he first derivative of 14 + 7/2*b**2 - 3*b + 1/4*b**4 - 5/3*b**3. Determine r, given that h(r) = 0.
1, 3
Let k(o) be the third derivative of 0*o + 1/15*o**3 - 1/10*o**5 + 31*o**2 - 17/300*o**6 - 1/20*o**4 + 0 - 2/175*o**7. Factor k(q).
-2*(q + 1)**3*(6*q - 1)/5
Let d(r) = r**2 - 1. Let q(f) = -10*f**2 - 25*f + 30. Let k(g) = 20*d(g) + q(g). Let v(m) = -11*m**2 + 25*m - 10. Let s(i) = 4*k(i) + 5*v(i). Factor s(n).
-5*(n - 1)*(3*n - 2)
Let a(j) be the first derivative of -2*j**3/3 + 28*j**2 + 120*j + 269. Factor a(k).
-2*(k - 30)*(k + 2)
Let i(n) = -9*n**2 + n + 2. Let u be i(-1). Let c(v) = -6*v**2 + 8*v - 8. Let p(k) = k**2 - k. Let r(b) = u*p(b) - c(b). Find l, given that r(l) = 0.
-2, 2
Find j, given that -15*j**2 - 1489*j - 53 + 1364*j + 13 = 0.
-8, -1/3
Let l(s) be the second derivative of s**5/390 - s**4/78 - s**2/2 + 2*s. Let c(y) be the first derivative of l(y). Factor c(v).
2*v*(v - 2)/13
Let q be (13 - 12)*(-10 - 1). Let w(d) = 23*d**3 - 35*d**2 - 23*d + 24. Let j(c) = 8*c**3 - 12*c**2 - 8*c + 8. Let y(g) = q*j(g) + 4*w(g). Factor y(n).
4*(n - 2)*(n - 1)*(n + 1)
Let w(p) be the second derivative of p**5/50 + 9*p**4/10 + 13*p**3 + 169*p**2/5 + 24*p. Factor w(s).
2*(s + 1)*(s + 13)**2/5
Let a be (56/30 - 2)*((-25)/15 - 0). What is r in 2/9*r + 0 + a*r**3 + 4/9*r**2 = 0?
-1, 0
Let w(c) be the third derivative of c**8/112 - 81*c**7/70 + 879*c**6/20 - 2399*c**5/10 + 4641*c**4/8 - 1521*c**3/2 - 165*c**2 - c. Factor w(v).
3*(v - 39)**2*(v - 1)**3
Let f(y) = 19*y**3 + 111*y**2 + 105*y + 7. Let j(t) = -20*t**3 - 112*t**2 - 106*t - 10. Let q(d) = -4*f(d) - 6*j(d). Let q(v) = 0. What is v?
-4, -1, -2/11
Let s(u) be the third derivative of -u**8/2100 + u**6/450 + 25*u**3/6 - 24*u**2. Let o(d) be the first derivative of s(d). Factor o(b).
-4*b**2*(b - 1)*(b + 1)/5
Suppose 0 = -9*v + 6*v + 66. Let n be ((-2)/(-7))/(23 - v). Factor -8/7*y + n*y**3 - 8/7 + 2/7*y**2.
2*(y - 2)*(y + 1)*(y + 2)/7
Let u be -1 - 14/(-12) - (-115)/30. Suppose -4/7*d**2 + 0*d - 8/7*d**3 + 0 - 4/7*d**u = 0. What is d?
-1, 0
Let p(l) be the first derivative of l**5/40 + 15*l**4/16 + 193*l**3/24 - 30*l**2 + 32*l - 185. Factor p(s).
(s - 1)**2*(s + 16)**2/8
Suppose -2*m - 222 = -a - 3*a, -5*a - 3*m = -305. Let j be 10/(-45) + a/18. Factor 3*g**j + 0*g**5 + g**3 + 4*g**4 + g**5 + g + 4*g**2 + 2*g**3.
g*(g + 1)**4
Factor 63/2 - 15/2*m + 3/8*m**2.
3*(m - 14)*(m - 6)/8
Let r be (2/3)/(6/9). Let g = -1 + r. Suppose g*q**3 - q**3 - 2*q**3 - 2*q - q**2 + 4*q**3 = 0. What is q?
-1, 0, 2
Suppose -2*r = -3*j - 106 + 35, 86 = 2*r + 2*j. Let v = r + -38. Find b such that -6/7*b + 2/7*b**v + 4/7 = 0.
1, 2
Let d(c) be the third derivative of 0 + 0*c**5 - 4*c**2 - 2/3*c**3 + 0*c**4 + 1/1440*c**6 + 0*c. Let v(p) be the first derivative of d(p). Factor v(o).
o**2/4
Let f(n) be the first derivative of n**5/180 + n**4/72 - 4*n**2 + 12. Let r(g) be the second derivative of f(g). Find l such that r(l) = 0.
