*k**2 + 5*k - 5. Let h(x) = -5*c(x) + 2*q(x). Find l, given that h(l) = 0.
-1, 0
Determine k, given that 14/13*k**4 - 18/13*k**3 - 2/13*k + 0 + 10/13*k**2 - 4/13*k**5 = 0.
0, 1/2, 1
Let d be (0 + 5)*1/1. Suppose -u + 26 = 4*f, -5*u - d*f - 11 + 81 = 0. Find b such that -13*b**2 - 11*b**2 - 7 - 18*b + 3 - u*b**3 = 0.
-1, -2/5
Suppose 0 = -4*q - 4, -4*a + 3*q + 11 = -0*q. Let -4/5*k - 2/5 - 2/5*k**a = 0. What is k?
-1
Let b(z) be the second derivative of -z**9/15120 + z**8/3360 + z**4/12 + 3*z. Let m(g) be the third derivative of b(g). Solve m(d) = 0.
0, 2
Let s(i) = -i**3 - i**2 - i + 1. Let h(y) = 2*y**4 - 11*y**3 + 5*y**2 - 3*y + 3. Let u(w) = -2*h(w) + 6*s(w). Factor u(k).
-4*k**2*(k - 2)**2
Let m(w) be the first derivative of 4*w**3/3 - 20*w**2 + 58. Factor m(q).
4*q*(q - 10)
Let i(k) = -k**2 + 7*k + 18. Let u be i(9). Suppose 1/3*l**2 + 0 - 1/3*l**4 + u*l - 1/3*l**5 + 1/3*l**3 = 0. What is l?
-1, 0, 1
Let d(n) be the second derivative of n**6/30 - n**5/6 + n**4/4 - n**3/9 + 7*n. Factor d(m).
m*(m - 2)*(m - 1)*(3*m - 1)/3
Let v(d) = 62*d + 11. Let h be v(8). Let f be (-2)/7 - h/(-84). Determine w, given that -13/4*w + 1/4*w**3 + 21/4*w**2 + 1/2 - f*w**4 + 3*w**5 = 0.
-1, 1/4, 2/3, 1
Let c(p) = -2*p**5 + 4*p**4 - 22*p**3 + 2*p**2 + 6*p + 6. Let b(t) = -t**4 - t**3 - t**2 + t + 1. Let o(f) = 6*b(f) - c(f). Factor o(y).
2*y**2*(y - 2)**2*(y - 1)
Let i = 56 + -56. Let k(a) be the third derivative of i*a - 1/120*a**6 + 0 + 1/24*a**4 + 2*a**2 + 2/105*a**7 + 0*a**3 - 1/15*a**5. Factor k(v).
v*(v - 1)*(v + 1)*(4*v - 1)
Let g be (99/(-24) - -3)*114. Let j = g + 129. Factor -1/4 - 1/4*d**3 - j*d - 3/4*d**2.
-(d + 1)**3/4
Let x(w) = 70*w**4 - 435*w**3 + 85*w**2 + 85*w - 85. Let u(s) = 5*s**4 - 31*s**3 + 6*s**2 + 6*s - 6. Let f(b) = -85*u(b) + 6*x(b). What is n in f(n) = 0?
0, 5
Let x = -8 + 11. Let t = 0 + x. Suppose 0 + 0*a + 2/7*a**t + 2/7*a**5 + 0*a**2 + 4/7*a**4 = 0. Calculate a.
-1, 0
Let b = -20 - -14. Let t = b + 8. Factor -t*q + 11 - 11 - q**2.
-q*(q + 2)
Factor m + 16*m**2 - 15*m**2 - 2*m.
m*(m - 1)
Let l = -64 - -578/9. Suppose -2/9*r**2 + l + 0*r = 0. Calculate r.
-1, 1
Let m(d) be the third derivative of 2*d**7/105 - d**6/6 + 8*d**5/15 - 2*d**4/3 + 19*d**2. Factor m(k).
4*k*(k - 2)**2*(k - 1)
Suppose 0*p + 4*b - 11 = -5*p, -11 = -3*p + 2*b. Factor -4*g**3 + p*g + 3*g**2 - 11*g**4 + g**3 + 8*g**4.
-3*g*(g - 1)*(g + 1)**2
What is q in -1/6*q**2 - 10/3*q - 50/3 = 0?
-10
Let s(w) = 4*w**2 - 2. Suppose -2*l = -0 + 2. Let m(f) = -f**2 - f + 1. Let y(x) = l*s(x) - 2*m(x). Find q, given that y(q) = 0.
0, 1
Factor -16*p**2 + p**5 + 14*p**3 - 12*p**4 + 7*p**4 - 2 + 9*p - p**4.
