et b(s) = -12*s + 84. Let z be b(7). What is c in 0*c + 2/13*c**4 + 0*c**2 - 2/13*c**5 + 0 + z*c**3 = 0?
0, 1
What is d in 0 - 2/7*d + 2/7*d**2 = 0?
0, 1
Factor 40/7*o**2 + 20/7*o**4 + 4/7 - 20/7*o - 4/7*o**5 - 40/7*o**3.
-4*(o - 1)**5/7
Let y(m) be the first derivative of m**8/1176 + m**7/245 + m**6/140 + m**5/210 + 5*m**2/2 + 4. Let d(r) be the second derivative of y(r). Factor d(a).
2*a**2*(a + 1)**3/7
Let x(j) = -4*j + 4. Let w(o) = -3*o + 5. Let p(m) = -5*w(m) + 4*x(m). Let h be p(-9). Factor -2/3*l + h - 2/3*l**2.
-2*l*(l + 1)/3
Find u such that -4 - 4*u**2 + 18*u**4 - 10*u**3 - 9*u**4 - 3*u**2 + 12*u + 2*u**2 - 2*u**5 = 0.
-1, 1/2, 1, 2
Let h(n) be the first derivative of n**4/32 + 10. Suppose h(y) = 0. Calculate y.
0
Suppose 5*t + 48 = t. Let d be (t/(-18))/(4/18). Factor 0*u - u**2 + 4/3 - 1/3*u**d.
-(u - 1)*(u + 2)**2/3
Solve 12 + 20*q - 26*q**2 + 10 - 7 + 31*q**2 = 0 for q.
-3, -1
Let h(n) be the second derivative of n + 0*n**3 + 0*n**2 + 0*n**4 + 0 + 1/42*n**7 + 0*n**6 - 1/20*n**5. Determine p so that h(p) = 0.
-1, 0, 1
Suppose 3 - 3 + 0*x - 2*x**2 + 2*x = 0. Calculate x.
0, 1
Determine k, given that 3*k + 1 - 7/4*k**2 = 0.
-2/7, 2
Let l(p) = 7*p**4 + 13*p**3 + 12*p**2 + 8*p - 3. Let s(u) = u**4 + u**3 - 1. Let m(b) = l(b) - 5*s(b). Suppose m(r) = 0. Calculate r.
-1
Let p be (92/(-138))/(16/(-18)). What is f in 3/4*f**2 + p + 18*f**3 + 12*f**4 - 9/2*f = 0?
-1, 1/4
Let j(b) be the third derivative of -b**5/40 - 7*b**4/96 - b**3/24 - 2*b**2. Let j(w) = 0. Calculate w.
-1, -1/6
Let f = -34 + 36. Factor -1/4*a**f + 1/4*a + 0.
-a*(a - 1)/4
Let l = 94 + -563/6. Let j(k) be the first derivative of -1/15*k**5 + 0*k**3 + 1/3*k**2 - l*k**4 + 1/3*k - 3. Find x, given that j(x) = 0.
-1, 1
Let o(g) = g - 2. Let r be o(4). Determine w so that 10*w - 3*w**4 - 8*w + 3*w**2 + 6*w**3 - 8*w**5 + 7*w**r - 7*w**4 = 0.
-1, -1/4, 0, 1
Suppose s = -1, 2*o + 5*s + 3 = -2. Let n(c) be the second derivative of 0 + 4*c + o*c**4 + 0*c**2 - 1/6*c**3 + 1/20*c**5. Factor n(j).
j*(j - 1)*(j + 1)
Let q = -1333/11 - -121. Let h = q + 15/22. Determine x so that 1 + 3/2*x + h*x**2 = 0.
-2, -1
Let x(v) be the third derivative of -v**7/14 + v**6/12 + 3*v**5 + 5*v**4 - 80*v**3/3 - 24*v**2. Solve x(y) = 0 for y.
-2, 2/3, 4
Solve -89*t**2 + t**3 + 64*t**2 - 9*t**3 + 13*t**3 - 15 + 35*t = 0.
1, 3
Let w(q) = -3*q**3 - 3*q**2 + 2. Let o(l) = -16*l**3 - 16*l**2 + 11. Let y(i) = 4*o(i) - 22*w(i). Determine a so that y(a) = 0.
-1, 0
Suppose -9*p + 4*p = -30. Suppose 10*o = 13*o - p. Factor -2/7*l + 0 + 6/7*l**3 - 4/7*l**4 + 0*l**o.
-2*l*(l - 1)**2*(2*l + 1)/7
Let s be (1/(-8))/((-1)/4). Factor -3/2*p**4 + 3/2*p**3 + 0 + s*p**5 - 1/2*p**2 + 0*p.
p**2*(p - 1)**3/2
Let z be (-8)/(-28) - (-1226)/294. Let c = -6/49 + z. Let -c*n - 38/3*n**3 + 32/3*n**2 - 5/3*n**5 + 2/3 + 22/3*n**4 = 0. Calculate n.
