v).
v**3*(2*v + 1)
Factor -4*y + 22 - y**2 + 2 + 0 - 3*y**2.
-4*(y - 2)*(y + 3)
Let y(d) be the third derivative of -d**5/300 - d**4/120 + d**3/15 + 9*d**2. Let y(s) = 0. What is s?
-2, 1
Let g(b) be the third derivative of b**5/140 - 7*b**2. What is z in g(z) = 0?
0
Let q be (-12)/(0 + -3) + 3. Let d be q/21 - 0/1. Find z such that d*z**2 + 1/3*z**3 + 0 + 0*z = 0.
-1, 0
Let b(r) be the third derivative of r**8/168 - r**7/21 + 7*r**6/60 + r**5/30 - 2*r**4/3 + 4*r**3/3 + 3*r**2. Determine h so that b(h) = 0.
-1, 1, 2
Let i(p) be the third derivative of p**6/120 + 7*p**5/60 + 2*p**4/3 + 2*p**3 + 12*p**2. Factor i(s).
(s + 2)**2*(s + 3)
Let v(b) be the second derivative of -b**7/7560 - b**4/3 + 2*b. Let j(g) be the third derivative of v(g). Determine u so that j(u) = 0.
0
Let c(h) = -h**4 + h. Let f(m) = 24*m**5 - 64*m**4 + 54*m**3 - 18*m**2 + 4*m. Let j(i) = 2*c(i) - f(i). Let j(n) = 0. What is n?
0, 1/4, 1/3, 1
Let c(b) be the third derivative of -b**7/165 - 23*b**6/660 - b**5/55 + 28*b**2. Factor c(y).
-2*y**2*(y + 3)*(7*y + 2)/11
Let s(m) be the third derivative of m**8/2352 - m**7/294 + m**6/120 - m**5/140 - 22*m**2. Factor s(v).
v**2*(v - 3)*(v - 1)**2/7
Factor 5/3*a - 1 - 1/3*a**2 - 1/3*a**3.
-(a - 1)**2*(a + 3)/3
Factor -10*j**3 - 5*j**5 - 8 - 66*j**4 + 21*j**4 + 135*j - 90*j**2 + 143 - 120*j**3.
-5*(j - 1)*(j + 1)*(j + 3)**3
Let -6/5*w**2 - 9/5*w - 4/5 - 1/5*w**3 = 0. Calculate w.
-4, -1
Let j(m) = -7*m**3 + 28*m**2 + 115*m + 144. Let r(i) = 12*i**3 - 57*i**2 - 231*i - 288. Let z(h) = -9*j(h) - 5*r(h). Let z(b) = 0. Calculate b.
-4, -3
Suppose -w + i - 6*i + 11 = 0, -3*w + 3*i + 33 = 0. Let o = w + -9. Let 0*c**3 - o*c - 2*c**2 + 2*c**3 + 4*c**4 - 2*c**4 = 0. Calculate c.
-1, 0, 1
Suppose -5*c - 5*s + 303 - 28 = 0, 4*c - s - 220 = 0. Suppose -75/2*q**4 + 4*q - 26*q**2 + 0 + c*q**3 = 0. Calculate q.
0, 2/5, 2/3
Let k = -248 + 250. What is u in 5/3*u - 10/3*u**k - 1/3 - 5/3*u**4 + 1/3*u**5 + 10/3*u**3 = 0?
1
Suppose 0 = -2*v + 6*v. Suppose v = 3*p + 2*t - 6, 5*p + t - 5 = 5. Find s such that 0 - 2*s**2 - 3*s - s - p = 0.
-1
Suppose 2/7 + 0*n - 2/7*n**2 = 0. Calculate n.
-1, 1
Let w be 7 - (-1 - (-20)/4). Determine d so that 7*d**2 - 7*d + 7*d**2 + 71*d + 4*d**w + 18*d**2 = 0.
-4, 0
Suppose 3*f + 1 - 17 = 2*h, 2*f + h + 1 = 0. Suppose 1 + 5 = 2*o + 2*g, -f*g = 4*o - 6. Suppose 1/3*w**2 + 0 + o*w = 0. Calculate w.
0
Let v be 6/(-21) - 7493/63. Let q = -119 - v. Factor -2/9*x**2 - 4/9*x - q.
-2*(x + 1)**2/9
Let b(i) be the second derivative of i**5/4 - 5*i**4/4 + 5*i**3/2 - 5*i**2/2 + 4*i. Let b(m) = 0. Calculate m.
1
Let v(j) be the second derivative of -j**5/12 - 5*j**4/9 - 10*j**3/9 - 44*j. Let v(g) = 0. What is g?
-2, 0
Let m = 11 - 9. Factor -3*r**3 - 5*r**2 - 4*r**2 + 2*r**2 + 10*r**m.
-3*r**2*(r - 1)
Let h(s) be the second derivative of 3/8*s**4 - 1/14*s**7 - 1/2*s**2 - 7/60*s**6 + 7/40*s**5 - s - 1/12*s**3 + 0. Determine d so that h(d) = 0.
-1, -2/3, 1/2, 1
Let p(q) be the third derivative of -1/3*q**3 + 1/72*q**6 + 3*q**2 + 0 - 1/10*q**5 + 1/6*q**4 + 0*q. Let s(t) be the first derivative of p(t). Factor s(a).
(a - 2)*(5*a - 2)
Suppose 4*w - 2 = 2*m, 0 = -0*w - 5*w + 3*m + 4. Let o be 32/(-12) - -3 - w. Let 0*t + 0 + 2/3*t**4 + 2/3*t**2 + o*t**3 = 0. Calculate t.
