2)/22. Determine c, given that 6*c**2 - 10*c - 2*c**2 + j*c - 2*c**3 = 0.
0, 1
Let y(c) be the second derivative of 2*c - 1/42*c**4 + 0 + 0*c**2 + 2/21*c**3. Factor y(n).
-2*n*(n - 2)/7
Let h(f) be the third derivative of f**9/20160 + f**8/3360 + f**7/1680 - 13*f**5/60 + 9*f**2. Let k(n) be the third derivative of h(n). Factor k(b).
3*b*(b + 1)**2
Factor 1/3*x**2 - 38/3*x + 361/3.
(x - 19)**2/3
Let k be 34/14 - 12/(-21). Find w such that -15 + 6*w**3 + 5*w**3 + 5*w**3 - 21*w**k - 35*w - 25*w**2 = 0.
-3, -1
Let 20/11*l + 78/11 - 2/11*l**2 = 0. What is l?
-3, 13
Let t = -100 - -103. Factor 4*v + 8 + 12 - 20*v**2 - 8*v - v**t + 5*v**3.
4*(v - 5)*(v - 1)*(v + 1)
Determine n, given that 46*n - 36*n**3 + 4*n**4 - 248*n**2 + 1584 - 1808 - 478*n = 0.
-2, -1, 14
Let o(y) be the second derivative of -1/27*y**4 + 1/135*y**6 - 8/9*y**2 - 4/9*y**3 + 0 + 1/30*y**5 + y. What is u in o(u) = 0?
-2, -1, 2
Suppose 6*u = 132 - 114. Let b be 0 + 9/2 - u. Solve 1/2*g**4 + 0 + 1/2*g + b*g**2 + 3/2*g**3 = 0 for g.
-1, 0
Suppose 39*q**3 - 48 + 3*q**4 - 110*q**2 + 55*q + 49*q - 25*q**2 + 58*q - 21*q = 0. Calculate q.
-16, 1
Let s(c) be the second derivative of -c**6/4 + 21*c**5/40 + 13*c**4/4 - 7*c**3 - 18*c**2 - 113*c. Let s(g) = 0. Calculate g.
-2, -3/5, 2
Suppose -9 + 9 = 37*p. Let x = 9 + -6. Let -2/5*y**x + 6/5*y + 4/5 + p*y**2 = 0. Calculate y.
-1, 2
Suppose -5*b - 8 + 23 = 0. Find m, given that -7*m**3 - 6*m - b*m**2 + 14*m**3 - 4*m**3 = 0.
-1, 0, 2
Suppose -t + 2*t = 14. Let q be (-382)/(-56) + -7 + 6/t. Let -3/4*d**2 - q*d + 1/4*d**4 + 1/4*d**3 + 1/2 = 0. What is d?
-2, -1, 1
Suppose 4*a - 1 = 5*w, 7*a - 2*a = 4*w - 1. Let t(y) = -3*y**3 - 3*y**2 + 9*y + 6. Let o(k) = -k**2. Let s(c) = a*t(c) + 3*o(c). Factor s(h).
3*(h - 2)*(h + 1)**2
Let p(u) be the third derivative of 0 + 0*u**4 + 1/90*u**6 + 0*u + 4*u**2 + 1/15*u**5 - 1/3*u**3. Let i(t) be the first derivative of p(t). Factor i(n).
4*n*(n + 2)
Let z(k) = 0*k**2 + 2*k**4 - 9*k**2 + 11*k**4 + 7*k**3 - 9*k - 6*k**4. Let n(o) = -2*o**4 - 2*o**3 + 2*o**2 + 2*o. Let j(r) = 9*n(r) + 2*z(r). Factor j(c).
-4*c**3*(c + 1)
Let q(i) = -5*i**3 + 2*i**2 + 6*i. Let h(p) = 9*p**3 - 4*p**2 - 11*p. Let x(j) = -6*h(j) - 11*q(j). Find r such that x(r) = 0.
-2, 0
Suppose -17/4*m + 1/4*m**3 + 0 - 4*m**2 = 0. What is m?
-1, 0, 17
Let i(a) = a + 0*a**5 - 6*a**2 + 6*a**4 - a**4 + 2*a**3 - 2 - a**4 - 3*a**5. Let z(r) = r**4 - r**3 + r + 1. Let j(u) = i(u) + 2*z(u). Factor j(o).
-3*o*(o - 1)**3*(o + 1)
Find t such that 525*t - 25*t**2 - 6125/3 + 1/3*t**3 = 0.
5, 35
Let x(u) be the second derivative of -u**8/23520 + u**7/1470 + u**6/360 + 3*u**4 - 38*u. Let k(q) be the third derivative of x(q). Suppose k(n) = 0. What is n?
