(-6). Let v(t) = -9*t**2 + 17. Let z(n) = u*y(n) - 6*v(n). Determine s, given that z(s) = 0.
0
Let p = 18 - 18. Let j = -501 + 503. Let p + 10/3*q**3 + 0*q - 14/3*q**4 + 4/3*q**j = 0. What is q?
-2/7, 0, 1
Let h(z) = -z + 1. Let u be (-18)/22 - (-6)/(-33). Let r be h(u). Suppose 16/5*c**5 + 8/5*c + 8/5*c**4 - 2/5*c**r - 2/5 - 4*c**3 = 0. What is c?
-1, 1/2
Suppose 4*z - 7 - 1 = 0. Suppose -5 = -z*s + 1. Factor -s*l + 0 - 3*l**2 + 5*l**2 + 9*l + 4.
2*(l + 1)*(l + 2)
Let k(l) be the third derivative of l**8/2520 - l**7/180 + l**6/36 - l**5/20 + 4*l**3/3 + l**2. Let v(m) be the first derivative of k(m). Factor v(d).
2*d*(d - 3)**2*(d - 1)/3
Let y(l) be the third derivative of l**6/360 + 113*l**5/180 + 1045*l**4/24 - 361*l**3/2 - l**2 - 24*l. Factor y(z).
(z - 1)*(z + 57)**2/3
Let s(y) be the first derivative of y**3/9 - y**2/6 - 20*y/3 - 18. Let s(d) = 0. Calculate d.
-4, 5
Let p(k) = -119*k - 4161. Let w be p(-35). Factor 2/13*c**w - 2/13*c + 2/13*c**3 + 0 - 2/13*c**2.
2*c*(c - 1)*(c + 1)**2/13
Let m = 166/801 - -4/267. Determine g so that 0 - m*g**3 + 0*g**2 + 8/9*g = 0.
-2, 0, 2
Let j = 2326 + -4643/2. Let b(c) be the first derivative of -9 - 5*c**3 + 3/4*c**4 + 0*c + j*c**2 + 3/5*c**5. Factor b(k).
3*k*(k - 1)**2*(k + 3)
Let r(g) = -14*g - 37. Let t be r(-3). Let f(l) be the second derivative of -3/40*l**t - 1/4*l**3 + 0 + l + 1/4*l**4 + 0*l**2. Solve f(q) = 0.
0, 1
Let z(y) be the third derivative of -y**7/315 + 7*y**6/180 - y**5/15 - 8*y**4/9 + 32*y**3/9 - y**2 + 1. Determine t, given that z(t) = 0.
-2, 1, 4
Suppose 4*n - 3*h + 7 = 0, -n = 2*n + 3*h - 21. Factor 10*g**2 - 5*g**2 - 5*g**4 - 12*g**3 - 6*g + 2*g**4 - 20*g**n.
-3*g*(g + 1)**2*(g + 2)
Let p(o) be the first derivative of -2*o**4/13 + 2*o**3/13 + o**2/13 + 91. Factor p(a).
-2*a*(a - 1)*(4*a + 1)/13
Suppose 0 = 4*a - 5*s + s + 12, -s + 4 = 0. Let r(n) = -2*n**2 - 7*n + 7. Let l(p) = p**2 + p - 1. Let j(x) = a*r(x) + 3*l(x). Factor j(u).
(u - 2)**2
Solve -64 + 18 - 162*m - 30*m**2 + 12*m**3 + 297*m**2 - 23 - 48*m = 0.
-23, -1/4, 1
Let p(g) be the third derivative of 3/56*g**8 + 38*g**2 - 18/5*g**5 - 27/35*g**7 + 0*g - 8*g**4 + 0 + 53/15*g**6 + 64/3*g**3. Suppose p(d) = 0. Calculate d.
-2/3, 2/3, 1, 4
Let h(d) be the second derivative of 2*d**6/15 - d**5/5 - d**4 + 10*d**3/3 - 4*d**2 + 3*d - 15. Factor h(l).
4*(l - 1)**3*(l + 2)
Let d(l) be the first derivative of -2/11*l**4 - 4/11*l**3 - 4/11*l**2 - 2/11*l - 2/55*l**5 - 17. Solve d(z) = 0 for z.
-1
Let d(p) = 22*p - 13. Let a be d(3). Determine z so that 2*z**3 - 35*z**4 + 3*z + a*z**4 + 10*z**2 - 6*z**5 - 28*z**4 + z = 0.
-1, -2/3, 0, 1
Suppose -4*k + s - 4 = 0, -81*k = -83*k - 3*s + 12. Factor -87/4*a**3 + 0 - 9/2*a**2 + k*a - 27/4*a**4.
-3*a**2*(a + 3)*(9*a + 2)/4
Let j = 1964 - 1964. Factor -3/2*t**2 + j - 3*t.
