he first derivative of y**4/4 - y**3 + y + 47. Let k(n) be the first derivative of o(n). Determine q, given that k(q) = 0.
0, 2
Let v(m) be the third derivative of m**7/1890 + m**6/540 + m**4 + 8*m**2. Let w(u) be the second derivative of v(u). Let w(d) = 0. What is d?
-1, 0
Suppose 15 = y + 5*k, 0*y + k - 3 = -y. Let i(o) be the first derivative of 6 + y*o + 2/3*o**3 + 1/4*o**4 + 1/2*o**2. Determine v so that i(v) = 0.
-1, 0
Let n(z) = z**2 - 72*z + 1009. Let d be n(53). Factor -8/5*q - 8/5 - 2/5*q**d.
-2*(q + 2)**2/5
Let g be 0*((1 - -1) + 4 + (-1665)/270). Factor 0*q + 4/5*q**3 - 2/5*q**4 + g - 2/5*q**2.
-2*q**2*(q - 1)**2/5
Factor 3/2*h**2 + h**3 - 1/2*h**4 + 0*h + 0.
-h**2*(h - 3)*(h + 1)/2
Let y = -26 - -53/2. Factor y*x**2 - 1/12 - 5/12*x.
(x - 1)*(6*x + 1)/12
Let o(i) = 2*i**2 + 36*i + 4. Let w be (4/(-6))/(30/810). Let t be o(w). Solve -2*s**2 + 32/5*s**3 + 0 - 4/5*s - 18/5*s**t = 0 for s.
-2/9, 0, 1
Let g(y) = y**2 - y + 1. Suppose 14*o = 19*o - 15. Let h(w) = 28*w**2 + 17*w + 7. Let p = -6 - -5. Let k(t) = o*g(t) + p*h(t). Factor k(q).
-(5*q + 2)**2
Let h(z) be the third derivative of -z**8/84 + 4*z**7/35 - 3*z**6/10 + 4*z**5/15 - 195*z**2. Factor h(o).
-4*o**2*(o - 4)*(o - 1)**2
Suppose 2/7*c**2 + 0 - 12/7*c = 0. Calculate c.
0, 6
Let d(n) be the first derivative of 3*n**6/10 + 3*n**5/4 - n**4/2 + 7*n - 10. Let u(y) be the first derivative of d(y). Find b, given that u(b) = 0.
-2, 0, 1/3
Let m = 99 + -56. Factor 59 + 48*d - 24*d**2 - 4*d**2 - m.
-4*(d - 2)*(7*d + 2)
Let a = -136 - -133. Let l be (1/(-1) - a)/(780/240). Factor 2/13*z + 0 + l*z**2.
2*z*(4*z + 1)/13
Let i = 6974/3 - 13933/6. Factor 0*t**2 - i*t - 5/2*t**5 + 0 + 5*t**3 + 0*t**4.
-5*t*(t - 1)**2*(t + 1)**2/2
Suppose 3*d + 2*d - y = -3, 0 = 2*y - 6. Suppose -8*g + 11*g - 105 = d. Factor -2*z + 2*z**2 + g - 35.
2*z*(z - 1)
Suppose 3*v - 7*v + 12 = 0. Solve -j**5 + 4*j**2 + 0*j - 8*j + 6*j - 6*j**v + 4*j**4 + j = 0.
0, 1
Let m(h) be the third derivative of -h**5/40 - 17*h**4/16 + 9*h**3/2 + 132*h**2. Factor m(s).
-3*(s - 1)*(s + 18)/2
Let h = 15 - 14. Suppose 2*j = -5*q - h - 18, -4*q = 20. Factor -5*b**2 - 2*b**2 - b**4 + 4*b**2 + b + j*b**3.
-b*(b - 1)**3
Let p(y) be the second derivative of y**4/16 - 13*y**3/24 - 5*y**2/4 + 313*y. Factor p(w).
(w - 5)*(3*w + 2)/4
Let v(t) = -1 + 7*t**2 + 3*t**2 - t - 9*t**2. Let h(j) = -45*j**2 + 90*j + 10. Let c(w) = -h(w) - 25*v(w). Solve c(l) = 0 for l.
1/4, 3
Let g(m) be the second derivative of 10/33*m**3 - 25/11*m**2 + 4*m + 0 - 1/66*m**4. Factor g(y).
-2*(y - 5)**2/11
Let 5/2*p**2 - 2*p**3 - 1/2*p**4 + 0*p + 0 = 0. What is p?
-5, 0, 1
Let u be ((-51)/(5865/(-92)))/(1*3/10). Factor -4 + 4/3*f**2 - u*f.
