he first derivative of -2*m**3/3 + 13*m**2 - 24*m - 17. Determine c so that v(c) = 0.
1, 12
Let s = -233 - -233. Let d(h) be the third derivative of 0*h**3 + 0*h**4 + s + 1/20*h**5 + 0*h + 1/120*h**6 - h**2. Factor d(l).
l**2*(l + 3)
Let n be 5 + -1 + 1498/(-6). Let z = n + 246. Factor q**2 + 0 + z*q**3 + 2/3*q.
q*(q + 1)*(q + 2)/3
Let f(w) = -3*w**2 + 365*w + 7. Let n(h) = -2*h**2 + 247*h + 5. Let t(m) = 5*f(m) - 7*n(m). Factor t(r).
-r*(r - 96)
Let w(r) = r**2 - 95*r - 821. Let j be w(-8). Let -8/3*z**j + 6*z**2 + 1/3*z**4 + 0*z - 9 = 0. What is z?
-1, 3
Let q = 2321/1358 - -1/194. Let i(w) be the first derivative of -48/7*w - q*w**2 - 1/7*w**3 - 1. Let i(c) = 0. Calculate c.
-4
Let b be 3/30*6 - (-6 - 4376/(-760)). Find k, given that 20/19*k**3 + b*k - 2/19*k**4 + 0 - 34/19*k**2 = 0.
0, 1, 8
Let p = 7917/4 + -1979. Factor 0 + p*f + 1/4*f**2.
f*(f + 1)/4
Suppose 4*q - 5*h - 4 = 0, -4*q + 1 = -4*h - 3. Let i be q + (-42)/36 - (-6)/4. Factor 2/3*z**3 - 2/3*z + 4/3 - i*z**2.
2*(z - 2)*(z - 1)*(z + 1)/3
Factor h**3 - 4/7 - 8/7*h + 3/7*h**2 + 2/7*h**4.
(h - 1)*(h + 2)**2*(2*h + 1)/7
Let r(f) be the second derivative of f**5/70 + 19*f**4/7 + 160*f**3 + 896*f**2 + 227*f. Let r(m) = 0. Calculate m.
-56, -2
Let q(k) be the third derivative of k**9/420 + k**8/280 + k**7/630 + 5*k**4/12 - 9*k**2. Let g(w) be the second derivative of q(w). Factor g(c).
4*c**2*(3*c + 1)**2
Let v(d) = -d**3 - d**2 + d - 1. Let j(b) = 3*b**5 - 33*b**4 - 161*b**3 - 215*b**2 - 94*b + 4. Let m(c) = j(c) + 4*v(c). Find k such that m(k) = 0.
-2, -1, 0, 15
Let y(a) be the third derivative of a**5/100 + 9*a**4/20 + 81*a**3/10 - 4*a**2 + 6*a. Factor y(v).
3*(v + 9)**2/5
Let 5/4*o + 7/2 + 1/4*o**3 - 2*o**2 = 0. Calculate o.
-1, 2, 7
Let t(x) be the first derivative of 0*x + 0*x**2 + 2/51*x**3 - 16. Suppose t(w) = 0. What is w?
0
Factor 481*o**2 - 238*o**2 - 16*o - 242*o**2 + 16 + 12.
(o - 14)*(o - 2)
Let c(x) be the first derivative of 3*x**4/28 + 15*x**3 + 1575*x**2/2 + 18375*x - 115. Suppose c(o) = 0. Calculate o.
-35
Let n(q) be the third derivative of q**5/240 - 5*q**4/32 + 13*q**3/12 + 2*q**2 - 2*q. Factor n(b).
(b - 13)*(b - 2)/4
Factor -1 + 56*f - 220*f**2 + 1 + 448*f**3 + 15*f - 121*f - 192*f**4.
-2*f*(4*f - 5)**2*(6*f + 1)
Let c(b) be the first derivative of 2/3*b**2 + 0*b + 14/27*b**3 - 14 + 1/18*b**4. Solve c(t) = 0 for t.
-6, -1, 0
Let -153/5 - 1/5*o**2 - 54/5*o = 0. What is o?
-51, -3
Let l(f) be the first derivative of 3/2*f - 3/16*f**4 + 0*f**3 + 9/8*f**2 - 11. Factor l(p).
-3*(p - 2)*(p + 1)**2/4
Find b, given that 39/2*b - 21 + 3/2*b**2 = 0.
-14, 1
Let w(a) be the second derivative of 9/11*a**3 - 3/22*a**4 + 4*a - 3/110*a**5 + 1/165*a**6 + 0*a**2 + 4. Solve w(c) = 0 for c.
-3, 0, 3
Let x(s) = 17*s**2 + 33*s + 12. Let a(c) be the first derivative of -3*c**3 - 17*c**2/2 - 6*c + 14. Let r(j) = -11*a(j) - 6*x(j). Factor r(v).
