) = n**2 - 1. Let z be d(2). Suppose -3*k**z - 3 - 2*k - 3*k - 4*k - 9*k**2 = 0. What is k?
-1
Suppose -10 = -5*s, 3*n = -n - 2*s + 4. Factor -3*z**2 + 1 + n*z**2 + 0 + 2*z + 4*z**2.
(z + 1)**2
Let o(d) be the second derivative of d**7/294 + d**6/105 - d**4/42 - d**3/42 + 18*d. Factor o(w).
w*(w - 1)*(w + 1)**3/7
Let p = 179 - 524. Let x be p/(-105) - 1*3. Determine n so that x*n**2 - 2/7*n**3 + 0*n + 0 = 0.
0, 1
Let q(h) = -3*h**5 + h**4 + 8*h**3 - 6*h**2 - h + 1. Let o(u) = -3*u**5 + 9*u**3 - 6*u**2. Let y(a) = 2*o(a) - 3*q(a). Factor y(f).
3*(f - 1)**3*(f + 1)**2
Suppose -2*j = 3*t - 228, 6*j - t = 11*j - 596. Determine u so that -75/2*u**5 + j*u**4 - 96*u**2 + 0 - 24*u - 36*u**3 = 0.
-2/5, 0, 2
Let c(y) be the first derivative of -y**4/4 + 6*y**3 - 54*y**2 + 216*y - 49. Factor c(h).
-(h - 6)**3
Let y be ((-240)/(-70))/((-2)/(-7)). Let o be (-2)/y*-26 - 3. Solve -o*u + 1/3 + u**2 = 0.
1/3, 1
Let p be 0 + 4 - (-14)/(-4). Factor -1/2*k**3 + 0 - p*k**2 + 0*k.
-k**2*(k + 1)/2
Let c be ((1 + -1)/(-1))/1. Suppose c = -3*t - t + 12. Factor -2*d**4 - 2*d**3 - 3*d**2 + t*d**2.
-2*d**3*(d + 1)
Let t be 8/(-6)*(-1)/3. Factor 4/9 + 2/9*m - 2/9*m**3 - t*m**2.
-2*(m - 1)*(m + 1)*(m + 2)/9
Let y(k) be the second derivative of 4*k + k**2 + 1/6*k**4 + 0 - 2/3*k**3. Factor y(b).
2*(b - 1)**2
Let r be (6 + -5)*(-2)/(-8). Suppose 5*h = 7 + 3. Factor -r*y + 1/4*y**h - 1/2.
(y - 2)*(y + 1)/4
Let k(y) be the third derivative of -y**8/336 - y**7/30 - 3*y**6/20 - y**5/3 - y**4/3 - 23*y**2. Let k(s) = 0. What is s?
-2, -1, 0
Let c(f) = 9*f**5 + 4*f**4 - 5*f**3 - 7*f. Let d(u) = -u**5 + u**3 + u. Let b = 12 + -14. Let q(v) = b*c(v) - 14*d(v). Factor q(z).
-4*z**3*(z + 1)**2
Let z(l) be the second derivative of 0*l**3 + 0 - 2/105*l**6 + 1/70*l**5 + l + 1/42*l**4 + 0*l**2. Suppose z(j) = 0. What is j?
-1/2, 0, 1
Suppose -b + 19 = 5*m + 2*b, 1 = -m - 3*b. Let h = -5 + m. Factor -1/2*l**2 - 1/2*l + h.
-l*(l + 1)/2
Suppose -3*p + 13 = -2. Suppose p*g = -o - 7, o + 0*o = g + 5. Factor 2/7*v**o + 2/7 + 6/7*v**2 + 6/7*v.
2*(v + 1)**3/7
Let q(x) = 4*x + 4. Let v be q(-8). Let d = v + 202/7. Factor -6/7*h**2 - 2/7*h**4 + 0 + 2/7*h + d*h**3.
-2*h*(h - 1)**3/7
Let g(i) = -i - 6. Let q be g(-8). Factor 0*f + f**2 - q + 4 + 3*f.
(f + 1)*(f + 2)
Let y(f) be the first derivative of -4*f**5/5 + f**4 + 8. Factor y(w).
-4*w**3*(w - 1)
Let h(g) be the first derivative of g**4/2 - 3*g**2 + 4*g + 8. Find r such that h(r) = 0.
-2, 1
Let m(i) be the second derivative of -i**5/10 + i**4/6 + i**3/3 - i**2 + 44*i. Factor m(o).
-2*(o - 1)**2*(o + 1)
Let k(r) = -r**3 - r - 1. Let b(p) = 4*p**4 + 7*p**3 + 4*p**2 - 17*p - 13. Let o(i) = -b(i) + 5*k(i). Factor o(t).