4*(f - 3)*(f + 1)/3
Let m be (2/3)/(35/56) - 0. Let k(a) be the third derivative of 0 + 0*a - a**2 + 24/5*a**5 + 9*a**3 - m*a**6 - 9*a**4. Suppose k(g) = 0. Calculate g.
3/4
Let k(b) = b**2 + 10*b + 11. Let a be k(-9). Let -16*n**3 + 180*n + 18*n**2 - 184*n + a*n**2 = 0. What is n?
0, 1/4, 1
Let u(p) be the second derivative of -p**7/56 + 3*p**5/16 - p**3/2 - 2*p + 21. Suppose u(o) = 0. What is o?
-2, -1, 0, 1, 2
Suppose 205*n - 207*n = -2*g + 8, 4*g - 5*n - 18 = 0. Factor -38/13*s**3 - 2/13*s - 14/13*s**4 - 30/13*s**g + 4/13.
-2*(s + 1)**3*(7*s - 2)/13
Let p(v) be the second derivative of -v**4/30 - 29*v**3/5 + 88*v**2/5 + 320*v. Factor p(f).
-2*(f - 1)*(f + 88)/5
Solve -2/15*a**4 + 86/15*a**2 + 82/15*a**3 - 82/15*a - 28/5 = 0 for a.
-1, 1, 42
Let u(s) be the third derivative of -s**5/12 + 5*s**4/12 - 5*s**3/6 + 37*s**2. Factor u(o).
-5*(o - 1)**2
Let j be 2*6*(-6)/9. Let m(s) = 18*s**2 - 45*s - 19. Let i(h) = -6*h**2 + 15*h + 6. Let d(q) = j*i(q) - 3*m(q). Suppose d(v) = 0. Calculate v.
-1/2, 3
Let l be -12*12/(-16) - -1. Suppose 4*i = g + 10, l + 9 = 5*g + 3*i. Factor -10/9*h**3 + 8/9*h**4 + 0 + 4/9*h**g + 0*h - 2/9*h**5.
-2*h**2*(h - 2)*(h - 1)**2/9
Let z be (-5)/(-15) - 1*5/(-3). Let m(w) be the first derivative of 0*w - 1/4*w**4 - 1 + 3/2*w**z - 2/3*w**3. Let m(i) = 0. Calculate i.
-3, 0, 1
Let r(n) = -3 + 3 + 3 - 9*n**3 + 8*n**2 + 8*n**3. Let y be r(8). Factor -1/7 - 3/7*i**2 - 1/7*i**y - 3/7*i.
-(i + 1)**3/7
Let w(m) = -m**3 + m. Let t(p) = -60*p**2 + 15 + 6*p**3 - 26*p + 34*p**2 + 31*p**2 + 0*p. Let g(h) = -t(h) - w(h). Factor g(n).
-5*(n - 1)**2*(n + 3)
Let j(c) be the third derivative of 13*c**4/12 + 18*c**3 + 35*c**2. Let z be j(-4). Let 1/2 - 3/4*p**2 + 1/4*p - 1/4*p**3 + 1/4*p**z = 0. What is p?
-1, 1, 2
Suppose 935*q - 930*q - 10 = 0. Let x(n) be the third derivative of -1/30*n**4 + 0 + 0*n + 2*n**q + 1/50*n**5 + 0*n**3. Solve x(z) = 0.
0, 2/3
Let a = -83 - -85. Let l(h) be the third derivative of 1/4*h**4 + 0 + 0*h - 2/3*h**3 + 0*h**5 + a*h**2 - 1/60*h**6. Factor l(i).
-2*(i - 1)**2*(i + 2)
Let k(o) be the third derivative of 0*o**4 + 0*o + 1/240*o**6 - 1/120*o**5 + 6*o**2 + 0*o**3 + 0. Find x such that k(x) = 0.
0, 1
Let h be ((-12)/(-8))/(2/(-4)). Let q = 4 + h. Determine b, given that -3*b**3 + 84*b**3 - 5 + 72*b**2 - q - 15*b = 0.
-1, -2/9, 1/3
Let y(t) = t - 1. Let m(a) = a**2 + 3*a + 10. Let o(x) = 3*m(x) + 12*y(x). Factor o(s).
3*(s + 1)*(s + 6)
Let u(m) be the second derivative of -1/24*m**4 + 1/9*m**3 - 6*m + 3*m**2 + 0 + 1/180*m**5. Let x(o) be the first derivative of u(o). Factor x(b).
(b - 2)*(b - 1)/3
Let l(x) be the first derivative of x**5/60 + x**4/3 + 8*x**3/3 - 16*x**2 + 35. Let s(z) be the second derivative of l(z). Determine u, given that s(u) = 0.
-4
Let d(i) = i**2 - 1. Let m be d(-2). Find y, given that 13*y**4 - 8*y**2 - 4*y**5 - 12*y**2 + 7*y**2 + 4*y - y + y**m = 0.