-1, 0, 7
Let s(k) be the first derivative of -k**8/1176 + k**6/140 + k**5/105 - 19*k**2 + 2. Let i(p) be the second derivative of s(p). Let i(w) = 0. Calculate w.
-1, 0, 2
Factor 8*b + 2 + 23 - 15 - 2*b**2.
-2*(b - 5)*(b + 1)
Let x = -639 - -639. Let b(j) be the third derivative of 0*j + 0*j**7 + 0*j**3 + 8*j**2 - 1/588*j**8 + 0 + 1/70*j**6 + x*j**4 - 2/105*j**5. Solve b(z) = 0.
-2, 0, 1
Let o(i) be the second derivative of -i**4/54 - 4*i**3/27 - 4*i**2/9 - 12*i. Determine g so that o(g) = 0.
-2
Suppose -4*h - 30 = 3*q, 4*h + 68 = -4*q + 8*h. Let p be (q/(-8) - 1)/((-4)/(-16)). Suppose 20/7*b**2 + 4/7*b - 14*b**4 - b**p + 0 = 0. What is b?
-2/7, 0, 1/2
Let l(a) be the third derivative of -a**7/5040 - a**6/720 - a**5/360 + a**3/2 - 15*a**2. Let s(m) be the first derivative of l(m). Factor s(g).
-g*(g + 1)*(g + 2)/6
Let -7/5*j**3 + 103/5*j**2 - 28/5 - 68/5*j = 0. Calculate j.
-2/7, 1, 14
Let d = -1 + 4. Let i be (-4)/(-16)*-4 - -5. Factor -1/2*h**5 + 0*h - i*h**2 - 6*h**3 + 0 - d*h**4.
-h**2*(h + 2)**3/2
Let u(l) be the second derivative of -l**5/60 - 23*l**4/36 - 80*l**3/9 - 50*l**2 - 183*l. Let u(n) = 0. Calculate n.
-10, -3
Let j(h) = -2*h**3 + 30*h**2 + 6. Let i(p) = -5*p**3 + 60*p**2 + 10. Let v(f) = 3*i(f) - 5*j(f). Factor v(y).
-5*y**2*(y - 6)
Let b(c) = c**4 - 25*c**3 + 5*c**2 - 5*c + 5. Let d(u) = -12*u**3 + 3*u**2 - 3*u + 3. Let g(t) = 3*b(t) - 5*d(t). Factor g(n).
3*n**3*(n - 5)
Let c(t) be the third derivative of t**8/1008 - t**7/90 + t**6/20 - 11*t**5/90 + 13*t**4/72 - t**3/6 - 48*t**2. Find r, given that c(r) = 0.
1, 3
Let r = -34 + 36. Suppose 4*g - 3*u = 0, 4*g + 2*u = 2*g. Let 3*c**2 - 2 + r*c + g - 2*c**2 - 3*c = 0. What is c?
-1, 2
Let v(w) = 60*w**2 + 350*w. Let s(l) = -21*l**2 - 117*l. Let r(d) = -17*s(d) - 6*v(d). Find u, given that r(u) = 0.
-37, 0
Let p(t) = -11*t**5 - 2*t**4 - 16*t**3 + 8*t**2 + 8*t + 4. Let l(d) = -3*d**5 + d**4 + 2*d**2 + 2*d + 1. Let o(r) = 4*l(r) - p(r). What is f in o(f) = 0?
-2, 0, 8
Let h be ((-180)/15 - -14)/(2 - (1 + -2)). Factor -h*a**2 + 2*a - 4/3.
-2*(a - 2)*(a - 1)/3
Solve z**3 + 23*z + 620 - 14*z**2 + 17*z - 620 = 0 for z.
0, 4, 10
Suppose -b + 3*s = -19, -6 = -3*b + s + 11. Suppose 0 = -0*f + b*f. Factor -1/2*m**2 + 0 - 1/2*m**3 + f*m.
-m**2*(m + 1)/2
Let i(m) be the second derivative of 3*m**5/100 + 9*m**4/20 + 12*m**3/5 + 24*m**2/5 + 99*m. Factor i(g).
3*(g + 1)*(g + 4)**2/5
Let p(g) = -g**4 - 33*g**3 + 18*g**2 + 20. Let h(i) = -6*i**4 - 165*i**3 + 90*i**2 + 96. Let n(a) = 5*h(a) - 24*p(a). Find c, given that n(c) = 0.
-6, 0, 1/2
Suppose 15*j - 805 + 398 = -407. Factor 16/5*q**4 + j + 4/5*q**5 + 4/5*q + 24/5*q**3 + 16/5*q**2.
4*q*(q + 1)**4/5
Factor -63*o**4 - 5*o**3 - 1102*o**2 - 12*o**4 + 675*o**3 - 146*o**2 - 1152*o.
