 Let g(z) = 6*h(z) + 11*x(z). Let g(k) = 0. What is k?
20
Suppose 3*y + 6 = 0, 0 = -4*r - 5*y - 4 - 2. Suppose -3*w - r = -7. Determine u so that 2 - w + u**2 + u**2 = 0.
0
Let s = 1231/15 - 82. Let r(v) be the second derivative of 1/30*v**6 + s*v**5 + 0*v**2 + 0*v**3 + 0 + 1/36*v**4 - 3*v. Factor r(x).
x**2*(x + 1)*(3*x + 1)/3
Suppose -2*m = 2*m - 16. Let v(j) be the third derivative of 0*j + 0 + 1/60*j**5 + 2/3*j**3 + j**2 - 1/6*j**m. Factor v(q).
(q - 2)**2
Let t be 82/40 - (-8)/(-32). Factor 0 - t*u**4 + 3/5*u - 3*u**2 + 21/5*u**3.
-3*u*(u - 1)**2*(3*u - 1)/5
Let g(l) be the first derivative of l**5/15 - l**4/6 + l**2/3 - l/3 + 6. Find o, given that g(o) = 0.
-1, 1
Let t(j) be the first derivative of -j**7/105 + j**6/75 + j**5/25 - j**4/15 - j**3/15 + j**2/5 + j - 3. Let s(w) be the first derivative of t(w). Factor s(m).
-2*(m - 1)**3*(m + 1)**2/5
Let k = -5/11 - -37/33. Find q, given that 0 - 4/3*q**3 + 2/3*q**2 + k*q**4 + 0*q = 0.
0, 1
Let h(u) be the first derivative of -u**6/27 + 4*u**5/45 + 7. Factor h(n).
-2*n**4*(n - 2)/9
Solve -2*i**3 - 1 + 6*i - 1 + 0 - 2 = 0.
-2, 1
Let f(y) be the second derivative of -y**5/14 + y**4/21 + 5*y**3/21 - 2*y**2/7 - 7*y. Solve f(d) = 0.
-1, 2/5, 1
Let d(r) be the third derivative of r**6/450 - r**5/120 + r**4/120 + r**3/2 - 2*r**2. Let l(g) be the first derivative of d(g). Factor l(s).
(s - 1)*(4*s - 1)/5
Let f(b) be the second derivative of -b + 0*b**4 + 0 + 0*b**6 + 1/28*b**7 + 1/4*b**3 - 3/20*b**5 + 0*b**2. Factor f(n).
3*n*(n - 1)**2*(n + 1)**2/2
Let b(p) be the first derivative of p**6/6 - p**5/3 + p**4/12 + p**3/9 + 48. Let b(l) = 0. What is l?
-1/3, 0, 1
Let a(x) be the first derivative of -2*x**3/9 - x**2/3 + 42. Factor a(z).
-2*z*(z + 1)/3
Let j(m) = m**3 - 26*m**2 - 21*m. Let n(k) = 2*k**3 - 77*k**2 - 62*k. Let o(c) = -17*j(c) + 6*n(c). Factor o(t).
-5*t*(t + 1)*(t + 3)
Factor -2/5*i + 0 + 2/5*i**3 - 2/5*i**2 + 2/5*i**4.
2*i*(i - 1)*(i + 1)**2/5
Let u(m) = -3*m**4 - 5*m**3 + 12*m**2 + 4*m - 4. Let v(n) = -2*n**4 - 6*n**3 + 11*n**2 + 3*n - 3. Let z(r) = -3*u(r) + 4*v(r). Factor z(x).
x**2*(x - 8)*(x - 1)
Let g(a) be the third derivative of 41/120*a**6 - a**2 + 17/60*a**5 - 1/3*a**3 + 0 - 5/24*a**4 + 1/10*a**7 + 0*a. Factor g(p).
(p + 1)**2*(3*p - 1)*(7*p + 2)
Let u(h) be the second derivative of -h**4/5 - 14*h**3/15 + 12*h**2/5 + 15*h. What is w in u(w) = 0?
-3, 2/3
Let p(z) be the first derivative of -z**3/3 + z**2/2 - 2. Let n(j) = -j**2 + 15*j + 18. Let k(m) = -n(m) + 3*p(m). Find a such that k(a) = 0.
-3
Let m(t) = -6*t**2 - 16. Let g(h) = 3 + 2 + 2*h**2 + 0*h**2. Let y(s) = 16*g(s) + 5*m(s). Determine n so that y(n) = 0.
0
Let u(v) be the third derivative of -v**6/48 - v**5/12 - 5*v**4/48 - 8*v**2. Find y, given that u(y) = 0.
-1, 0
Let k(s) = 42*s**3 + 420*s**2 - 608*s + 220. Let b(l) = -l**3 - 2. Let x(n) = 6*b(n) + k(n). Factor x(c).
