50/7*c**4 + d*c = 0. Calculate c.
-2, -1, 2/5
Let d(j) be the first derivative of 10 - 2/7*j**4 - 2/7*j - 6/7*j**3 - 6/7*j**2. Factor d(x).
-2*(x + 1)**2*(4*x + 1)/7
Suppose 54*y - 113*y = -55*y. Find k such that 0*k - 4/7*k**4 + 0 + y*k**3 + 0*k**2 + 2*k**5 = 0.
0, 2/7
Let b be -8*((-10)/(-4) - (-36)/(-12)). Let i**2 + 6*i**4 - b*i**2 - 10*i**4 + i**4 - 6*i**3 = 0. Calculate i.
-1, 0
Let k(a) be the first derivative of 1/240*a**6 - 1/8*a**4 + 0*a - 1/80*a**5 - 1 + 1/3*a**3 + 0*a**2. Let t(j) be the third derivative of k(j). Factor t(n).
3*(n - 2)*(n + 1)/2
Suppose -3*x = -6*x + 12, 5*x - 4 = 4*l. Let s = l + -3/2. Factor 1/2*v**3 - s*v - 3/2*v**2 + 1/2*v**4 - 1.
(v - 2)*(v + 1)**3/2
Suppose 3*a + 7*a + 241 = 301. What is p in -9/4 + 9/4*p**2 + a*p = 0?
-3, 1/3
Let g(o) be the first derivative of 8/21*o**3 + 0*o - 4/7*o**2 + 5 - 1/14*o**4. Factor g(q).
-2*q*(q - 2)**2/7
Let d = -1262 + 2525/2. Factor 0 + 0*p + d*p**3 + p**2 - 1/2*p**4.
-p**2*(p - 2)*(p + 1)/2
Let h(r) be the second derivative of 36*r + 0 + 1/2*r**5 + 1/6*r**6 + 0*r**3 + 5/12*r**4 + 0*r**2. Determine j, given that h(j) = 0.
-1, 0
Suppose -3*b + 54 = -39. Let p = 0 + b. Suppose -t**2 - 6*t**3 - p*t**5 + 39*t**5 - t**2 = 0. Calculate t.
-1/2, 0, 1
Let q(j) be the second derivative of -j**4/48 - 7*j**3/24 + 9*j**2/4 - 19*j + 3. Factor q(m).
-(m - 2)*(m + 9)/4
What is n in -3/4*n**2 - 3/4*n + 0 = 0?
-1, 0
Factor 0*b - 2*b**2 - 1/2*b**5 - 3*b**4 + 0 - 9/2*b**3.
-b**2*(b + 1)**2*(b + 4)/2
Let b(w) = -w**3 + 16*w**2 + 16*w + 19. Let l be b(17). Suppose 3*a - 2*x = 7, 0 = -x + 3*x - l. Find m such that 3 + 291/4*m**2 + 12*m**4 - 54*m**a - 27*m = 0.
1/4, 2
Let n(b) be the first derivative of -8*b**5/5 - 29*b**4/2 - 94*b**3/3 - 10*b**2 + 148. Let n(o) = 0. What is o?
-5, -2, -1/4, 0
Let o be 1/28 - (-1)/4. Determine g so that -16/7 + o*g**3 + 24/7*g - 12/7*g**2 = 0.
2
Find j such that -j**2 - 13/7*j + 1/7*j**4 - 6/7 + 1/7*j**3 = 0.
-2, -1, 3
Let k(o) = -o**3 + 5*o**2 + 10*o - 19. Let t be k(6). Let p(a) be the first derivative of -5 + 0*a - 10*a**3 + 2*a**2 + 12*a**4 + 32/5*a**t. Factor p(d).
2*d*(d + 2)*(4*d - 1)**2
Let i = -11 - -13. Factor -2*v**2 - 3*v + v**5 - 1 + 2*v**3 + v**i + 3*v**4 - v**2.
(v - 1)*(v + 1)**4
Let n(u) be the first derivative of -u**8/1008 + u**7/315 - u**5/90 + u**4/72 - 23*u**2/2 - 12. Let h(x) be the second derivative of n(x). Factor h(k).
-k*(k - 1)**3*(k + 1)/3
Let m(y) be the third derivative of -y**7/1365 - y**6/390 + y**5/26 - y**4/39 - 20*y**3/39 - 82*y**2. Find d, given that m(d) = 0.
-5, -1, 2
Let t(h) = -4*h**3 + 3*h**2 + 15*h - 8. Let v = 97 + -98. Let a(d) = d**2 + d. Let c(x) = v*t(x) + 3*a(x). Solve c(z) = 0 for z.
-2, 1
Let b be 10/25*5 + 1. Factor 6 - 12*i**3 + 9*i + b*i**3 + 6*i**3.
