 276. Let i(d) = 6*k(d) - 15*y(d). Let i(h) = 0. Calculate h.
-23, -6, -1
Let v = 8735 - 8725. Let h(x) be the second derivative of -v*x - 1/21*x**4 + 0 + 1/70*x**5 - 1/21*x**3 + 2/7*x**2. Factor h(m).
2*(m - 2)*(m - 1)*(m + 1)/7
Suppose 4*v + 3*r = 387, -2*v + 211 = 10*r - 5*r. Let u be 1/((-7)/6) - (-372)/v. Suppose u*i**2 - 8/7*i**3 + 1/7*i**4 + 9/7 - 24/7*i = 0. What is i?
1, 3
Suppose -4/3*g**4 + 10/3*g**2 + 4/3*g - 1/3*g**3 - 8/3 - 1/3*g**5 = 0. Calculate g.
-2, 1
Let w(q) be the first derivative of -40 + 2*q - 1/2*q**4 - 4/3*q**3 + 1/6*q**6 + 2/5*q**5 + 1/2*q**2. What is o in w(o) = 0?
-2, -1, 1
Suppose -24 = 2*q - 2*n, 0 = -5*q + n - 24 - 24. Let w be (80/90 + 2/q)*21. Factor 5*u - 20*u**3 - w + 2*u**4 + 11*u - 18 + 2*u**4 + 24*u**2.
4*(u - 2)**3*(u + 1)
Let y(v) be the second derivative of v**4/6 + 8*v**3/3 - 425*v**2 - 2725*v. Suppose y(j) = 0. What is j?
-25, 17
Let s be (-318)/8 + (278 - 238). Determine x, given that -27/8*x + 29/8*x**2 - s = 0.
-2/29, 1
Let v(t) = -5*t**5 - t**4 + t**3 + t**2 - 12*t. Let h(s) = -6*s**5 + s**3 - 15*s. Let b(p) = 4*h(p) - 5*v(p). Suppose b(z) = 0. What is z?
-5, -1, 0, 1
Let u be 2 + -5*((-2058)/630 - 16/(-6)). Let 0 + 12/5*l + 2/5*l**u + 38/5*l**2 + 42/5*l**3 + 18/5*l**4 = 0. What is l?
-6, -1, 0
Let s(h) be the second derivative of h**4/18 - 335*h**3/9 - 338*h**2 - 2*h - 128. Suppose s(w) = 0. Calculate w.
-3, 338
Let c = -156643 - -783227/5. Factor 0 + 24*r**2 + c*r + 243/5*r**4 + 351/5*r**3.
3*r*(r + 1)*(9*r + 2)**2/5
Suppose 37*j - 1150 = -13*j. Factor j*r**3 + 15*r**2 - 3*r - 4*r**3 - 15 - 16*r**3.
3*(r - 1)*(r + 1)*(r + 5)
Let i = -58559/1777200 + 13/400. Let y = 26668/22215 + i. Factor -96/5 - y*h**2 - 48/5*h.
-6*(h + 4)**2/5
What is h in -40/7*h - 20/7*h**4 + 0 - 12/7*h**3 + 68/7*h**2 + 4/7*h**5 = 0?
-2, 0, 1, 5
Let m(i) = -39*i**3 + 6337*i**2 - 497025*i + 12977879. Let k(n) = -3*n**3 - 2*n**2 + 1. Let a(w) = 4*k(w) - m(w). Find f, given that a(f) = 0.
235/3
Solve 900 - 3986*t**4 - 11*t - 675*t**2 - 216*t**3 - t + 3989*t**4 = 0 for t.
-2, 1, 75
Factor -12*a**2 + 30 + 141*a - a**2 + 23*a**2 + 17*a**2.
3*(a + 5)*(9*a + 2)
Let g(l) be the third derivative of -l**6/720 - 31*l**5/360 + 5*l**4/6 + 17*l**3 + 4093*l**2 + 1. Let g(a) = 0. Calculate a.
-34, -3, 6
Let u = 78774 + -551206/7. Find a such that -u*a**2 + 50/7*a**5 + 258/7*a**3 + 240/7*a**4 - 264/7*a + 144/7 = 0.
-2, 3/5
Suppose 27*d = 24*d + 81. Suppose -d = -n - 8*n. Suppose 3*c + c**3 + 5*c**2 + 11*c**n + 10*c**2 = 0. What is c?
-1, -1/4, 0
Suppose -y = 2*j - 12, -4*j = -58*y + 56*y + 8. Let k(w) be the first derivative of 5 - 1/5*w**4 - 8/15*w**3 - 16/5*w + 14/5*w**j. Find c such that k(c) = 0.