(p - 2)*(p - 1)**4
Let i(r) be the first derivative of r**6/6 + r**5/5 + r**4/16 + 1. Factor i(o).
o**3*(2*o + 1)**2/4
Let t = 3 - 0. Let y(i) = i**3 - i. Let a(o) = -o**5 - 4*o**4 - 9*o**3 - 4*o**2 + 2*o. Let s(p) = t*y(p) + a(p). Suppose s(j) = 0. What is j?
-1, 0
Let b(g) be the first derivative of g**7/6 + 8*g**6/15 + 11*g**5/20 + g**4/6 + 3*g + 5. Let t(p) be the first derivative of b(p). Factor t(q).
q**2*(q + 1)**2*(7*q + 2)
Let x(q) = q - 2. Let f be x(4). Suppose -5*k + f*k = 0. Determine j, given that -j**2 + k*j**3 - 2*j**3 + 1 - 2*j**2 = 0.
-1, 1/2
Let k be -1 - (-10)/(4/2). Suppose -2*r - 2 = 3*i - k, 0 = -i - 3*r - 4. Find g, given that 0 - 2/7*g**i - 2/7*g = 0.
-1, 0
Let y(t) = -4*t**3 - 7*t**2 + 5*t + 21. Let n(u) = 4*u**3 + 8*u**2 - 4*u - 20. Let h(x) = -5*n(x) - 4*y(x). Factor h(d).
-4*(d - 1)*(d + 2)**2
Factor -3*h**2 + 0 + 12*h - 28*h + 13*h - 1 - h**3.
-(h + 1)**3
Solve -7*n + 9*n + 8*n + 5*n**2 + 5 = 0.
-1
Let f = 13 + -13. Factor f*i**3 - 2/7*i**4 + 0*i + 4/7*i**2 - 2/7.
-2*(i - 1)**2*(i + 1)**2/7
Let o = -31 + 43. Let n be (1/o)/((-6)/(-18)). Factor -1/4*d**4 + 0 - 3/4*d**2 + n*d + 3/4*d**3.
-d*(d - 1)**3/4
Let r(w) be the third derivative of -w**6/200 + w**5/25 - w**4/8 + w**3/5 - 3*w**2. Factor r(g).
-3*(g - 2)*(g - 1)**2/5
Factor 2/5*x**4 + 8/5*x + 12/5*x**2 + 2/5 + 8/5*x**3.
2*(x + 1)**4/5
Let l(d) = -3*d + 1 - 3 + d + 2*d**2. Let b be l(2). Let -5*r**2 + b + 7*r - 3 - 1 = 0. Calculate r.
2/5, 1
Let w(v) be the first derivative of -v**3/3 + 5. Let l(u) = -u**2 + 8*u + 8. Let j = -2 + 5. Let i(y) = j*w(y) - l(y). Solve i(d) = 0 for d.
-2
Factor -26*c**2 + 11*c + 31*c**2 + 4*c.
5*c*(c + 3)
Solve 0*z + 0*z**2 + 0*z**3 + 1/4*z**5 - 1/4*z**4 + 0 = 0 for z.
0, 1
Let u(j) = -2*j**3 + j**2 + 2*j + 1. Let z be u(-1). Factor -3*n**2 + 4*n - 4 + 2*n**2 + 2 - n**z.
-2*(n - 1)**2
Factor -1/4*m**4 + 0 + 1/4*m**3 + 0*m + 0*m**2.
-m**3*(m - 1)/4
Let o(p) be the second derivative of 5*p**4/12 - 10*p**3 + 90*p**2 + 15*p. Suppose o(y) = 0. Calculate y.
6
Factor -8/7*r**2 - 3/7*r - 3/7*r**3 + 2/7.
-(r + 1)*(r + 2)*(3*r - 1)/7
Let f(d) be the second derivative of d**7/294 + d**6/35 + d**5/140 - 2*d**4/7 + 8*d**3/21 + 36*d. What is r in f(r) = 0?
-4, 0, 1
Let t(f) = f - 4. Let x be t(5). Let u be 27/12 + x/(-4). Determine b so that b - b**2 + b**3 + 0*b**3 - u*b + b**4 = 0.
-1, 0, 1
Let r(f) be the third derivative of -f**7/35 + f**6/40 + f**5/20 + 27*f**2. Determine g, given that r(g) = 0.
-1/2, 0, 1
Let q = 65/12 - 1/12. Determine n so that 10/3*n - q*n**2 - 2/3 + 8/3*n**3 = 0.
1/2, 1
Let -4*t - 12 - 1/3*t**2 = 0. What is t?
-6
Let q(w) be the second derivative of -w**6/15 + w**4/2 + 2*w**3/3 + 2*w. Factor q(p).
-2*p*(p - 2)*(p + 1)**2
Let z = 128 - 380/3. What is t in -2/3*t**3 + 2/3*t + z - 4/3*t**2 = 0?