-3*(i - 2)*(i + 1)**2
Factor 0 + 14/3*j**3 + 2/3*j**4 + 0*j + 0*j**2.
2*j**3*(j + 7)/3
Let w(o) be the first derivative of -o**3/5 - 93*o**2/5 - 183*o/5 - 579. Factor w(u).
-3*(u + 1)*(u + 61)/5
Let i(r) be the second derivative of r**4/16 + 49*r**3/4 + 7203*r**2/8 - 52*r. Find q such that i(q) = 0.
-49
Let k(l) be the first derivative of l**6/10 + 9*l**5/20 + 3*l**4/4 + l**3/2 - 19*l - 13. Let z(x) be the first derivative of k(x). Factor z(m).
3*m*(m + 1)**3
Let v(n) = -3*n**2 + 18*n + 12. Let u(q) = 2*q**2 - 18*q - 10. Let x(m) = 6*u(m) + 5*v(m). Factor x(i).
-3*i*(i + 6)
Let p(y) = -2*y**2 + 3*y + 3. Let k(i) = -i**2 + i + 1. Let d(s) = -5*k(s) + 2*p(s). Let c(q) = 8*q**2 + 16*q + 6. Let o(f) = -2*c(f) + 20*d(f). Factor o(x).
4*(x - 2)*(x - 1)
Let z(p) = -6*p**2 - 21*p + 192. Let h(i) = -7*i**2 - 16*i + 192. Let c(g) = 3*h(g) - 4*z(g). Factor c(k).
3*(k - 4)*(k + 16)
Let r(a) be the first derivative of -10 + 4/5*a + 4/15*a**3 + a**2. Find k, given that r(k) = 0.
-2, -1/2
Let f(b) = 3*b**2 - 3*b - 6. Let n(l) = l**2. Let t(z) = -2*z**2 - 2*z - 6. Let c(x) = -6*n(x) - t(x). Let k(w) = 5*c(w) + 6*f(w). Factor k(m).
-2*(m + 1)*(m + 3)
Let b = 2 + 2. Suppose -3*c - 2*d = -4*c + 12, -18 = -b*c + 2*d. Factor -12 - 7*y - 3*y**c - 3*y - 2*y.
-3*(y + 2)**2
Let u(z) = z + 12. Let r be u(-10). Factor 20 - 8*p**r - 55*p + 3 - 3 - 7*p**2.
-5*(p + 4)*(3*p - 1)
Factor 25*x + 5*x**5 + 39 + 28 - 30*x**3 - 52 - 5*x**4 - 10*x**2.
5*(x - 3)*(x - 1)*(x + 1)**3
Let f = 37 - 25. Determine z, given that -f*z**3 + 11*z**2 + 0*z**3 - 39*z**2 - 8*z = 0.
-2, -1/3, 0
Let l(h) be the second derivative of 7*h**5/220 - h**4/11 - 25*h**3/66 - 3*h**2/11 - 90*h. Let l(y) = 0. Calculate y.
-1, -2/7, 3
Let k(x) be the first derivative of 14 + 10*x - 5*x**3 - 5/2*x**2. Let k(p) = 0. Calculate p.
-1, 2/3
Factor 60*n**3 + 12*n**2 + 23*n**5 - 36*n**4 - 12*n**2 - 20*n**5.
3*n**3*(n - 10)*(n - 2)
Let n be 0/(-1 + 12 + -10). Suppose 2/21*o**3 + 0 - 2/21*o + n*o**2 = 0. Calculate o.
-1, 0, 1
Let s be ((-152)/(-133))/((-66)/(-21)). Factor -2/11*d**5 + 0 + 0*d**4 + 6/11*d**3 + 0*d - s*d**2.
-2*d**2*(d - 1)**2*(d + 2)/11
Let f(m) be the third derivative of m**5/90 + 31*m**4/18 + 961*m**3/9 + 224*m**2. Let f(y) = 0. What is y?
-31
Let s(w) be the first derivative of -w**7/126 - 15*w - 5. Let u(d) be the first derivative of s(d). Factor u(g).
-g**5/3
Let k(d) = 2*d**2 - 3*d - 4. Let x be k(4). Let c be (4/10)/(x/80). Suppose 7*h - 2 - h + h - 3*h**c = 0. What is h?
1/3, 2
Let u(k) be the first derivative of k**3/6 - 53*k**2/8 + 13*k/2 + 7. Factor u(w).
(w - 26)*(2*w - 1)/4
Let s(g) = -25*g**2 + 50*g - 50. Let l(n) = 8*n**2 - 17*n + 11*n**2 + 25 - 11*n**2 - 8. Let b(j) = 10*l(j) + 3*s(j). Factor b(y).
5*(y - 2)**2
Factor 0 - 9/2*l**3 + 3/4*l**2 + 9/2*l - 3/4*l**4.