-3*t*(t + 2)/2
Let k(t) = 5*t**2 + 21*t + 13. Let a(o) = 10*o**2 + 40*o + 25. Let v(z) = -3*a(z) + 5*k(z). Factor v(m).
-5*(m + 1)*(m + 2)
Let x(s) be the first derivative of s**8/10920 + s**7/1365 + s**6/468 + s**5/390 - 2*s**3 - 3. Let i(l) be the third derivative of x(l). Factor i(t).
2*t*(t + 1)**2*(t + 2)/13
Let j(h) be the third derivative of h**5/30 + 23*h**4/12 - 8*h**3 - 113*h**2 - 3*h. Determine k so that j(k) = 0.
-24, 1
Let g = -35 + 40. Suppose g*v - 2*f = 5, 3*v - 2*f - 2*f + 11 = 0. Find x such that -2/3*x + 0*x**2 + 2/9*x**v + 4/9 = 0.
-2, 1
Let o(j) be the second derivative of -j**7/2520 + j**6/360 - j**5/180 - 5*j**3/3 + 8*j. Let u(c) be the second derivative of o(c). Find w, given that u(w) = 0.
0, 1, 2
Let g be ((-8)/(-44) + (-80)/(-44))/(34/85). Factor -4/7*y - 22/7*y**2 + 24/7 - 1/7*y**g + 9/7*y**3 + 2/7*y**4.
-(y - 2)**3*(y + 1)*(y + 3)/7
Solve -4*j + 0 + 1/2*j**2 = 0.
0, 8
Factor 43*a**2 + 3*a**4 + 279*a - 114 - 358*a**2 + 102*a**2 + 45*a**3.
3*(a - 2)*(a - 1)**2*(a + 19)
Let x(p) be the first derivative of 22 + 39/2*p**2 + 24*p**3 + 5*p - 4*p**4. Factor x(i).
-(i - 5)*(4*i + 1)**2
Factor 14413*q - 4*q**2 - 28648*q + 14431*q.
-4*q*(q - 49)
What is b in 9/5*b + 0 - 3/5*b**2 = 0?
0, 3
Let q be 6/(-57) + 6/(3192/(-36500)). Let z = q + 69. Factor 2/7*b**4 - 6/7*b**2 - 2/7*b**3 + 4/7 + z*b.
2*(b - 2)*(b - 1)*(b + 1)**2/7
Let k(b) be the first derivative of -b**3 + 9*b**2/2 - 6*b + 99. Factor k(a).
-3*(a - 2)*(a - 1)
Let p = -1482 - -1485. Suppose -1 - 5/3*d**2 + 1/3*d**p + 7/3*d = 0. What is d?
1, 3
Factor 68/5*o + 2/5*o**3 - 48/5 - 22/5*o**2.
2*(o - 6)*(o - 4)*(o - 1)/5
Let x(q) = -1 - 3*q + 3*q + q**2. Let c(i) = 0 + 8*i**2 - 7 - 138*i + 137*i. Let y(u) = 2*c(u) - 14*x(u). Factor y(f).
2*f*(f - 1)
Factor -2/3*x**4 + 26*x**3 + 0 + 0*x + 0*x**2.
-2*x**3*(x - 39)/3
Suppose 12 = -3*f + 7*f, -3*s + 2*f = 0. Suppose -i = -s*z + i - 4, 0 = -z + 5*i - 18. Suppose -z*b**3 + 1 + 13*b**4 + 9*b**4 - 23*b**4 + 2*b = 0. What is b?
-1, 1
Suppose -t = 3*r - 0*t + 273, -3*r - 273 = 5*t. Let x be (-3)/6 - r/70*1. Determine q, given that 28/5*q**2 + 48/5 + 64/5*q + x*q**3 = 0.
-3, -2
Suppose -105 = -5*a + 2*b - 7*b, a - b = 11. Suppose 4*q = -0 + a. Factor 2*t**q - t + t**5 - 6*t**2 + 4*t**2 + 0*t.
t*(t - 1)*(t + 1)**3
Let d be (-2 - 11) + (-1375)/(-99). Factor -8/9*n**3 + 4/9*n**2 + 0 + d*n - 4/9*n**4.
-4*n*(n - 1)*(n + 1)*(n + 2)/9
Let x(i) be the third derivative of i**9/4536 - i**8/840 + i**7/420 - i**6/540 - 7*i**3/3 - 13*i**2. Let n(z) be the first derivative of x(z). Factor n(v).
2*v**2*(v - 1)**3/3
Factor 7*i**2 - 4*i - 12*i**2 - 3*i**4 + 4*i**4 + i**3 + 7*i.
i*(i - 1)**2*(i + 3)
Let b be (5/4*-2)/((-1)/14). Let u be 83/b + 8/(-14). Solve -3/5*m**2 - u*m + 0 = 0 for m.
