t q(s) = s + 5. Suppose -5*k = -5*b, 0 = 7*b - 3*b + 5*k. Let n be q(b). Determine w, given that w**2 + 3*w**n - 2*w**3 - w + w**2 - 6*w**2 + 4*w**4 = 0.
-1, -1/3, 0, 1
Let n = -6 - -9. Let c(m) be the third derivative of 0 + 5/12*m**4 + 2/3*m**n + 7/240*m**6 - 3*m**2 - 13/60*m**5 + 0*m. Factor c(w).
(w - 2)**2*(7*w + 2)/2
Let r(l) = 5*l**2 + l - 1. Let z be r(1). Suppose 6*y**3 - 3*y**4 - 3*y**2 + 3*y**2 - z*y**2 + 2*y**2 = 0. Calculate y.
0, 1
Let k(h) be the second derivative of -3*h**5/20 - h**4 - 5*h**3/2 - 3*h**2 + 22*h. Let k(n) = 0. What is n?
-2, -1
Suppose -j + 48 = j. What is w in -4 + 15*w**2 - w**3 + 10 + 4*w**3 + j*w + 6 = 0?
-2, -1
Let d(i) be the third derivative of i**8/2520 - i**7/630 + i**6/540 - i**3/6 + 2*i**2. Let r(g) be the first derivative of d(g). Suppose r(c) = 0. Calculate c.
0, 1
Let i be (-20)/(-50)*(11 + -1). Let m(u) be the second derivative of 0 + 0*u**2 - 1/27*u**3 - 3*u - 1/18*u**i. Suppose m(a) = 0. Calculate a.
-1/3, 0
Let k(s) be the second derivative of -s**7/1260 + s**6/360 - s**4/6 + 4*s. Let m(y) be the third derivative of k(y). Factor m(h).
-2*h*(h - 1)
Let 0 + 1/4*h**3 - 1/4*h + 0*h**2 = 0. What is h?
-1, 0, 1
Let y(t) = -t**2 + t - 1. Suppose 24 = 3*b - 7*b. Let c(k) = -3*k**2 + 4*k - 2. Let n(g) = b*y(g) + 3*c(g). Find o, given that n(o) = 0.
0, 2
Let g = -21/10 + 5/2. Let 2/5*j**2 + 2/5*j**3 - 2/5*j - g = 0. What is j?
-1, 1
Let x(a) be the first derivative of a**6/3 - 2*a**5/5 - a**4/2 + 2*a**3/3 + 1. Factor x(v).
2*v**2*(v - 1)**2*(v + 1)
Let z(t) be the third derivative of t**2 + 0 + 0*t**7 + 0*t + 0*t**5 + 0*t**3 + 0*t**4 - 1/15*t**6 + 1/168*t**8. Factor z(k).
2*k**3*(k - 2)*(k + 2)
Let x = 11 - 11. Suppose x*v - 12 = -4*v. Determine t so that 0 + 0*t - 1/3*t**2 - 1/3*t**v = 0.
-1, 0
Let w(i) = i**2 + 4*i**2 + 0*i**2 - 4*i**2 + i. Let h(u) = u + 2*u - 2*u - 2*u. Let x(v) = -2*h(v) - w(v). Factor x(t).
-t*(t - 1)
Let u(k) = 110*k**2 + 595*k - 45. Let p(t) = -5*t**2 - 27*t + 2. Let l(b) = 45*p(b) + 2*u(b). Find x such that l(x) = 0.
-5, 0
Suppose 4*q - 2 = -j - 12, 3*j - 15 = 3*q. Factor -d**2 - j*d**2 - 1 + 5*d**2 - d**4 + 0*d**4.
-(d - 1)**2*(d + 1)**2
Let i(t) be the second derivative of 25*t**7/84 - 2*t**6/3 + t**5/8 + 5*t**4/12 + 12*t. Factor i(c).
5*c**2*(c - 1)**2*(5*c + 2)/2
What is i in 4/5 - 1/5*i**3 + 7/5*i + 2/5*i**2 = 0?
-1, 4
Suppose -6/13*q**2 + 8/13*q**4 - 22/13*q**3 + 32/13*q + 8/13 = 0. What is q?
-1, -1/4, 2
Let o(i) be the first derivative of 2*i**4/3 + 7*i**3/3 - 2*i**2 - i + 5. Let t(j) be the first derivative of o(j). Find b, given that t(b) = 0.
-2, 1/4
Let b(o) be the second derivative of -o**6/20 - 3*o**5/40 + o**4/8 + o**3/4 - 8*o. Solve b(u) = 0.
-1, 0, 1
Let l(q) = -17*q**2 - 29*q - 3. Let w(o) = -8*o**2 - 14*o - 2. Let z(x) = -6*l(x) + 13*w(x). Let z(i) = 0. What is i?