2/5, 1
Let j(p) be the first derivative of 7 + 3/4*p**4 + p**3 + 0*p + 0*p**2. Factor j(o).
3*o**2*(o + 1)
Let c(f) be the second derivative of -f**5/60 - f**4/12 + 2*f**3/9 - 3*f + 3. What is d in c(d) = 0?
-4, 0, 1
Let b = -5 - -9. Solve b*q**4 - 7*q**4 + q**5 + 2*q**4 = 0.
0, 1
Let s = 16 + -12. Let l(k) be the first derivative of 0*k**2 + 1 - 3/4*k**s + 3/5*k**5 + 0*k - 1/6*k**6 + 1/3*k**3. Factor l(r).
-r**2*(r - 1)**3
Let q = 480 - 28799/60. Let v(c) be the third derivative of 1/6*c**3 + c**2 + 1/48*c**6 + 0*c - q*c**5 + 0 - 5/48*c**4. Suppose v(h) = 0. What is h?
-1, 2/5, 1
Let r(o) = 97*o**3 + 57*o**2 - 39*o + 4. Let z(q) = 484*q**3 + 284*q**2 - 196*q + 20. Let h(v) = 16*r(v) - 3*z(v). Factor h(b).
4*(b + 1)*(5*b - 1)**2
Let t(l) be the first derivative of -l**6/2 + 3*l**4/2 - 3*l**2/2 - 7. Factor t(m).
-3*m*(m - 1)**2*(m + 1)**2
Let m(u) be the first derivative of 6*u + 5*u**3 + 3 - 21/2*u**2. Factor m(o).
3*(o - 1)*(5*o - 2)
Let q(c) = 12*c**2 - 6*c. Let x(l) = -l**3 - l**2. Let p(h) = q(h) + 3*x(h). Suppose p(r) = 0. What is r?
0, 1, 2
Let m(d) be the second derivative of 0 + 1/15*d**6 + 0*d**2 + 0*d**5 + 0*d**3 - 1/6*d**4 - 2*d. Suppose m(w) = 0. Calculate w.
-1, 0, 1
Let l(i) be the third derivative of -1/1512*i**8 - 4/135*i**5 + 1/270*i**6 + 0 - 2/27*i**3 + 2*i**2 + 0*i + 2/945*i**7 + 7/108*i**4. Factor l(c).
-2*(c - 1)**4*(c + 2)/9
Factor 0 - 1/8*n - 1/2*n**2.
-n*(4*n + 1)/8
Let i(l) = -l**3 - 2*l**2 - 2. Let d be 32/24*(-3)/(-2). Let c(n) = n**2 + 1. Let g(o) = d*c(o) + i(o). Factor g(f).
-f**3
Let f be (-2)/(-3) - 99/162. Let n(y) be the second derivative of 0*y**5 - 1/126*y**7 - 3*y - 1/45*y**6 + f*y**3 + 1/18*y**4 + 0 + 0*y**2. Factor n(i).
-i*(i - 1)*(i + 1)**3/3
Let l(j) be the first derivative of j**6/15 + j**5/30 + 2*j - 6. Let r(u) be the first derivative of l(u). Determine x so that r(x) = 0.
-1/3, 0
Let a = -1118/7 + 160. Suppose 34*o - 40*o = -18. Factor -2/7*r**2 - 2/7*r**o + a + 2/7*r.
-2*(r - 1)*(r + 1)**2/7
Suppose 4*q = 3*q + 5. Factor 3*o**3 - 7*o**3 + o**5 + 0*o + 2*o + o**q.
2*o*(o - 1)**2*(o + 1)**2
Let d(l) = 2*l**4 - 4*l**3 - 3*l**2 + 5*l. Let f(r) = r**4 - 2*r**3 - 2*r**2 + 3*r. Let j(t) = -3*d(t) + 5*f(t). Factor j(n).
-n**2*(n - 1)**2
Let f(z) be the first derivative of -z**5/50 - z**4/10 - 2*z**3/15 + 3*z - 6. Let w(o) be the first derivative of f(o). Factor w(v).
-2*v*(v + 1)*(v + 2)/5
Let m(y) = -y**3 + y**2 - y. Let i(p) = -25*p + 27*p**2 - 12*p**3 + p + 6 + 6*p**3. Let s(r) = i(r) + 3*m(r). Solve s(c) = 0.
1/3, 1, 2
Let c(s) = -s - 3. Let p(l) = -3*l + 19. Let k be p(8). Let b be c(k). Let -1/2*a**b + 1/2 + 1/4*a**3 - 1/4*a = 0. Calculate a.