-1, 0
Let i(p) be the third derivative of 24*p**2 + 8/21*p**3 + 29/105*p**5 - 5/49*p**7 + 0 + 1/12*p**6 - 11/21*p**4 + 0*p. Suppose i(x) = 0. Calculate x.
-1, 2/5, 2/3
Factor 0 + 4/9*o**2 - 2/9*o - 4/9*o**4 + 0*o**3 + 2/9*o**5.
2*o*(o - 1)**3*(o + 1)/9
Let o = 27 - 20. Let o*j**3 + 3*j**4 + 2 - 1 - 4 - j**3 - 6*j = 0. What is j?
-1, 1
Suppose 2*h = 5*h. Suppose -5*d + 20 = -h*d. Factor 3*z - 3*z**3 + z**2 - 10*z**4 - 2 + 6*z**d + 5*z**4.
(z - 2)*(z - 1)**2*(z + 1)
Factor -20*h**4 + 77*h**4 - 25*h + 71*h**4 - 656*h**3 + 1 + 214*h**2 + 1024*h**5.
(h + 1)*(2*h - 1)*(8*h - 1)**3
Let z = 31 + -20. Suppose -2*x + z = -5*h, -x + 2*h = 4*h - 1. Find r such that -23*r + 12*r - x*r**2 + 2*r - 6 = 0.
-2, -1
Let n(b) be the first derivative of b**4/22 + 26*b**3/33 - 64*b**2/11 + 136*b/11 - 277. Factor n(j).
2*(j - 2)**2*(j + 17)/11
Let c(n) be the second derivative of n**7/1680 - n**6/360 - n**5/80 - 4*n**3/3 + 33*n. Let y(x) be the second derivative of c(x). Factor y(s).
s*(s - 3)*(s + 1)/2
Let p be (8/(-5))/(64 + -65 - (-1)/5). Factor -1/4*b**4 + 0*b + 1/4*b**5 + 0*b**p - 1/2*b**3 + 0.
b**3*(b - 2)*(b + 1)/4
Solve 0*x + 4/3*x**3 - 16/9*x**2 + 0 - 2/9*x**4 = 0.
0, 2, 4
Let v(q) be the first derivative of q**3 - 24*q**2 - 51*q + 219. Let v(l) = 0. Calculate l.
-1, 17
Let n = -470 - -6116/13. Let i(h) be the first derivative of -2/13*h**3 + 1/26*h**4 - 1/13*h**2 - 5 + n*h. Suppose i(w) = 0. Calculate w.
-1, 1, 3
Suppose u = 2*d + 13, -2*u + 2*d - 7*d + 53 = 0. Suppose 3*o = 2*h + 3*h - u, -4*h + 5*o = -23. Factor 8*k**h + 2/3*k**3 + 32*k + 128/3.
2*(k + 4)**3/3
Let k(g) = 3*g + 10. Let f be k(5). Suppose f = 5*h + 3*s, -h - 4*s + 0*s + 22 = 0. Find b such that 2*b**3 + b**h + 0*b**2 + 2*b - 4*b - 2*b**4 + b**4 = 0.
-1, 0, 1, 2
Let x(q) = 23 + 5*q + q - 4*q. Let s be x(0). Solve 14*i + s*i**4 - 9 + 4 + 12*i**2 - 50*i**3 + 5*i**4 + 1 = 0 for i.
-1/2, 2/7, 1
Let k(n) = -2*n - 14. Let z be k(-14). Let b be z/6 + (-7 - -4) - -1. Factor 2/3*s**2 - b*s**3 + 1/3*s - 2/3.
-(s - 2)*(s - 1)*(s + 1)/3
Find z, given that -2*z**5 + 14*z**3 + 22*z**3 - 40*z**3 - 6*z**4 = 0.
-2, -1, 0
Let r(a) = a**3 + 5*a**2 - 5*a + 7. Suppose -2*j - j = 18. Let o be r(j). Factor -o - 4*y**2 + 2*y**2 + 4*y + 1.
-2*y*(y - 2)
Suppose 3*l = 3*t, -2*t + 4*l - 6 = -0*t. Factor -9*f + 63 + 63 + t*f**2 - 126.
3*f*(f - 3)
Let b be (-1)/2 + 299/2. Suppose -5*o + b = -71. Factor -o*n - 6 + 25*n**2 + 2 - 146*n**2.
-(11*n + 2)**2
Let f(l) be the second derivative of -l**6/200 + 3*l**5/100 - 9*l**2/2 - 6*l. Let i(y) be the first derivative of f(y). Find m, given that i(m) = 0.
0, 3
Factor 1/3*c**2 + 9 + 28/3*c.
(c + 1)*(c + 27)/3
Determine t so that 26711*t - 74 - 2*t**3 + 20 - 26605*t - 50*t**2 = 0.
