. Suppose s(o) = 0. What is o?
0, 1
Let b(u) be the first derivative of u**4 + 92*u**3/3 - 2*u**2 - 92*u - 55. Determine l, given that b(l) = 0.
-23, -1, 1
Let d(p) be the third derivative of p**7/420 - p**6/60 - 7*p**5/40 + 517*p**2. Factor d(g).
g**2*(g - 7)*(g + 3)/2
Let y = 4 + 0. Suppose 4*s + y*v + 8 = v, 0 = 2*s - 3*v - 14. Factor -o**5 - 19*o**2 - 1 - 3*o**3 - 3*o**4 + s + 18*o**2.
-o**2*(o + 1)**3
Let k(l) = -20*l**3 + 95*l**2 + 310*l + 360. Let a(q) = q**3 - q**2 - q. Let d(x) = -25*a(x) - k(x). Factor d(g).
-5*(g + 3)**2*(g + 8)
Let b be ((-164)/(-123))/((-4)/18). Let o be b/(-10) + ((-81)/5)/(-3). Let 2/3*n**3 - o*n**2 - 32/3 + 16*n = 0. What is n?
1, 4
Let l = -53 + 97. Suppose 2*i - l = -2*i. Factor -8 + i - 2 - j**2.
-(j - 1)*(j + 1)
Let o(s) be the first derivative of 1/6*s**4 - 4/3*s**2 + 7 + 0*s + 2/3*s**3. Factor o(c).
2*c*(c - 1)*(c + 4)/3
Let t(a) = 4*a**2 + 95*a + 78. Let y be t(-23). Let z(b) be the third derivative of -8/3*b**3 + 1/3*b**4 + 0*b + 0 - 1/60*b**5 - y*b**2. Solve z(l) = 0.
4
Let s(i) be the first derivative of 4*i**3/3 - 23*i**2/2 - 6*i - 132. Factor s(b).
(b - 6)*(4*b + 1)
Let i(z) be the second derivative of -z**7/17640 + z**6/2520 - z**5/840 - 7*z**4/12 + z. Let w(u) be the third derivative of i(u). Solve w(f) = 0.
1
Let z(m) be the third derivative of 6*m**2 + 5/24*m**4 + 0 + 5/9*m**3 + 0*m + 1/36*m**5. Determine w, given that z(w) = 0.
-2, -1
Let g be (-714)/(-612) - 1/(1 - 0). Find a, given that -g*a**3 + 1/6*a + 1/3*a**2 - 1/3 = 0.
-1, 1, 2
Factor 0*y + 1/3*y**3 + 0 - 1/2*y**2 + 1/6*y**4.
y**2*(y - 1)*(y + 3)/6
Let f(r) be the third derivative of -r**7/105 - 19*r**6/150 - 89*r**5/150 - 4*r**4/5 + 12*r**3/5 - 691*r**2. Find d, given that f(d) = 0.
-3, -2, 2/5
Let d(w) = -w**3 - 4*w**2 + 5*w. Suppose 0 = -7*h + 2*h + 10. Let q(n) = 29*n - n**h + 1 - 29*n. Let v(r) = 4*d(r) - 12*q(r). Determine i so that v(i) = 0.
-3, 1
Let z(m) be the third derivative of -4/75*m**5 + 0*m**3 + 1/30*m**4 + 0*m + 6*m**2 - 1/350*m**7 + 0 + 13/600*m**6. Suppose z(w) = 0. Calculate w.
0, 1/3, 2
Let p = 179/20 + -149/20. Factor -p*f**2 + 1/2*f**3 + 0 + 0*f.
f**2*(f - 3)/2
Factor 38/3*c + 8/3*c**5 - 52/3*c**4 - 4/3 + 241/6*c**3 - 115/3*c**2.
(c - 2)**3*(4*c - 1)**2/6
Find j, given that 7*j**5 + 16*j**3 - 66*j**3 - 49*j**3 - 9*j**4 + 10*j**3 + 4 + 201*j**2 + 20 - 134*j = 0.
-4, 2/7, 1, 3
Suppose 263 = c + 261. Let p(q) be the third derivative of c*q**2 + 0*q**3 + 1/280*q**7 - 1/80*q**5 + 0 - 1/32*q**4 + 1/160*q**6 + 0*q. Factor p(v).
3*v*(v - 1)*(v + 1)**2/4
Let g(t) = -9 + 4*t + 2 + t**3 - 162*t**2 + 169*t**2. Let w be g(-6). Let 2/3*f**w + 2*f**3 + 2/3*f**2 + 0*f + 0 + 2*f**4 = 0. What is f?
-1, 0
Suppose 0 = -26*u + 3261 - 3105. Suppose -15/2*n + 3/2*n**2 + u = 0. Calculate n.
1, 4
Let h(d) be the second derivative of d**6/120 - d**5/16 + d**4/24 + 5*d**3/6 - 3*d**2 + 96*d. Let h(w) = 0. Calculate w.
-2, 2, 3
Let w = 31/18 - 8/9. Find g, given that w*g**3 - 4/3 + g**2 + 1/6*g**4 - 2/3*g = 0.
-2, 1
Let j(r) = -r**2 - 58*r - 61. Let v(p) = -5*p**2 - 173*p - 182. Let m(h) = 7*j(h) - 2*v(h). Factor m(b).