-4*(t - 1)*(t + 1)**2*(t + 2)
Let j be (-500)/(-5)*10/16. Let a = j - 61. Suppose -6*r + a*r**2 + 6 = 0. Calculate r.
2
Let v(t) = 3*t**2 + 16*t - 11. Let g(p) = -12*p**2 - 63*p + 45. Let w(q) = 4*g(q) + 15*v(q). Determine r, given that w(r) = 0.
-5, 1
Suppose -4*r - 47 = 13. Let l be r/(-6)*(-4)/(-5). Factor -l*z - z + 0*z + 1 + 2*z**2.
(z - 1)*(2*z - 1)
Let w(z) be the second derivative of -3*z**6/2 - 3*z**5/2 + 55*z**4/12 + 10*z**3/3 - 10*z**2 + 14*z - 2. Factor w(d).
-5*(d + 1)**2*(3*d - 2)**2
Let a(n) = -7*n**4 + 9*n**3 - 2*n**2 + 5. Let f(h) = 4*h**4 - 5*h**3 + h**2 - 3. Let z(m) = -3*a(m) - 5*f(m). Factor z(i).
i**2*(i - 1)**2
Let l(k) be the second derivative of -1/2*k**2 + 1/60*k**5 - 1/12*k**4 - 2*k + 0 + 1/6*k**3. Let h(f) be the first derivative of l(f). Factor h(u).
(u - 1)**2
Let y(w) be the first derivative of w**5/90 + w**4/36 - 2*w**3/9 + 3*w**2 + 9. Let o(m) be the second derivative of y(m). Suppose o(f) = 0. Calculate f.
-2, 1
Solve 12*n - 10 - 9*n - n**3 + 8 = 0.
-2, 1
Let l(z) = z**2 - 4*z + 8. Let r(p) = -p - 1. Let a(o) = -l(o) - 2*r(o). Let h be a(4). Factor k - h*k**5 + 2*k**3 - k.
-2*k**3*(k - 1)*(k + 1)
Let i(u) be the third derivative of u**2 + 0*u - 1/36*u**4 - 1/336*u**8 + 1/72*u**6 + 0*u**3 - 1/630*u**7 + 1/180*u**5 + 0. Let i(y) = 0. Calculate y.
-1, 0, 2/3, 1
Let d(c) be the second derivative of -c**7/126 + 2*c**6/45 - c**5/15 - c**4/18 + 5*c**3/18 - c**2/3 + 10*c. Let d(o) = 0. What is o?
-1, 1, 2
Let i(r) be the second derivative of 0*r**3 - 1/60*r**4 + 7*r + 0 + 1/100*r**5 + 0*r**2. Factor i(y).
y**2*(y - 1)/5
Let a = 17 - 17. Determine h so that 2/3*h**2 + 2/3*h + a = 0.
-1, 0
Let p = 169 - 839/5. Solve 2/5*i**4 - 2*i + 2/5*i**3 - p*i**2 - 4/5 = 0.
-1, 2
Let k be (-2)/25*(-900)/120. Factor 0 - 3/5*q + k*q**3 + 0*q**2.
3*q*(q - 1)*(q + 1)/5
Let w be (-2)/(-3) - (-16)/3. Let -9*r**2 - w - 2*r**3 - r**2 - 2 - 16*r = 0. What is r?
-2, -1
Determine j so that -1 - 32*j**2 - 5 + 24*j - 27*j**3 + 3*j + 26*j**2 + 12*j**4 = 0.
-1, 1/4, 1, 2
Let x(o) be the third derivative of 0*o + 0*o**3 + 1/10*o**5 - 2*o**2 + 1/40*o**6 + 0*o**4 + 0. Solve x(j) = 0.
-2, 0
Factor -2*v**2 + 4/3*v**3 - 1/3 + 4/3*v - 1/3*v**4.
-(v - 1)**4/3
Let x(r) be the first derivative of -r**4/60 + r**3/15 - 2*r - 2. Let j(f) be the first derivative of x(f). What is v in j(v) = 0?
0, 2
Let l(b) be the first derivative of 3/2*b**2 + b**3 - 6*b + 1. Factor l(u).
3*(u - 1)*(u + 2)
Find t, given that 5/2*t**2 + 10 + 30*t**3 + 10*t**4 - 30*t = 0.
-2, 1/2
Let k(r) be the first derivative of -r**4/20 - 4*r**3/15 - r**2/2 - 2*r/5 - 19. Factor k(s).
-(s + 1)**2*(s + 2)/5
Let t(a) be the third derivative of a**6/420 + a**5/42 + a**4/28 - 3*a**3/7 - 34*a**2. Factor t(g).