4*(c + 13)*(3*c - 2)**2
Let v(i) = i**2 - 3*i + 6. Let t be v(5). Let a be t/8 + (1 - 1). Factor 1/5 - 1/5*k**a - 1/5*k**3 + 1/5*k.
-(k - 1)*(k + 1)**2/5
Let w = -39/4 + 121/12. Solve 0 + 1/3*i + w*i**3 + 5/6*i**2 = 0 for i.
-2, -1/2, 0
Factor 1/2*c - 1/2 + 3/2*c**3 + 5/2*c**2.
(c + 1)**2*(3*c - 1)/2
Let u(m) be the third derivative of -m**8/120 - m**7/210 + 7*m**6/180 + m**5/30 + m**3 - 3*m**2. Let f(k) be the first derivative of u(k). Factor f(v).
-2*v*(v - 1)*(v + 1)*(7*v + 2)
Let o(s) = -s**2 - 5*s - 3. Let r be o(-3). Let 4*u**3 + u**4 - r*u + 8*u**2 + u**3 + 5*u + 2*u = 0. What is u?
-2, -1, 0
Find n, given that -3 + 6*n**3 - 5*n**4 - 4*n**4 - 6*n**5 + 12*n**2 + 1482*n - 1482*n = 0.
-1, 1/2, 1
Let t(q) = 5*q - 20. Let o be t(4). Let p(l) be the second derivative of -1/8*l**4 - 1/2*l**2 + o - 2*l + 5/12*l**3. What is f in p(f) = 0?
2/3, 1
Suppose -z = 5*y - 27, -5*z + 30 = -0*y + 4*y. What is t in 48/5*t**y - 21/5*t**3 + 0*t + 0 + 3/5*t**2 + 24/5*t**4 = 0?
-1, 0, 1/4
Let s(y) = -y**2 - 5*y. Let x be s(-4). Let t(j) be the third derivative of 0*j - 2*j**2 + 0 + 1/6*j**x - 1/3*j**3 - 1/30*j**5. Factor t(u).
-2*(u - 1)**2
Let j(o) be the second derivative of o**6/90 - o**4/24 + o**3/18 + o**2 - o. Let q(g) be the first derivative of j(g). Let q(x) = 0. Calculate x.
-1, 1/2
Let z(p) be the second derivative of -p**7/147 - p**6/35 - p**5/70 + p**4/14 + 2*p**3/21 - 5*p. Suppose z(o) = 0. What is o?
-2, -1, 0, 1
Solve 5*m**4 - 3*m**4 - 5*m**5 + 6*m**4 - 5*m**2 + 5*m**3 - 3*m**4 = 0.
-1, 0, 1
Let j(l) be the second derivative of -1/21*l**3 + 0*l**2 - 1/70*l**5 + 4*l + 0 + 1/21*l**4. Factor j(h).
-2*h*(h - 1)**2/7
Let z be 6/8*(-88)/(-11). Factor -4*j**4 - j**3 + z*j**4 + 0*j**4 - j**5.
-j**3*(j - 1)**2
Determine n so that 0 + 0*n + 7/3*n**2 - 1/3*n**3 = 0.
0, 7
Let i be (-4)/10 - 34/(-10). Let 0 + 3*b + 12*b**2 - i - 12*b = 0. What is b?
-1/4, 1
Let v(o) be the second derivative of o**6/24 - o**5/40 - 5*o**4/48 + o**3/12 - o. Let v(q) = 0. Calculate q.
-1, 0, 2/5, 1
Let g(k) = -k**2 - 32*k + 33. Let j be g(-33). Let 0 - 8/3*n**5 + 0*n + 2*n**3 + j*n**4 - 2/3*n**2 = 0. Calculate n.
-1, 0, 1/2
Suppose -8*f - 16 = -4*f. Let o be f/(16/(-4)) - -1. Factor -3/2*g - 1/2 - 1/2*g**3 - 3/2*g**o.
-(g + 1)**3/2
Suppose 2*g - 5 = s, -g = -2*g + 5*s - 11. Suppose -g*o = -0*o - 8. Factor 3*k**2 - 5*k**o - 3*k**3 - 10*k**2 - 12*k.
-3*k*(k + 2)**2
Determine z, given that 18/11*z**5 + 0*z - 8/11*z**2 - 16/11*z**3 + 6/11*z**4 + 0 = 0.
-2/3, 0, 1
Suppose 0 = -2*o - 3*j + 13, -3*o - o + j = -19. Let p(x) = -9 + x**2 - x - 2*x**2 + x. Let d(w) = 4. Let i(b) = o*d(b) + 2*p(b). Factor i(g).
-2*(g - 1)*(g + 1)
Factor 252*d**2 + 24*d + 58*d - 2*d - 1296*d**3 - 16.