-(v + 3)*(3*v + 2)
Let u = -2 - -6. Determine x, given that -2254 + 2251 - 3*x**3 + 15*x**2 - 2*x**u - x - 6*x**2 = 0.
-3, -1/2, 1
Let w(x) = -x**3 + x**2 - x. Let f(q) = -5*q**4 - 36*q**3 + 46*q**2 + 24*q - 35. Let u(s) = -f(s) + 6*w(s). Factor u(j).
5*(j - 1)**2*(j + 1)*(j + 7)
Let a(g) = -4*g**2 - g + 15. Let p(x) = -5*x**2 - 2*x + 15. Let q(w) = 4*a(w) - 3*p(w). Let q(l) = 0. What is l?
-3, 5
Suppose 4*k - 11 = o, -k = -2 - 2. Suppose 4*s - 4*i = 16, o*s - i - 8 = -2*i. Factor -4*m**2 + 2*m**3 + 4*m**2 + 2*m**s + 2*m**2.
2*m**2*(m + 2)
Factor 10/17*k**2 + 2/17*k**3 + 0 + 0*k.
2*k**2*(k + 5)/17
Let i(x) = -x**5 + x**4 + x**3. Let v(d) = d**2 - 12*d + 16. Let r be v(11). Let j(m) = 6*m**5 - 6*m**4 - 7*m**3. Let f(y) = r*j(y) + 35*i(y). Factor f(c).
-5*c**4*(c - 1)
Let u(l) be the third derivative of -l**6/24 + l**5/3 + 55*l**4/24 + 5*l**3 + 3*l**2 - 6*l. Factor u(w).
-5*(w - 6)*(w + 1)**2
Let y be (-80)/20 + (-2 - (-3 + -4 - -1)). Solve -8/3*l**3 + y*l + 0 - 4/3*l**2 - 4/3*l**4 = 0 for l.
-1, 0
Factor -16/3*g**3 - 12*g**2 - 10/3 - 32/3*g - 2/3*g**4.
-2*(g + 1)**3*(g + 5)/3
Suppose 5*b - 5*l = 5, -17 = -5*b - 4*l + 6. Suppose -b*t = 3*t. Solve t*g**3 - 1/4*g**4 + 0*g + 1/4*g**2 + 0 = 0 for g.
-1, 0, 1
Suppose 13 = -k + 1. Let w be -5 + 1 + (-57)/k. Let -1/4*r**2 - 1/2 + w*r = 0. What is r?
1, 2
Let l(z) be the second derivative of z**5/50 - 2*z**4/15 + z**3/3 - 2*z**2/5 - 10*z. Factor l(f).
2*(f - 2)*(f - 1)**2/5
Let j = -13465/3 - -4489. Factor 1/3 + 1/3*p**2 - j*p.
(p - 1)**2/3
Let -56/9*b + 6 + 2/9*b**2 = 0. Calculate b.
1, 27
Let d(h) = h**3 - 27*h**2 - 34*h + 48. Let g(b) = 2*b**2 + 4*b. Let l(u) = -4*d(u) - 36*g(u). Let l(o) = 0. What is o?
-2, 3, 8
Let r(p) = 92*p**2 - 78*p - 14. Let w(v) = 92*v**2 - 77*v - 15. Let h(x) = -7*r(x) + 6*w(x). Solve h(k) = 0 for k.
-2/23, 1
Suppose -2*u - 3*q + 168 = 0, -2*u - 2*q + 336 = 2*u. Factor u*v - v**3 + v**2 + 2*v**3 - 84*v.
v**2*(v + 1)
Let d = -1351/24 + 113/2. Let g(x) be the second derivative of -d*x**4 + 0*x**2 - 1/16*x**5 + 5/8*x**3 + 0 - 6*x. Factor g(y).
-5*y*(y - 1)*(y + 3)/4
Let b = 4 - 1. Suppose f + 4*p + 9 = 0, 3*f + 2*p + b*p = -6. Factor -7*h + 3*h - 8*h - 8 + h**f + 3*h**3.
4*(h - 2)*(h + 1)**2
Let v = -39913 + 360673/9. Let f = 162 - v. Factor -2/9*l**5 + f*l**3 + 0*l**4 + 0*l + 0 + 0*l**2.
-2*l**3*(l - 1)*(l + 1)/9
Let i(n) = 8*n**2 - 29*n - 1. Let h(j) = j**2 + j + 3. Let o(c) = -3*h(c) - i(c). Factor o(l).
-(l - 2)*(11*l - 4)
Let u = -26364/5 - -5252. Let p = u - -21. What is s in 0 + 0*s**4 - 2/5*s**3 + p*s**5 + 1/5*s + 0*s**2 = 0?