-27, 1
Let 0 - 4/7*f**2 + 2/7*f + 2/7*f**3 = 0. Calculate f.
0, 1
Let m(j) be the second derivative of -j**5/30 - j**4/6 + 4*j**2/3 + 65*j. Factor m(a).
-2*(a - 1)*(a + 2)**2/3
Let i(l) = -2*l**2 - 3 - 6 - 3*l + 8*l + 4 + l**3. Let u be i(2). Factor 5*r**2 + 2 - r**2 - 3 + u - 8*r.
4*(r - 1)**2
Let i(z) = 3*z**2 - 6*z + 4. Let x(o) be the third derivative of -7*o**5/60 + 13*o**4/24 - 4*o**3/3 - 13*o**2. Let h(j) = -15*i(j) - 6*x(j). Solve h(s) = 0.
2
Determine v so that 0 + 1/2*v**4 + 2*v + 0*v**2 - 3/2*v**3 = 0.
-1, 0, 2
Factor -8/9*h**3 + 22/9*h**2 + 0 - 14/9*h.
-2*h*(h - 1)*(4*h - 7)/9
Let q = 27017/204 - 397/3. Let h = 6/17 - q. Factor 0 - 1/4*c**2 - h*c.
-c*(c + 1)/4
Let o(t) be the second derivative of -t**4/6 + 116*t**3/3 - 3364*t**2 + 178*t. Solve o(w) = 0.
58
Let l(d) be the third derivative of 0*d**3 - 1/360*d**6 - 1/630*d**7 - 15*d**2 + 0 + 1/90*d**5 + 0*d**4 + 0*d. Suppose l(o) = 0. What is o?
-2, 0, 1
Factor -5*m**2 + 19/4*m - 1/4*m**5 - 3/2 + 3/2*m**3 + 1/2*m**4.
-(m - 2)*(m - 1)**3*(m + 3)/4
Suppose -4*w - w = -90. Factor 3 - 27*p - 3*p**3 + 3 - 18*p**2 - w.
-3*(p + 1)**2*(p + 4)
Factor 14*c + 139*c**3 + 7*c**2 + 6 - 75*c**3 - 1 - 66*c**3.
-(c - 5)*(c + 1)*(2*c + 1)
Solve 10 - 10*p**2 - 5/2*p + 5/2*p**3 = 0 for p.
-1, 1, 4
Let x = -59 - -16. Let v = 46 + x. Factor 0 + 2/5*r**4 + 4/5*r - 4/5*r**v - 2/5*r**2.
2*r*(r - 2)*(r - 1)*(r + 1)/5
Let u(n) = -2*n**3 - 11*n**2 + 7*n. Let f(y) = 57 + 3*y**3 - 4*y**2 - 15*y - 57 + 27*y**2. Let b(m) = -6*f(m) - 14*u(m). Suppose b(s) = 0. Calculate s.
-2, 0, 2/5
Let k(g) = 3*g**4 + 6*g**3. Let l(w) = w**3 + 2*w**2. Let h(d) = -k(d) + 6*l(d). Solve h(m) = 0.
-2, 0, 2
Let d(t) be the second derivative of 13/50*t**5 + 2/25*t**6 + 11*t + 1/105*t**7 + 2/5*t**4 + 0*t**2 + 0 + 4/15*t**3. Factor d(f).
2*f*(f + 1)**2*(f + 2)**2/5
Factor 2/3*d**5 + 4*d**3 + 0*d + 0*d**2 + 0 + 10/3*d**4.
2*d**3*(d + 2)*(d + 3)/3
Let s(m) = 4*m + 3. Let a be s(5). Let g = -21 + a. Solve -4*q - 5*q**2 + 6*q**2 - 7*q**2 - 10*q**g = 0.
-1/4, 0
Let g = -19/2298 - 2585117/16086. Let x = g + 161. Factor 2/7*v - x*v**2 + 0.
-2*v*(v - 1)/7
Suppose i = 11 - 8. Let c(v) be the third derivative of 1/30*v**5 - i*v**2 + v**3 + 1/3*v**4 + 0*v + 0. Suppose c(j) = 0. What is j?
-3, -1
Factor 1/4*p**4 + p**3 - 3/4 - p + 1/2*p**2.
(p - 1)*(p + 1)**2*(p + 3)/4
Let b(r) be the first derivative of 0*r**2 + 1/1620*r**6 + 0*r**5 + 0*r - 1/27*r**4 + 8/3*r**3 + 5. Let d(c) be the third derivative of b(c). Solve d(t) = 0.
-2, 2
Let p be 48 - 468/(-195)*10/(-3). Let -50/3*i**2 - p - 125*i**3 - 35/3*i**5 + 220/3*i**4 + 460/3*i = 0. What is i?
-1, 2/7, 2, 3
Le