-4*(4*d + 1)*(9*d - 2)**2
Let a(x) be the first derivative of -14*x**3/3 + 16*x**2 - 8*x + 1. Solve a(u) = 0 for u.
2/7, 2
Suppose 5*v - 33 = v - 5*l, 0 = 5*v + 3*l - 25. Factor 10*a + v*a - 8*a**2 + 28*a**3 + 8 + 4*a**5 - 44*a**3.
4*(a - 2)*(a - 1)*(a + 1)**3
Let d(l) be the third derivative of -l**9/120960 + l**8/20160 - l**7/10080 + l**5/60 + 8*l**2. Let n(i) be the third derivative of d(i). Factor n(q).
-q*(q - 1)**2/2
Suppose 0 + 14 = 7*i. What is g in -3/5 + 1/5*g**i + 2/5*g = 0?
-3, 1
Let l(v) be the third derivative of v**6/24 + v**5/12 - 5*v**4/24 - 5*v**3/6 - 16*v**2. Factor l(z).
5*(z - 1)*(z + 1)**2
Let j(s) be the first derivative of -3*s**4/28 - 2*s**3/21 + s**2/2 - 2*s/7 - 7. Let j(d) = 0. Calculate d.
-2, 1/3, 1
Let q(i) = -i**2 + i - 1. Let t be 3 + (-2 - (0 - -2)). Let g(w) = w**3 + 5*w**2 - 2*w + 2. Let x(f) = t*g(f) - 2*q(f). Let x(v) = 0. What is v?
-3, 0
Let f(o) = -o + 10. Let u be f(7). Let t(m) be the first derivative of -1/2*m**2 + 1 + 0*m + 1/3*m**u. Determine i, given that t(i) = 0.
0, 1
Factor 10*u**2 - 5*u**3 - 32*u**2 - 7*u**3 - 60*u - 29*u**2 - 12.
-3*(u + 2)**2*(4*u + 1)
Let y(a) be the second derivative of 2*a + 1/5*a**6 + 0*a**2 + 1/6*a**3 - 3/14*a**7 - 1/2*a**4 + 0 + 2/5*a**5. Find n, given that y(n) = 0.
-1, 0, 1/3, 1
Let h be (9/3)/3 - -7. What is y in 98*y**2 - 1 + 1 + h - 22*y - 34*y = 0?
2/7
Let j be 1/((-2)/68*2). Let b = j - -35/2. Solve -1/2*y**4 + 1/2*y**2 - 1/2*y + 0 + b*y**3 = 0 for y.
-1, 0, 1
Suppose 2*v = 5*v. Factor v*c**3 + 3*c**3 + 0 + 0 - 3*c**2.
3*c**2*(c - 1)
Suppose 19 = 4*n - 13. Let r = n + -6. Solve 4*k**r - k + 0*k**2 - k**3 - 3*k**2 - 1 + 2*k**3 = 0 for k.
-1, 1
Let r(u) = -93*u - 2. Let z be r(-3). Let f = 1943/7 - z. Let f*o - 10/7*o**2 + 0 - 2*o**3 = 0. Calculate o.
-1, 0, 2/7
Let q(k) = -k**3 + 5*k**2 + 4*k + 13. Let l be q(6). Let u(x) = 43*x**2 + 19*x + 3. Let s(v) = v**2 + v. Let o(b) = l*u(b) + 5*s(b). Factor o(r).
3*(4*r + 1)**2
Factor 0*h - h**2 + 2*h + 6 - h.
-(h - 3)*(h + 2)
Let b be (-202)/18 - (-2)/9. Let r = -7 - b. Factor -2*w**3 - 2*w**r + 0*w**4 + 0*w**3.
-2*w**3*(w + 1)
Suppose -9*c = -4*c - 10. Factor -8*n**c + 6*n**2 + 26*n**4 - 8*n + 4*n + 20*n**2 + 48*n**3.
2*n*(n + 1)**2*(13*n - 2)
Factor -1/3*o - 1/9*o**2 - 2/9.
-(o + 1)*(o + 2)/9
Let k be 6/4*(-80)/(-30). Let l(w) be the third derivative of 0 + 0*w + 1/240*w**6 - 1/6*w**3 - 2*w**2 - 1/16*w**k + 0*w**5. Factor l(q).
(q - 2)*(q + 1)**2/2
Let t(g) be the second derivative of 1/2*g**3 + 2*g + 0 - 3/20*g**5 + 0*g**2 + 0*g**4. Factor t(b).
-3*b*(b - 1)*(b + 1)
Let z(u) = -6*u**4 + 15*u**3 - 21*u**2 + 3*u + 9. Let m(d) = -3*d**4 + 7*d**3 - 10*d**2 + d + 5. Let t(w) = 9*m(w) - 5*z(w). What 