2*(g - 1)*(g + 3)**2/7
Suppose 0 = -a + 4 + 5. Let l(v) = -v**3 - 2*v**2 - v. Let b(r) = 2*r**3 + 4*r**2 + 2*r. Let z(f) = a*l(f) + 4*b(f). What is s in z(s) = 0?
-1, 0
Suppose -11*r = -6*r. Suppose 4*t = -r*t. Factor 0*g**2 + 0*g + t + 0*g**4 + 2/5*g**5 - 2/5*g**3.
2*g**3*(g - 1)*(g + 1)/5
Let y(l) = -3*l + 34. Let p be y(10). Let r(t) be the first derivative of -8*t**2 - 3 - 10/3*t**3 - 8*t - 1/2*t**p. Factor r(j).
-2*(j + 1)*(j + 2)**2
Let p(r) be the first derivative of -r**8/4200 - r**7/2100 + r**6/900 + r**5/300 - 4*r**3/3 + 2. Let u(x) be the third derivative of p(x). Factor u(f).
-2*f*(f - 1)*(f + 1)**2/5
Let i(j) be the second derivative of -j**4/96 + j**3/24 + 10*j. Suppose i(y) = 0. What is y?
0, 2
Suppose 0 = -0*f + 5*f - 3*m - 22, 0 = -4*m - 16. Let p be 2*2 + (-120)/35. Factor -6/7*z**3 + 6/7*z + 4/7*z**f - p.
-2*(z - 1)*(z + 1)*(3*z - 2)/7
Factor 21/2*a**4 + 75/2*a**2 + 24*a + 3/2*a**5 + 6 + 57/2*a**3.
3*(a + 1)**3*(a + 2)**2/2
Let a be (-8)/(-5) + (-6)/(-15). Factor 0*r**a + 2*r**2 - r**2.
r**2
Let b(s) be the first derivative of 2*s + 2. Let h(j) = -j**2 - j + 6. Let f(c) = -6*b(c) + 2*h(c). Factor f(u).
-2*u*(u + 1)
Let v(j) = -j**2 - j + 1. Let s(a) = 3*a**2 + 3*a - 28. Let z(m) = s(m) - 2*v(m). Factor z(r).
5*(r - 2)*(r + 3)
Let f(a) be the third derivative of a**8/30240 - a**7/7560 + a**5/20 - a**2. Let p(g) be the third derivative of f(g). Factor p(b).
2*b*(b - 1)/3
Let g(x) = -5*x**2 + 103*x - 199. Let d(o) = 3*o**2 - 69*o + 133. Let y(m) = -7*d(m) - 5*g(m). Factor y(s).
4*(s - 4)**2
Let r(x) be the second derivative of -3*x**6/10 + x**4/3 - 9*x. Solve r(p) = 0.
-2/3, 0, 2/3
Factor 42*z**3 + 24*z**2 - 115*z**4 + 234*z**4 + 2*z - 99*z**4.
2*z*(z + 1)**2*(10*z + 1)
Let b(d) = -5*d**2 + 7*d + 5. Let i(k) = -k**2. Let f(o) = b(o) - 4*i(o). Let j be f(7). Factor 2 + 2*y**3 - 6*y - 4*y**3 - 6*y**4 + 2*y**j + 6*y**3 + 4*y**2.
2*(y - 1)**4*(y + 1)
Let g(b) = 5*b**2 + 2*b - 2. Let t(q) = 11*q**2 + 5*q - 5. Let m(o) = -5*g(o) + 2*t(o). What is r in m(r) = 0?
0
Let z(h) be the third derivative of -h**6/1080 - h**3/3 + 3*h**2. Let d(m) be the first derivative of z(m). Find g, given that d(g) = 0.
0
What is x in -15*x - 10*x**2 + 3 + 11*x**2 + 19*x = 0?
-3, -1
Let r be (5 + -10)/(-15) - 2/6. Factor 0 + 2/5*l**2 + r*l.
2*l**2/5
Let w(x) be the first derivative of -x**8/4200 + x**6/450 - x**4/60 + 2*x**3/3 - 5. Let d(t) be the third derivative of w(t). Suppose d(j) = 0. Calculate j.
-1, 1
Let m be (7/84)/(3/8). Factor 0*z - m*z**2 + 2/9.
-2*(z - 1)*(z + 1)/9
Suppose 3*n - 10 = n. Suppose 1 + 4 = n*i. Suppose x + i + 1/4*x**2 = 0. Calculate x.
-2
Let d be 1/(-3) - (-62)/6. Let z(p) = p**3 - 11*p**2 + 9*p + 12. Let i be z(d). Find x such that 0 - 2/5*x + x**3 - 3/5*x**i = 0.
-2/5, 0, 1
Let k be 16*5/50 - 6/(-15). Find j, given that 4/5 - 6/5*j + 2/5*j**k = 0.
1, 2
Let w be (