-4, 1
Let w = -110548037/121017237 - 5/194718. Let n = -1/226 - w. Factor -8/11 - 2/11*s**2 + n*s.
-2*(s - 4)*(s - 1)/11
Factor -562*f**4 + 1 - 1752*f**2 - 1128*f**3 - 1 + 1744*f**2.
-2*f**2*(f + 2)*(281*f + 2)
Factor 829*b - 185*b - 951*b**3 + 955*b**3 - 1568 + 31*b**2 - 119*b**2.
4*(b - 8)*(b - 7)**2
Let s(c) be the first derivative of c**4/12 + 11*c**3/6 - 6*c**2 + 50*c + 34. Let r(u) be the first derivative of s(u). Solve r(y) = 0 for y.
-12, 1
Let v(x) = -21*x**3 + 42*x**2 - 121*x + 4. Let n(b) = -17*b**3 + 44*b**2 - 122*b + 3. Let s(f) = 4*n(f) - 3*v(f). Suppose s(p) = 0. What is p?
0, 5
Let n(y) be the first derivative of y**4/48 + 3*y**3/4 - 5*y**2 + 204*y - 276. Let i(j) be the first derivative of n(j). Let i(w) = 0. What is w?
-20, 2
Let l = 332 + -145. Let m(z) = 4 - z**4 - 3 - l*z**3 + 188*z**3. Let f(o) = -o**4 + o**3 + 5*o**2 - 5*o - 4. Let x(h) = -f(h) - 4*m(h). Factor x(n).
5*n*(n - 1)**2*(n + 1)
Let a(u) = -u**3 + 87*u**2 + 502*u + 6. Let t(n) = 2*n**3 - 173*n**2 - 992*n - 11. Let m(s) = -11*a(s) - 6*t(s). Factor m(k).
-k*(k - 86)*(k + 5)
Let x be -2 + 6 + (7 - 8). Let z = -257/7 + 37. Suppose 2/7 + 6/7*w**2 - z*w**x - 6/7*w = 0. Calculate w.
1
Suppose 2/13 + 1856/13*o + 430592/13*o**2 = 0. What is o?
-1/464
Let m(p) be the first derivative of 5*p**6/3 - 33*p**5 + 125*p**4 - 610*p**3/3 + 165*p**2 - 65*p + 2343. Determine k, given that m(k) = 0.
1/2, 1, 13
Suppose 6*d = 30*u - 29*u + 45, 0 = 4*u - 3*d - 9. Factor -6*f**3 + 57/2*f + u - 63/2*f**2.
-3*(f - 1)*(f + 6)*(4*f + 1)/2
Let o be 50/475 - 444/(-114). Let k(b) be the third derivative of 3*b**2 - 1/24*b**o + 0*b**3 + 1/30*b**6 + 0 + 1/20*b**5 + 0*b. Factor k(g).
g*(g + 1)*(4*g - 1)
Let w(t) be the third derivative of 2/105*t**7 + 0*t + 130*t**2 + 100/3*t**3 - 7/30*t**6 + 55/6*t**4 + 0 - 1/5*t**5. Factor w(y).
4*(y - 5)**2*(y + 1)*(y + 2)
Let u(z) be the second derivative of -65*z**4/22 + 196*z**3/11 - 9*z**2/11 - 4315*z. Factor u(b).
-6*(b - 3)*(65*b - 1)/11
Let y(i) be the second derivative of -i**6/3600 - 13*i**5/600 - 169*i**4/240 + 13*i**3 + 74*i. Let s(l) be the second derivative of y(l). Factor s(t).
-(t + 13)**2/10
Factor 242275*y**2 + 1 + 220*y**3 - 242117*y**2 + 19*y**5 + 42*y + 19*y**5 + 153*y**4 + 12*y**3.
(y + 1)**4*(38*y + 1)
Let c(x) be the second derivative of -x**7/13860 + x**6/330 - 3*x**5/55 - 5*x**4 - x**2 + 39*x. Let a(j) be the third derivative of c(j). Solve a(b) = 0.
6
Let k(l) = -l + 31. Let w be k(26). Suppose -16 = s - w*s. Factor -33 - 147 + 34*a**2 - 60*a - a**4 + 10*a**3 + 21*a**2 - 4*a**s.
-5*(a - 3)**2*(a + 2)**2
Let h = 524 - 520. Let n(p) be the first derivative of -8/5*p**3 + 10 + 3/20*p**h + 24/25*p**5 + 3/10*p**6 + 0*p - 6/5*p**2. Suppose n(j) = 0. What is j?
-2, -1, -2/3, 0, 1
Suppose -31*r = -44*r - 20371. Let c = 7837/5 + r. Factor c*n + 0 - 2/5*n**2.