-1, 0
Let h(a) = 5*a**2 + a + 5. Let x(d) = 4*d**2 + 2*d + 5. Let y(n) = 5*h(n) - 6*x(n). Let c be y(8). Factor 9 + 3*p**2 + p**c + 2*p - 9.
p*(p + 1)*(p + 2)
Let j(s) be the first derivative of -5*s**6/36 + s**5/3 + 5*s**4/12 - 20*s**3/9 + 35*s**2/12 - 5*s/3 - 23. Find b, given that j(b) = 0.
-2, 1
Suppose 4*l + 1 = -3*u + 5, 0 = -3*u + 5*l - 5. Let a = u + 2. Let -3/2*n + 3*n**a - 5/2*n**3 + 1/4 + 3/4*n**4 = 0. What is n?
1/3, 1
Suppose 0 = 5*r + 2*q - 6*q + 288, 2*q = 3*r + 174. Let g be 0/(-1) - r/50. Find a such that -4/5*a**3 - 2/5 + g*a**4 - 2/5*a**5 - 4/5*a**2 + 6/5*a = 0.
-1, 1
Let l be (-2*(-21)/56)/(-2 - -5). Factor 3/4*u - 1/2 - l*u**2.
-(u - 2)*(u - 1)/4
Let v = -36 - -36. Factor 1/3*d**5 + 0*d**2 + 0 + 0*d - 1/3*d**4 + v*d**3.
d**4*(d - 1)/3
Let n = -265061/6 - -803405171/18186. Let t = n + -2/433. Suppose -8/7*x**2 - 8/7*x - t*x**3 + 0 = 0. Calculate x.
-2, 0
Let m(n) be the third derivative of -n**5/60 - n**4/4 + 7*n**3/6 + 2*n**2. Let j be m(-7). Factor 3*c**2 - 4*c**2 - 3*c + j - 2.
-(c + 1)*(c + 2)
Determine v so that -1666/5*v**3 - 432/5*v - 8 + 162/5*v**5 - 1482/5*v**2 - 414/5*v**4 = 0.
-1, -2/9, 5
Let i(t) = t**2 + 6*t + 5. Let s(f) = 2*f**2 + 12*f + 10. Let y(x) = -7*i(x) + 4*s(x). Determine w so that y(w) = 0.
-5, -1
Let a(n) be the first derivative of n**5/10 + 2*n**4/3 + n**3 - n - 7. Let m(k) be the first derivative of a(k). Find s such that m(s) = 0.
-3, -1, 0
Suppose -8*w + 16 = -4*w. Suppose 5 - 16*n**2 - 1 - 6*n**3 - 2*n - w*n**3 = 0. What is n?
-1, 2/5
Let b(z) = z - 1. Let g(p) = -p**2 - 11*p + 9. Let f(q) = -6*b(q) - g(q). Let s be f(-6). Let -2*l + 4*l - l + l**s + 2*l**2 = 0. What is l?
-1, 0
Let h(r) be the third derivative of -r**6/360 + r**5/60 - 2*r**3/9 - r**2. Factor h(a).
-(a - 2)**2*(a + 1)/3
Let q(a) = -a + 5. Let o be q(5). Let m(n) be the third derivative of o*n**3 + 0*n + 0 + 1/240*n**6 + 1/60*n**5 + 1/48*n**4 - 2*n**2. Let m(p) = 0. Calculate p.
-1, 0
Let b(h) = -5*h + 0*h + 0*h - h**2 - h. Let s be b(-6). Let -6/7*o**3 + 10/7*o**2 + 4/7*o + s = 0. What is o?
-1/3, 0, 2
Let k = -2 - -4. Solve -12*f + 8*f + 5 - 3 + k*f**2 = 0 for f.
1
Let h(p) be the first derivative of p**4/4 - p**3 + p**2 + 10. Factor h(u).
u*(u - 2)*(u - 1)
Let m(j) = 2*j**3 + j**2 + j + 2. Suppose 5*k = 5*g + 20, -4*g - 19 = -5*k - 4. Let v(h) = -h**3 - h**2 - h - 1. Let t(d) = g*v(d) - 2*m(d). Factor t(q).
(q + 1)**3
Let a = 11921/60 - 596/3. Let w(h) be the third derivative of a*h**5 + 1/6*h**3 + 0*h + h**2 + 0 - 1/12*h**4. Factor w(d).
(d - 1)**2
Let d(j) = j**3 + 0*j**2 + 0*j + j + j**2 - 1. Let b(z) = -z**4 + 6*z**3 + 6*z**2 + 8*z - 9. Let f(u) = -2*b(u) + 18*d(u). Factor f(k).
2*k*(k + 1)**3
Let i = -2/355 - -107/6390. Let j(t) be the second derivative of 1/15*t**5 - 2*t - 1/6*t**4 - 1/6*t**2 + 0 + 2/9*t**3 - i*t**6. Factor j(a).
-(a - 1)**4/3
Let f = 981/56 + -127/7. Let y = f + 9/8. Determine l so that y - 1/2*l**2 - 1/2*l + 1/2*l**3 = 0.
-1, 1
Let l(z) be the second derivative of z**7/168 - z**6/60 + z**4/24 - z**3/24 + 8*z. Factor l(u).
u*(u - 1)**3*(u + 1)/4
Suppose 3*b = 13 - 4. Let y be -4*2/(-5