-2
Let f(n) be the first derivative of -n**5/90 + 3*n**2/2 - 1. Let o(h) be the second derivative of f(h). Solve o(g) = 0 for g.
0
Factor -3/4*l + 1/4*l**2 + 1/2.
(l - 2)*(l - 1)/4
Let p(n) = -n - 4. Let j be p(-3). Let q be 6 + j + -1 + 0. What is x in -2/3*x**3 + 2/3*x**q + 2/3*x - 2/3*x**2 + 0 = 0?
-1, 0, 1
Let x(y) be the third derivative of y**6/30 + 4*y**5/15 + 2*y**4/3 + y**2. Factor x(r).
4*r*(r + 2)**2
Let c(o) be the third derivative of -o**5/360 - 7*o**4/144 - 5*o**3/18 - 23*o**2. Factor c(p).
-(p + 2)*(p + 5)/6
Let h(g) = g**5 - g**4 + g**3 - g. Let k(n) = -5*n**5 + 5*n**4 - 7*n**3 + n**2 + 6*n. Let d(w) = -6*h(w) - k(w). Find b, given that d(b) = 0.
-1, 0, 1
Let z(o) = 2*o**2 + 3*o. Let j be z(-2). Find w, given that -4*w**4 + 4*w**5 + 0*w**4 - w**5 - w**5 + 4*w**2 - j*w = 0.
-1, 0, 1
Let o(w) = -w**2 + 12*w - 4. Let i be o(8). Let u be 82/i + (-15)/35. Find z such that -1 - u*z + 3/2*z**5 + 0*z**2 + 5*z**4 + 5*z**3 = 0.
-1, 2/3
Let w(l) = -55*l**2 - 330*l - 485. Let o(f) = 5*f**2 + 30*f + 44. Let t(q) = 45*o(q) + 4*w(q). Suppose t(r) = 0. Calculate r.
-4, -2
Factor -8/7 - 8/7*b - 2/7*b**2.
-2*(b + 2)**2/7
Let s be 30/(-135) - (-2)/9. Let x(z) be the first derivative of 0*z + s*z**3 - 1/6*z**2 + 1/12*z**4 + 2. Factor x(f).
f*(f - 1)*(f + 1)/3
Let m = 12 + -10. Let w be 1/(-7) + (-11)/(-28). Factor -w*c**m - 1/2*c - 1/4.
-(c + 1)**2/4
Let s(a) = -a**3 + 9*a**2 - 16*a - 16. Let f be s(5). Factor 0 - 3/7*t**f - 3/7*t**2 - 6/7*t**3 + 0*t.
-3*t**2*(t + 1)**2/7
Let y(k) be the second derivative of k**7/14 + k**6/10 - 3*k**5/4 - k**4/4 + 4*k**3 - 6*k**2 - 5*k. Factor y(t).
3*(t - 1)**3*(t + 2)**2
Let n be 644/160 - 8/2. Let c(o) be the third derivative of 3/8*o**4 + n*o**6 + 3/16*o**5 + 0*o + o**2 - 1/2*o**3 + 0. Determine x, given that c(x) = 0.
-2, 1/4
Let k(i) be the first derivative of -i**3/27 + 2*i**2/9 - 4*i/9 + 14. Solve k(b) = 0.
2
Let q be 1938/(-54) + 3/(-27). Let z be 20/(-30)*q/7. Let 22/7*g**2 - 8/7 + z*g - 50/7*g**4 - 60/7*g**3 = 0. Calculate g.
-1, 2/5
Suppose 3*q + 168 + 38 = -g, 132 = -2*q + 2*g. Let d = q + 139/2. Find n such that 1 - n**2 + d*n = 0.
-1/2, 2
Factor 224/13*p**3 + 2/13*p**5 - 34/13*p**4 - 704/13*p**2 + 1024/13*p - 512/13.
2*(p - 4)**4*(p - 1)/13
Factor -m**5 - 2*m**5 + 5*m**4 + m**2 - 4*m**3 + 4*m**5 - 3*m**5.
-m**2*(m - 1)**2*(2*m - 1)
Let h = -1 - -3. Suppose 2*y - y**2 + 2*y + 12 + 20*y + 10*y**h = 0. Calculate y.
-2, -2/3
Let k(g) = g**4 - 3*g**3 - 5*g**2 + 3*g + 1. Let z(s) = -s**4 + 2*s**3 + 4*s**2 - 2*s - 1. Let h(i) = 2*k(i) + 3*z(i). Factor h(a).
-(a - 1)**2*(a + 1)**2
Determine j, given that 3*j**4 + 0 - 15/4*j**3 + 3/2*j**2 + 0*j - 3/4*j**5 = 0.
0, 1, 2
Factor -22*a**2 - 9*a**3 + 9*a**2 + 7*a**2 + 3*a**5.