-2*n*(n - 1)/5
Let s(c) be the first derivative of -105/2*c**2 + 50*c - 311 - 5/4*c**4 + 20*c**3. Suppose s(f) = 0. Calculate f.
1, 10
Suppose -4*n = -3*f - n - 6, -5*f - 5*n = -10. Let d = -8797/2 - -4399. Factor -d*r**4 + f*r**2 + 0*r + 0 + r**3.
-r**3*(r - 2)/2
Let s = 682 - 429. Factor -44*z**2 + 265*z**4 - 7*z**3 - s*z**4 - 24*z - 7*z**3 + 2*z**3 + 4*z**5.
4*z*(z - 2)*(z + 1)**2*(z + 3)
Let u(c) be the second derivative of -3/10*c**5 - c + 1/40*c**6 + 0*c**3 - 81/8*c**2 - 31 + 9/8*c**4. Factor u(a).
3*(a - 3)**3*(a + 1)/4
Suppose 363*l**3 + 0 - 161/3*l**4 + 1/3*l**5 - 1699/3*l**2 + 770/3*l = 0. What is l?
0, 1, 5, 154
Let f(p) = 941*p**2 + 3*p - 5. Let v be f(1). Let s = v - 8443/9. Factor -2/9*o**2 + 8/9*o - s.
-2*(o - 2)**2/9
Suppose -9*k - 7*k + 96 = 0. Determine x, given that 4*x**2 + 9*x**3 - 6*x**2 - 4*x**2 - k*x**2 + 3*x**4 = 0.
-4, 0, 1
Let l(t) = t**3 + 2*t**2 - t - 4. Let h be l(4). Suppose -8*z - h = -16*z. Factor 5 + z*v - 25 - 5*v**2 + 9*v + 0.
-5*(v - 2)**2
Factor 46258 + 29466 + 304 + 4*n**3 - 1580*n**2 + 155232*n + 80788.
4*(n - 198)**2*(n + 1)
Let a(q) be the second derivative of -16/3*q**2 - 72*q + 3/20*q**5 + 11/18*q**4 + 0*q**3 + 0 + 1/90*q**6. Factor a(v).
(v - 1)*(v + 2)*(v + 4)**2/3
Let a(d) be the third derivative of d**7/504 - d**6/72 + 61*d**4/24 - d**3/6 + d**2 + 11*d. Let q(u) be the second derivative of a(u). Solve q(z) = 0.
0, 2
Let y(b) be the second derivative of 3*b**5/20 - 4*b**4 + 41*b**3/2 - 39*b**2 - 947*b. Factor y(x).
3*(x - 13)*(x - 2)*(x - 1)
Let c = 16 + -19. Let v be 6/(-3)*(1 + c). Determine z, given that 16*z**2 + v - 16*z**2 + 8*z**3 - 8*z - 4*z**4 = 0.
-1, 1
Let i = 41742/5 + -291894/35. Solve -12*o**2 - 48/7 + 46*o**3 - 50/7*o**5 + i*o**4 - 200/7*o = 0 for o.
-2, -2/5, 1, 3
Let k = 181/142 - -158/71. Determine i so that 4*i**2 + 3/2*i**4 - 9/4*i - k*i**3 + 1/2 - 1/4*i**5 = 0.
1, 2
Let z = 1253 + -1250. Let s(n) be the third derivative of 0*n**5 + 0*n**z + 0*n + 0 + 0*n**4 - 15*n**2 - 1/40*n**6 - 1/70*n**7. Let s(i) = 0. Calculate i.
-1, 0
Let f(z) be the third derivative of -53/90*z**5 - 148877/27*z**3 - 1/540*z**6 - 2809/36*z**4 + 55*z + z**2 + 0. Factor f(d).
-2*(d + 53)**3/9
Let x(v) be the first derivative of 2*v**3/15 - 7272*v**2/5 + 26440992*v/5 + 10811. Suppose x(y) = 0. What is y?
3636
Let x be -25 + (-61)/(1220/(-600)). Let r(h) be the second derivative of -1/15*h**x - 11/18*h**3 + 7*h + 13/36*h**4 + 0 + 1/3*h**2. Factor r(d).
-(d - 2)*(d - 1)*(4*d - 1)/3
Factor -323*c + 5*c**2 - 169*c + 4*c**2 - 7*c**2 - 494.
2*(c - 247)*(c + 1)
Let q be ((-22)/77)/((-6)/(-56) - 13/52). What is s in -6/7*s**3 + 12 + 162/7*s + 72/7*s**q = 0?
-1, 14
Let g(f) be the second derivative of -7*f**6/90 - 16*f**5/15 - 19*f**4/6 + 80*f**3/9 + 25*f**2