-o*(3*o + 2)*(5*o - 24)**2
Let z be 9 + (6/(-51) - (-6759)/(-1071)). What is k in 3/7*k**2 + 27/7 + z*k = 0?
-3
Suppose 20*b + 217 = 572 - 295. Find n, given that -2/13*n - 2/13*n**4 + 0 + 2/13*n**b + 2/13*n**2 = 0.
-1, 0, 1
Let v(b) = -2*b**3 - 3 - b**2 + 0 + 3*b**3 + 0*b**3. Let m(o) = o**2 + 1. Let h(c) = -3*m(c) - v(c). Determine d so that h(d) = 0.
-2, 0
Let g = -38 + 44. Suppose 4*h = 4*r + 2 + g, h - 2 = -r. Determine j, given that 0*j + r + 3/4*j**2 = 0.
0
Let d be 10/(-20)*0/16. Factor 0*p + d + 0*p**2 - 1/5*p**4 + 1/5*p**3.
-p**3*(p - 1)/5
Let o(z) = -7*z**3 - 6*z**2 - 3*z + 6. Let n(a) = 10*a**3 + 9*a**2 + 4*a - 9. Let m(c) = -5*n(c) - 7*o(c). Suppose m(t) = 0. What is t?
-3, -1, 1
Let d(z) be the third derivative of z**6/96 + 29*z**5/48 - 5*z**4/96 - 145*z**3/24 + 2*z**2 + 32*z. Let d(n) = 0. Calculate n.
-29, -1, 1
Let z(t) = -8*t**2 - 3*t + 2. Let b be z(2). Let c be (-24)/b - (-7)/3. Find s, given that c*s**3 + 3*s**2 + 9*s + 2*s**2 - 1 - 8*s = 0.
-1, 1/3
Factor 1/5*h**2 + 0 + 1/5*h**3 - 12/5*h.
h*(h - 3)*(h + 4)/5
Let j be 3 - (-2)/6*12/(-2). Let p(f) = 6*f**2 - 2*f. Let b be p(j). Solve 2*c**b - 4*c**5 + 1/4*c**2 + 0 + 0*c + 7/4*c**3 = 0 for c.
-1/4, 0, 1
Suppose -9 = 2*x - 97. Factor -13*n + 25*n**2 - x*n**3 - 8 + 3*n + 55*n**2 - 18*n.
-4*(n - 1)**2*(11*n + 2)
Let c(k) = -4*k**3 - 396*k**2 + 4364*k - 15964. Let o(g) = -2*g**3 - 132*g**2 + 1455*g - 5321. Let r(u) = 3*c(u) - 8*o(u). Determine b so that r(b) = 0.
11
Let v(y) be the first derivative of -y**5/10 - 3*y**4/8 + 13*y**3/6 + 15*y**2/4 + 234. Find n, given that v(n) = 0.
-5, -1, 0, 3
Let a(v) = -2*v**2 - 79*v - 112. Let l be a(-38). Factor 0*u + 8/3 - 2/3*u**l.
-2*(u - 2)*(u + 2)/3
Let c(w) be the second derivative of w**8/840 + w**7/210 - w**6/45 - 2*w**5/15 - 7*w**3/2 + 19*w. Let n(j) be the second derivative of c(j). Factor n(y).
2*y*(y - 2)*(y + 2)**2
Suppose -v + 2 = 1, 25 = 4*z + 5*v. Suppose -z*g = -4*w + 5, -5*w - 4*g + 0 = 4. Factor 2/7*d**2 - 2/7 + w*d.
2*(d - 1)*(d + 1)/7
Factor -1/3*l**4 + 80/3*l - 11 + 16/3*l**3 - 62/3*l**2.
-(l - 11)*(l - 3)*(l - 1)**2/3
Let c be (-2)/9 + 1190/90. Suppose c - 1 = 4*v. What is k in -3*k**4 - v*k + 3*k + 5*k**3 - 11*k**3 - 3*k**2 = 0?
-1, 0
Suppose 0 = a - 4*y - 14, -3*a + 3*y = -0*a - 15. Let h be 1 - (a - 0) - -4. Determine p, given that 0*p - p - 3*p**2 - 2*p - h*p - 3 = 0.
-1
Let l(p) be the third derivative of -p**7/1260 - p**6/90 - p**5/15 + 7*p**4/24 + 12*p**2. Let r(g) be the second derivative of l(g). What is j in r(j) = 0?
-2
Let s(u) be the first derivative of 4*u**6/105 - 3*u**5/70 - u**4/42 - 6*u - 11. Let l(y) be the first derivative of s(y). Factor l(i).
2*i**2*(i - 1)*(4*i + 1)/7
Suppose -2*i = -5*n + 14, -3*i - n - 31 = 7. Let y = 20 + i. What is u in -2 + 7*u**3 + 4 - y*u**3 + 3*u = 0?
-1, 2
Factor -8*