3*a**2*(a - 2)*(a + 1)**2
Let j(v) be the first derivative of -4*v**3/3 - 10*v**2 - 16*v - 39. Factor j(y).
-4*(y + 1)*(y + 4)
Let p(g) be the second derivative of g**6/105 - 6*g**5/35 + 23*g**4/21 - 20*g**3/7 + 25*g**2/7 + 52*g. Factor p(k).
2*(k - 5)**2*(k - 1)**2/7
Let h(f) be the third derivative of -f**8/784 + f**6/70 + 12*f**2. Solve h(c) = 0.
-2, 0, 2
Factor -5*f**3 + 5*f**5 + 6*f**2 + 15*f**4 - 11*f**2 - 10*f**2.
5*f**2*(f - 1)*(f + 1)*(f + 3)
Let r(y) be the second derivative of 3*y**7/70 - y**6/10 + 7*y**5/100 - y**4/60 - 7*y. Let r(f) = 0. What is f?
0, 1/3, 1
Let p be 28/30 + 6/(-10). Suppose -2*w - 3 = 1, 5*w + 10 = 3*u. Solve u + 0*k + 1/3*k**2 + p*k**3 = 0 for k.
-1, 0
Factor -4*d**3 + 15*d**2 + 10*d**2 + 3*d**2 + 8 - 12*d**2 - 20*d.
-4*(d - 2)*(d - 1)**2
Let f(x) be the second derivative of x**9/6048 - x**7/420 - x**6/360 + x**5/80 + x**4/24 - x**3/6 + 2*x. Let y(w) be the second derivative of f(w). Factor y(m).
(m - 2)*(m - 1)*(m + 1)**3/2
Factor 243/5 + 3/5*o**2 + 54/5*o.
3*(o + 9)**2/5
Let w = -21 - -26. Suppose 5*g - 3*k = -w*k + 10, k = g - 2. Factor -14/9*i**g + 0 + 4/9*i + 10/9*i**3.
2*i*(i - 1)*(5*i - 2)/9
Let r(b) be the first derivative of -b**6/60 - b**5/10 - b**4/4 - b**3/3 - b**2/4 - 9*b + 3. Let a(l) be the first derivative of r(l). What is d in a(d) = 0?
-1
Let i = 3/53 + 297/371. Suppose -8/7 - 20*s**3 + i*s**2 - 14*s**4 + 40/7*s = 0. What is s?
-1, 2/7
Let s(k) be the third derivative of -k**5/60 + k**4/6 + 2*k**2. Let f(w) = 4 - 4 + w. Let r(t) = -10*f(t) + 2*s(t). Factor r(h).
-2*h*(h + 1)
Suppose -l - 5*s = 16, 0 = -0*s - 3*s. Let p be 2*(l/7)/(-4). Determine b, given that 0 - 6/7*b**3 + 0*b + 2/7*b**2 - p*b**4 = 0.
-1, 0, 1/4
Let q = -414/5 + 83. Factor -q*d**2 - 1/5*d + 0.
-d*(d + 1)/5
Let j be 18 + -15 + 1 + 27. Let a = j - 29. Factor 2/11*w**a + 0*w - 2/11*w**5 + 0 - 2/11*w**4 + 2/11*w**3.
-2*w**2*(w - 1)*(w + 1)**2/11
Let g = 84 - 585/7. Let n(v) be the first derivative of -1/14*v**4 + 2 - 2/7*v - g*v**2 - 2/7*v**3. Factor n(f).
-2*(f + 1)**3/7
Factor 4/3 - 2/9*c**2 - 2/9*c.
-2*(c - 2)*(c + 3)/9
Let k be (2 + -1)*(6 + -3). Suppose -3 - k = -3*r. Factor 0*h - 1/2 + 1/2*h**r.
(h - 1)*(h + 1)/2
Factor -4*i + 13*i**2 + 2 - 28*i**2 + 4*i**2 + 13*i**2.
2*(i - 1)**2
Let p(k) = -20*k**5 + 72*k**4 + 32*k**2 + 32. Suppose r + 128 = 5*r. Let f(d) = 3*d**5 - 11*d**4 - 5*d**2 - 5. Let g(c) = r*f(c) + 5*p(c). Solve g(n) = 0.
0, 2
Suppose -4*h + 4*v - 12 = -0*v, v = 5. Let c(l) be the first derivative of -2*l**3 + 1/7*l**h + 4/7*l + 2. Suppose c(j) = 0. What is j?
-2/7, 1/3
Let q(i) = -15*i + 365. Let p be q(24). Factor 2/3*a**2 + 1/3*a**p - 1/3 - 1/3*a**4 + 1/3*a - 2/3*a**3.
(a - 1)**3*(a + 1)**2/3
Suppose 5*f + r + 4*