-3*l*(l - 1)*(l + 1)*(l + 6)/4
Let w(d) be the first derivative of -d**3/12 - 59*d**2/2 - 3481*d + 416. Factor w(s).
-(s + 118)**2/4
Factor 40/9*w + 4 + 4/9*w**2.
4*(w + 1)*(w + 9)/9
Let r = 2353 - 2350. Determine t so that -3/5*t**4 + 12/5*t + 3*t**r + 0 - 24/5*t**2 = 0.
0, 1, 2
Let w(v) = 3*v**4 - 41*v**3 + 100*v**2 + v. Let p(r) = 0*r**4 - 20*r**3 + 0*r**4 + 21*r**3 - r + r**4. Let d(j) = -p(j) - w(j). Factor d(g).
-4*g**2*(g - 5)**2
Suppose l - 5*p + 3*p + 1 = 0, -15 = -3*p. Let s be l/(-36) + 3/4. Factor 1/2*w**3 - 3/2 - s*w + 3/2*w**2.
(w - 1)*(w + 1)*(w + 3)/2
Suppose -1372 + 1702 = 66*t. Let 1/6*g**t + 3 + 2/3*g**4 - 11/3*g**2 + 1/2*g - 2/3*g**3 = 0. What is g?
-3, -1, 1, 2
Suppose -27 = -6*l + 21. Let w be (l/6)/(((-2)/3)/(-1)). Factor -3/4*i**w + 0*i + 3/4.
-3*(i - 1)*(i + 1)/4
Let a = 4 + 1. Suppose -5*q + 1 + a = -o, -4*q = -2*o. Determine n, given that q*n - 9*n**2 - 1 - 7*n**2 + 5 + 10*n**3 = 0.
-2/5, 1
Let j(u) be the second derivative of -1/3*u**3 + 0 + 3*u - 1/6*u**4 + 2*u**2. Factor j(d).
-2*(d - 1)*(d + 2)
Let y be 4/26 + ((-287)/91 - -5). Factor 0*l**y + 1/5*l**4 + 0 - 2/5*l**3 + 0*l.
l**3*(l - 2)/5
Let o be 3784/(-336) - -12 - 2*(-2)/(-24). Determine z, given that -1/7*z**5 + 0 - o*z**3 + 0*z - 4/7*z**4 + 0*z**2 = 0.
-2, 0
Suppose -3*z + 7*z = 84. Let u be 9/z + (122/42 - 3). Factor u*p**3 + 0*p + 1/6*p**4 + 1/6*p**2 + 0.
p**2*(p + 1)**2/6
Let v be -3 + (-54)/(-4)*((-52)/30 - -2). Factor 0*n**2 - 1/5*n**3 + v*n + 2/5.
-(n - 2)*(n + 1)**2/5
Let w be ((-2)/(-13))/((-170)/(-4420)). Factor -9/5*r**3 - 4/5 - 7/5*r**2 + w*r.
-(r - 1)*(r + 2)*(9*r - 2)/5
Let l(q) = 2*q**2 - 38*q - 156. Let y(p) = 6*p**2 - 77*p - 313. Let c(i) = 5*l(i) - 2*y(i). Determine v, given that c(v) = 0.
-11, -7
Let k = 9 + -7. Find o, given that -2*o + 1 + 0*o**3 - 36*o**4 + 35*o**4 + k*o**3 = 0.
-1, 1
Suppose -5*x = 2*n - 115 + 36, -4*x + 38 = n. Factor 80 - 75*d + 5*d**4 - n*d - 43*d + 120*d**2 - 40*d**3 + 0*d**4.
5*(d - 2)**4
Suppose 3*x + 9 = 3*l - 3, 5*x + 20 = 4*l. Suppose l*u + 5*u = 105. Solve 10*a**2 - u*a**2 + 12*a**2 + 2*a + 1 = 0 for a.
-1
Let y(u) = -u**2 + 9*u + 23. Let i be y(10). Determine l so that -13 - 26*l**2 + 20*l + 14*l**2 + 10*l**3 + 8 - i*l**2 = 0.
1/2, 1
Factor -11/5*c**2 - 5 - 7*c - 1/5*c**3.
-(c + 1)*(c + 5)**2/5
Let u(x) = x**2 - 32*x + 233. Let c be u(21). Factor 1/2*k**2 - c + 0*k.
(k - 2)*(k + 2)/2
Let k(l) be the third derivative of -l**6/60 - 23*l**5/30 - 143*l**4/12 - 121*l**3/3 - 52*l**2 + 3. Find o, given that k(o) = 0.
-11, -1
Let w(d) be the third derivative of 0 - 1/3*d**5 - 8/3*d**3 + 4/3*d**4 + 0*d + 1/30*d**6 + 15*d**2. Solve w(r) = 0.
1, 2
Let h be (-12 - 1360/(-119))/(-2 - (-13)/7). Determine u so that 10/7*u**3 + 2/