-3, 0
Let x(l) be the first derivative of -l**4/3 + l**3/6 + 3*l**2/2 + 48*l - 22. Let w(s) be the first derivative of x(s). Factor w(g).
-(g - 1)*(4*g + 3)
Let u = 84692/14777 - 36/2111. Suppose -36/7 - u*s**2 + 12/7*s**3 + 2/7*s**5 - 78/7*s + 12/7*s**4 = 0. What is s?
-3, -1, 2
Let g(r) be the third derivative of -r**7/315 - r**6/30 - r**5/18 - 48*r**2. Factor g(n).
-2*n**2*(n + 1)*(n + 5)/3
Suppose -18*j = 75*j + 21*j. Factor -2/3*p**2 + j*p**3 + 0*p + 2/3*p**4 + 0.
2*p**2*(p - 1)*(p + 1)/3
Factor 164*b + 22*b**2 - 127*b**2 + b**3 + 3*b**3 - 104 + 41*b**2.
4*(b - 13)*(b - 2)*(b - 1)
Suppose 0 = -3*g - 13 + 22. Suppose g*x - 3*u - 16 = -1, 0 = -3*x - 3*u - 3. Suppose -3/2*m - 1/2*m**4 - 1/3 - 11/6*m**3 - 5/2*m**x = 0. Calculate m.
-1, -2/3
Let i be (1 - 199/120) + (-26)/(-39). Let d(t) be the third derivative of 3*t**2 + 0*t**3 + 1/180*t**5 + 0*t - i*t**6 + 1/36*t**4 + 0. Let d(v) = 0. What is v?
-2/3, 0, 1
Let c be (2/135)/((-80)/(-800))*3. Factor 4/9*r**2 + 4/9*r - 4/9*r**3 + 0 - c*r**4.
-4*r*(r - 1)*(r + 1)**2/9
Solve -16 + 33/2*q**3 + 44*q - 9/4*q**4 - 169/4*q**2 = 0.
1, 8/3
Let y = 6974/3 - 2322. Factor -y + 20/3*t - 4*t**2.
-4*(t - 1)*(3*t - 2)/3
Let g = -2361 + 2365. Factor 8*w + g*w**2 + 16/3 + 2/3*w**3.
2*(w + 2)**3/3
Let m = 12/187 - -477/1309. Factor m*j + 0*j**2 - 1/7*j**3 + 2/7.
-(j - 2)*(j + 1)**2/7
Factor 13*r + 50 - 22*r + 34 - 7*r - 4*r**2.
-4*(r - 3)*(r + 7)
Suppose 182 = -3*v - 5*g + 147, -5*v = -3*g - 21. Let y be ((-9)/(-14))/((-18)/(-21)). Solve 0*z + 0 + y*z**5 - 9/2*z**4 + 27/4*z**3 + v*z**2 = 0.
0, 3
Let c(h) = h**4 + 11*h**3 - 6*h**2 - 6*h - 6. Let v(r) = -2*r**4 - 12*r**3 + 7*r**2 + 7*r + 7. Let q(s) = -7*c(s) - 6*v(s). Solve q(y) = 0 for y.
0, 1
Let r(p) be the first derivative of -2*p**5/65 - 4*p**4/13 + 20*p**3/39 + 8*p**2/13 - 18*p/13 - 323. Find q such that r(q) = 0.
-9, -1, 1
Let t(n) = -n**2 - 16*n - 57. Let b be t(-6). Find x such that 0*x**b + 2/11*x**4 + 0*x - 2/11*x**2 + 0 = 0.
-1, 0, 1
Let u be 2/(-5)*5/(-9). Let i = -28702 + 258322/9. Determine a so that -u*a**2 + i - 2/9*a = 0.
-2, 1
Let -30*l + 87/2*l**2 - 15*l**3 + 0 + 3/2*l**4 = 0. Calculate l.
0, 1, 4, 5
Let m(d) be the second derivative of d**7/840 - d**6/144 + d**5/60 - d**4/48 - 6*d**3 + 33*d. Let w(a) be the second derivative of m(a). Factor w(p).
(p - 1)**2*(2*p - 1)/2
Let a(y) = y. Let s(t) = t**2 - 5*t. Suppose -5*q - 40 = 5*o, q = o + 3*q + 13. Let d(i) = o*a(i) - s(i). Suppose d(g) = 0. Calculate g.
0, 2
Let h(f) be the second derivative of -f**6/80 - f**5/20 + f**4/16 + f**3/2 - 2*f**2 - 2*f. Let i(u) be the first derivative of h(u). Factor i(s).
-3*(s - 1)*(s + 1)*(s + 2)/2
Let g(j) = j**2 - j - 1. Let n(b) = 2*b**2 - 126*b + 88. Let h