-1, 0, 1/4, 1, 3
Let p(q) = 188*q - 2818. Let b be p(15). Let -1/2*u + 1/8*u**3 - 3/8*u**b + 0 = 0. Calculate u.
-1, 0, 4
Let y(l) be the second derivative of -l**5/100 + l**4/20 - l**3/15 - 180*l. Suppose y(r) = 0. What is r?
0, 1, 2
Let x(i) be the third derivative of -i**7/420 + i**6/120 + i**5/10 - i**4/6 - 8*i**3/3 - 245*i**2. Factor x(j).
-(j - 4)*(j - 2)*(j + 2)**2/2
Let s be (-1 + 208)*14/70. Let n = s - 41. Find h, given that n*h + 2/5*h**2 - 4/5 = 0.
-2, 1
Let q be (-4)/(-2) + (-14)/378*0. Factor -8/19*w**q - 2/19*w + 0.
-2*w*(4*w + 1)/19
Let l = -9 - -65. Factor -33*c**4 + l*c**5 + 0*c + 3*c - 3*c**2 - 27*c**3 - 68*c**5.
-3*c*(c + 1)**3*(4*c - 1)
Factor 104 + 71 + 2*m**2 + 33 + 40*m + 41 - 49.
2*(m + 10)**2
Let c(z) be the first derivative of 1 + 0*z**2 + 3*z**5 - 20/3*z**3 + 0*z + 5/6*z**6 + 0*z**4. Factor c(s).
5*s**2*(s - 1)*(s + 2)**2
Suppose -2*w + 9*l = 13*l + 60, -50 = 2*w + 2*l. Let k be (3/(w - -2))/(2/(-4)). Factor -1/3*y**2 - k*y**3 + 0*y + 1/3*y**4 + 0 + 1/3*y**5.
y**2*(y - 1)*(y + 1)**2/3
Let g(t) be the first derivative of 25/2*t + 9/8*t**4 - 5/4*t**2 - 7/2*t**3 + 23. Solve g(c) = 0 for c.
-1, 5/3
Let d(y) = -2*y**2 - 35*y - 23. Let l(c) = c**2 + 17*c + 12. Let b(u) = 6*d(u) + 15*l(u). Factor b(o).
3*(o + 1)*(o + 14)
Suppose 0 = 9*h - 154 + 127. Solve 36/7*d + 8/7 - 36/7*d**h + 20/7*d**2 - 4*d**4 = 0.
-1, -2/7, 1
Suppose -2*i = -13 - 7. Let r be 82/30 - 6/i. Factor r + 2/15*b**2 - 16/15*b.
2*(b - 4)**2/15
Let l(t) be the second derivative of -t**7/70 + 2*t**6/25 - 3*t**5/25 - 14*t. Factor l(h).
-3*h**3*(h - 2)**2/5
Factor 1100*h + 8 + 1118*h - 2240*h + h**4 + 21*h**2 - 8*h**3.
(h - 4)*(h - 2)*(h - 1)**2
Let b(g) be the first derivative of -g**4/38 + 22*g**3/19 - 363*g**2/19 + 2662*g/19 + 149. Factor b(w).
-2*(w - 11)**3/19
Let q(r) be the second derivative of -1/21*r**3 + 3*r - 1/42*r**4 + 0 + 3/2*r**2 - 1/210*r**5. Let s(h) be the first derivative of q(h). Factor s(u).
-2*(u + 1)**2/7
Suppose 13 = 3*f - s, 9 = 2*f - 2*s - 5. Suppose 0*p**4 - 6*p + 16*p**3 + 30*p + 2*p**f - 3*p**4 - 36*p**2 = 0. Calculate p.
0, 2
Suppose 66*o + 38 = 85*o. Let n(z) be the second derivative of o*z**3 + 6*z**2 + 1/4*z**4 + 0 + 5*z. Factor n(f).
3*(f + 2)**2
Let l be (-11 - -12)*((-3)/(-9))/(7/28). Find b, given that l + 1/3*b**2 - 5/3*b = 0.
1, 4
Suppose -86/19*k**3 - 200/19 - 482/19*k**2 + 34/19*k**4 - 2/19*k**5 - 560/19*k = 0. Calculate k.
-1, 10
Let l(r) be the third derivative of -r**9/75600 + r**8/33600 - 5*r**4/24 + 9*r**2. Let u(s) be the second derivative of l(s). Factor u(o).
-o**3*(o - 1)/5
Let l(g) = 2*g**2 + 50*g - 787. Let t(r) = 3*r**2 + 102*r - 1573. Let f(w) = 5*l(w) - 3*t(w). Determine q, given that f(q