-2, -1, 1
Let z(i) be the third derivative of -i**8/1008 + i**7/210 - i**6/120 + i**5/180 + 9*i**2. Factor z(t).
-t**2*(t - 1)**3/3
Suppose -4*f + 3*h = -h + 12, f - 4*h + 18 = 0. Factor 2*i**3 - i**3 + f*i**5 + i**2 - 3*i**2 - 3*i**3 + 2*i**4.
2*i**2*(i - 1)*(i + 1)**2
Let g(h) = -4*h**2 - 5 + h**2 + 4*h**2 + 5*h + h**2. Let y(n) = 0*n**2 - 2*n - 3*n**2 + 2*n**2 + 2. Let k(b) = 4*g(b) + 10*y(b). Factor k(l).
-2*l**2
Let w be (3/(-2))/((-4)/(-8)). Let j be w*56/108 + 2. Find q such that 0 + 2*q**2 + j*q + 14/9*q**3 = 0.
-1, -2/7, 0
Factor 0*d - 2/7*d**3 + 2/7*d**2 + 0.
-2*d**2*(d - 1)/7
Factor v**2 + 4/5 - 1/5*v**3 - 8/5*v.
-(v - 2)**2*(v - 1)/5
Suppose 3*d = 6*d - 12. Suppose k**2 + 4*k + 0*k**2 - d*k = 0. What is k?
0
Let b(o) = -5*o**3 - 3*o**2 + 4*o + 4. Let m(d) = -14*d**3 - 8*d**2 + 11*d + 11. Let v be (0 + 2)*11/2. Let c(u) = v*b(u) - 4*m(u). Factor c(x).
x**2*(x - 1)
Let j(p) be the first derivative of p**4 + 8*p**3/3 + 2*p**2 + 2. Determine b, given that j(b) = 0.
-1, 0
Suppose -6 = j - 4*v, 6 = -0*j + 2*j + v. Factor 6*g - 5*g**2 + 4*g**2 - 5*g - g**j.
-g*(2*g - 1)
Let z(n) be the third derivative of 11*n**7/735 - n**6/21 - 2*n**5/105 + 20*n**2. Factor z(v).
2*v**2*(v - 2)*(11*v + 2)/7
Let o be ((-4)/55)/((-60)/50). Let f(r) be the third derivative of 5*r**2 + 0 - o*r**3 + 0*r + 1/330*r**5 + 1/132*r**4. Let f(k) = 0. What is k?
-2, 1
Let t be 12/24*2/4. Let y(q) be the first derivative of t*q + 2 + 9/16*q**4 + 5/4*q**3 + 7/8*q**2. Let y(w) = 0. Calculate w.
-1, -1/3
Let u(b) be the second derivative of b**6/50 - b**4/20 + 7*b. Factor u(a).
3*a**2*(a - 1)*(a + 1)/5
Let b be 1/(-2)*(3 - (1 + 2)). Determine y so that 0 + b*y + 2/9*y**2 = 0.
0
Factor 0 - j**2 - 4/3*j + 1/3*j**3.
j*(j - 4)*(j + 1)/3
Let a be (0 - (-6 - -2)) + -1. Factor 3*o**2 + o**a - 2 + 5 + 3*o - 2.
(o + 1)**3
Let x(c) = -23*c**4 + 21*c**3 + 64*c**2 + 12*c + 4. Let q(u) = 162*u**4 - 147*u**3 - 447*u**2 - 84*u - 27. Let y(n) = 4*q(n) + 27*x(n). What is z in y(z) = 0?
-1, -2/9, 0, 2
Let t = 8 - -9. Let c = -15 + t. Factor 6/7*n**3 + 2/7*n**5 + 0 + 2/7*n**c + 6/7*n**4 + 0*n.
2*n**2*(n + 1)**3/7
Let k be -3 + 1 - (-28)/12. Determine x so that -k*x**2 - 2/3 + x = 0.
1, 2
Let s(m) be the second derivative of -m**5/50 - m**4/5 + m**3/15 + 6*m**2/5 + 11*m. Solve s(b) = 0.
-6, -1, 1
Let p(y) be the first derivative of y**4/60 + y**3/15 + y**2/10 - y - 3. Let v(j) be the first derivative of p(j). Solve v(q) = 0 for q.
-1
Let x(a) be the first derivative of 2*a**3/33 - a**2/11 + 8. Factor x(w).
2*w*(w - 1)/11
Let a(b) be the first derivative of -b**4/26 + 3*b**2/13 - 4*b/13 - 12. Find r such that a(r) = 0.
-2, 1
Let t(a) be the second derivative of 1/8*a**4 + a + 0 - 3/4*a**3 + 3/2*a**2. What is z in t(z) = 0?
1, 2
Suppose -1 = -2*u - 5*q + 6, 2*q = -u + 4. Determine r so that -6*r**3 + 0*r**2 - 3*