-1, 1, 2
Let c = -6 + 9. What is d in -3*d - d**c - 2*d**3 + 4*d + 6*d**3 + 4*d**2 = 0?
-1, -1/3, 0
Let m = -67 + 69. Factor 1/2*i**3 + 0 + 1/2*i + i**m.
i*(i + 1)**2/2
Let f(n) = n**2 + 10*n - 14. Let u be f(-14). Factor r**2 - 5*r**2 - 30 + 8*r + u.
-4*(r - 3)*(r + 1)
Let r be (-90)/81 + 4/3. Let s(x) be the first derivative of -1 + 0*x - r*x**3 - 1/3*x**2 + 1/8*x**4. Factor s(b).
b*(b - 2)*(3*b + 2)/6
Let m(j) = j + 28. Let x be m(-27). Factor x + 1/2*y - 1/2*y**2.
-(y - 2)*(y + 1)/2
Let c = 8916 - 44321/5. Let y = 52 - c. Factor -3/5*w**4 + 0*w - y*w**2 - 1/5*w**5 + 0 - 3/5*w**3.
-w**2*(w + 1)**3/5
Suppose 11*u - 9 = 8*u. Factor 2/5*i**4 + 2/5*i**2 + 0 + 0*i + 4/5*i**u.
2*i**2*(i + 1)**2/5
Let g(z) = 4*z**2 - 4*z - 2. Let k(p) = p**2 - p - 1. Let c(d) = -2*g(d) + 12*k(d). Factor c(s).
4*(s - 2)*(s + 1)
Let n(k) be the first derivative of -2*k - 3*k**2 + 6/5*k**5 - 5 - 4/3*k**3 + 1/3*k**6 + k**4. Solve n(y) = 0.
-1, 1
Let k(w) be the first derivative of -9*w**5/5 + 21*w**4/2 - 61*w**3/3 + 14*w**2 - 4*w - 5. Determine z so that k(z) = 0.
1/3, 2
Let y(n) = 3*n**2 + n + 1. Let l be y(-3). Suppose f + l = 6*f. Factor 0*p**3 - 49*p**4 - f*p + 24*p**2 - 21*p**3 + p.
-p*(p + 1)*(7*p - 2)**2
Let u = -46 + 416/9. Let r(l) be the first derivative of -3 + 4/9*l - 4/27*l**3 - 1/3*l**2 - 1/27*l**6 + 0*l**5 + u*l**4. Let r(z) = 0. Calculate z.
-2, -1, 1
Let h = 242/5 + -48. Factor -h*m**2 + 0 - 4/5*m.
-2*m*(m + 2)/5
Factor 71*m**3 - 131*m**3 + 5*m**5 + 65*m**3 + 10*m**4.
5*m**3*(m + 1)**2
Let j(x) be the third derivative of -x**8/2016 - x**7/420 + x**6/360 + x**5/60 - x**4/144 - x**3/12 - 3*x**2. Determine l, given that j(l) = 0.
-3, -1, 1
Suppose -4*q - 99 = -5*q. Let k = q - 491/5. Determine n, given that 8/5 - 1/5*n**4 - 6/5*n**2 - n**3 + k*n = 0.
-2, 1
Let l(a) be the third derivative of a**8/672 - a**7/105 + a**6/40 - a**5/30 + a**4/48 + 9*a**2. Factor l(t).
t*(t - 1)**4/2
Let p(x) be the first derivative of 0*x + 2*x**3 + 3*x + 2 + 3*x**2 + 0 - x**3. Suppose p(g) = 0. What is g?
-1
Let p(s) be the second derivative of -s**7/84 + 13*s**6/60 - 8*s**5/5 + 19*s**4/3 - 44*s**3/3 + 20*s**2 + 5*s. Factor p(w).
-(w - 5)*(w - 2)**4/2
Let f(c) = -c**2 - 7*c + 8. Let y(z) = -z + 1. Let p(o) = 5*f(o) - 35*y(o). Determine m so that p(m) = 0.
-1, 1
Factor 3/7 - 3/7*v**2 + 0*v.
-3*(v - 1)*(v + 1)/7
Factor -40*f + 48*f**2 + 11 + 4*f**4 - 267*f**3 + 1 + 243*f**3.
4*(f - 3)*(f - 1)**3
Suppose 5*t - 94 = 141. Let w = t + -234/5. Solve -1/5*v**5 - 1/5*v**4 - w*v + 2/5*v**2 + 2/5*v**3 - 1/5 = 0.
-1, 1
Suppose 0 = -7*g + 3*g + 72. Suppose -5*h - g + 62 = j, -3*j = h - 20. Factor -6*f**2 - 2*f - h*f**3 - 4 + 4 - 3*f**4 - f**2.
-f*(f + 1)**2*(3*f + 2)
Let c(j) be the first derivative of -j**4 + 28*j**3/3 - 30*j**2 + 36*j + 11. Fac