-1, 0, 1
Let b(s) = -2*s + 15. Let d be b(-8). Let y = 33 - d. Let 0*j**2 - 2/3*j**3 + y*j + 4/3 = 0. What is j?
-1, 2
Let g = -693/34 + 355/17. Suppose 5*z = 3*z. Factor z - r + g*r**4 - 3/2*r**2 + 0*r**3.
r*(r - 2)*(r + 1)**2/2
Let g(k) be the first derivative of 0*k + 2/21*k**3 + 16 - 2/7*k**2. Factor g(f).
2*f*(f - 2)/7
Let h(t) be the third derivative of -t**6/40 + t**5/20 - 134*t**2. Solve h(u) = 0 for u.
0, 1
Let z = 451/1085 + 2/155. Let x = -29759 + 29762. Let 0 - 6/7*j**2 + z*j + 3/7*j**x = 0. What is j?
0, 1
Let t(u) be the second derivative of -u**6/150 - u**5/20 + u**4/60 + 17*u**3/30 - 6*u**2/5 - 37*u + 2. Suppose t(a) = 0. Calculate a.
-4, -3, 1
Let c = 1/622 - -305/3732. Let x(v) be the first derivative of -c*v**3 - 3 + 0*v - 1/4*v**2. Factor x(g).
-g*(g + 2)/4
Let j(p) = p**3 - 14*p**2 - p + 19. Let w be j(14). Let 5*i**3 + i**3 - i**3 - 2*i**w + 4*i**4 - 7*i**3 = 0. What is i?
0, 1
Let j(s) be the third derivative of s**5/180 + 7*s**4/72 + 9*s**2 + 1. Factor j(a).
a*(a + 7)/3
Let h(q) be the first derivative of -16/3*q**3 + 0*q - 2*q**2 - 16/5*q**5 + 4 - 2/3*q**6 - 6*q**4. Factor h(f).
-4*f*(f + 1)**4
Factor 128/19 - 2/19*t**3 + 34/19*t**2 - 160/19*t.
-2*(t - 8)**2*(t - 1)/19
Find a such that 352/5*a + 128/5 + 58*a**2 + 2/5*a**5 - 26/5*a**4 + 38/5*a**3 = 0.
-1, 8
Let c(r) be the second derivative of r**6/10 + 27*r**5/20 + 15*r**4/2 + 22*r**3 + 36*r**2 + 14*r. Factor c(a).
3*(a + 2)**3*(a + 3)
Let y(o) be the second derivative of o**6/15 + 3*o**5/5 + 4*o**4/3 - 140*o. Determine v, given that y(v) = 0.
-4, -2, 0
Determine g, given that -2/17*g**5 - 2/17*g + 10/17 + 10/17*g**4 - 20/17*g**2 + 4/17*g**3 = 0.
-1, 1, 5
Let k(l) be the second derivative of l**7/6300 - l**5/75 + 7*l**4/6 + 8*l. Let j(n) be the third derivative of k(n). Factor j(q).
2*(q - 2)*(q + 2)/5
Let t(c) be the second derivative of -c**4/24 + 2*c**3 - 36*c**2 + 47*c - 1. Solve t(y) = 0 for y.
12
Let v = 160 - 37. Let a = v + -14. Let a*k**2 + 27*k**4 + 90*k**3 + 29*k**2 + 91 + 3*k**5 - 64 + 99*k = 0. Calculate k.
-3, -1
Suppose -4*d - o + 7 = 0, 64*o - 5 = -4*d + 61*o. Factor -8/5*h**d + 2/5 - 6/5*h.
-2*(h + 1)*(4*h - 1)/5
Let w = -23 - -23. Let v be (w/(0 + -2))/(-1). Determine s so that -1 + 0*s**3 + v*s**3 - s**3 + s**2 + s + 0*s**3 = 0.
-1, 1
Let q be ((-10)/15 - 0)*-9. Let x be 2/3*(1 + 21/q). Factor -4/5*d**2 - 6/5*d**x + 6/5*d + 4/5.
-2*(d - 1)*(d + 1)*(3*d + 2)/5
Find p, given that 2/17*p**2 + 0 + 10/17*p = 0.
-5, 0
Factor 4826809/3 + 169*k**2 - 28561*k - 1/3*k**3.
-(k - 169)**3/3
Let h(m) = -8*m + 7. Let i be h(1). Let l(f) = -f**4 - 3*f**3 + 7*f**2 - 13*f + 6. Let c(b) = b**3 + b**2 + b - 1. Let y(j) = i*l(j) - 2*c(j). Factor y(z).
(z - 1)**3*(z + 4)
Factor -86*r**2 + 2*r**3 - 72*r**2 + 140*r**2 + 36*r.
2*r*(r - 6)*(r - 3)
Solve 2/3*p**2 + 22/21*p + 2/21*p