3*(b - 21)*(b + 1)
Suppose -45 = 60*m - 75*m. Let s(o) be the second derivative of -6*o + 3/10*o**5 + 0 + 1/4*o**4 - 1/8*o**6 + 0*o**m + 0*o**2. Factor s(g).
-3*g**2*(g - 2)*(5*g + 2)/4
Find a, given that 5/4*a - 1/4*a**2 + 3/2 = 0.
-1, 6
Let i = 171/2 + -337/4. Factor i*q**2 + 5/2 + 15/4*q.
5*(q + 1)*(q + 2)/4
Let r = -165 - -497/3. Let 4/3*w**2 + 0 + 0*w + r*w**3 = 0. Calculate w.
-2, 0
Let h(b) be the second derivative of -b**6/195 + 7*b**5/130 - 4*b**4/39 - 16*b**3/39 - 139*b. Factor h(n).
-2*n*(n - 4)**2*(n + 1)/13
Let t(o) be the third derivative of o**6/180 + 7*o**5/30 + 49*o**4/12 - 5*o**3 - 20*o**2. Let r(u) be the first derivative of t(u). Factor r(w).
2*(w + 7)**2
Let s(k) be the first derivative of 13 + 0*k + 4/3*k**3 - 1/18*k**6 + 1/6*k**4 - 3/2*k**2 - 4/15*k**5. Determine r so that s(r) = 0.
-3, 0, 1
Determine q, given that -10*q - q**2 + 16*q**2 - 8 - 16 - 4*q**2 = 0.
-12/11, 2
Let u(j) be the first derivative of 10*j**3/3 + 8*j**2 - 8*j + 6. What is i in u(i) = 0?
-2, 2/5
Let a(c) = c**2 - c + 1. Let q(l) = -l**4 + 14*l**3 - 47*l**2 + 43*l - 3. Let r(b) = 3*a(b) + q(b). Find t such that r(t) = 0.
0, 2, 10
Let c be -20 - 242/(-21 - -10). Factor 0 + 1/8*q**c + 9/8*q.
q*(q + 9)/8
Let 72/7 + 69/7*f - 3/7*f**2 = 0. What is f?
-1, 24
Find v, given that -2/9*v - 4/9*v**2 + 0 + 2/3*v**3 = 0.
-1/3, 0, 1
Factor -4/9*y**2 + 0*y + 0 - 2/9*y**3.
-2*y**2*(y + 2)/9
Let z(x) be the first derivative of -5*x**6/6 + 12*x**5 + 575*x**4/4 + 1610*x**3/3 + 930*x**2 + 760*x + 256. Let z(c) = 0. What is c?
-2, -1, 19
Let f = 3/148 + 17/74. Determine l so that -2*l - f*l**2 - 4 = 0.
-4
Let l(w) be the second derivative of 1/3*w**3 + 0*w**2 - 2*w + 1/5*w**5 + 1/30*w**6 + 0 + 5/12*w**4. Factor l(o).
o*(o + 1)**2*(o + 2)
Suppose i - 4*i + 9 = 0. Solve 48*d - 3*d**i - 10*d + 6 - 3*d**4 - 5*d - 18*d + 9*d**2 = 0 for d.
-1, 2
Suppose g + 31 = -4*x, 42 = -4*x - 3*g + 5. Let r be (4/x)/((-24)/588). Factor -3*p - 4 + 3*p**3 + 11*p**2 - r*p**2 + 7.
3*(p - 1)**2*(p + 1)
Suppose 25 = -2*a + 7. Let k = -5 - a. Find t, given that k*t**3 + 5*t**2 - 2*t**2 + 1 + 3*t - 3*t**3 = 0.
-1
Let d = 73 - 258. Let o = 568/3 + d. What is v in -4*v - 2*v**3 - 1/3*v**4 - o*v**2 - 4/3 = 0?
-2, -1
Factor -64/9*c - 512/9 - 2/9*c**2.
-2*(c + 16)**2/9
Let a(o) = 23*o**2 - 37*o - 96. Let u(h) = 148*h**2 - 240*h - 624. Let w(t) = -32*a(t) + 5*u(t). Factor w(i).
4*(i - 6)*(i + 2)
Let v(i) be the first derivative of 31 + 0*i - i**2 + 0*i**4 + 1/5*i**5 - i**3. Factor v(s).
s*(s - 2)*(s + 1)**2
Let i(f) = -6*f**2 - 84*f - 356. Let j(o) = -13*o**2 - 165*o - 713. Let d(v) = 9*i(v) - 4*j(v). Solve d(r) = 0 for r.
-44, -4
Let t(x) be the third derivative of 1/750*x**5 + 0*x + 0*x**3 + 0 + 9*x**2 - 1/100*x**4. Solve t(i) = 0.
0, 3
Let k = -12348 + 37048/3. Determine v so that 4/3 - k*v**2 - 5*v = 0.
-4, 1/4
Let f(l) = 3*l**3 + 37*l**2 + 75*l + 26. Let h(i) = -12*i**3 - 148*i**2 - 301*i - 106. Let u(d) = 26*f(d) + 6*h(d). Factor u(m).
2*(m + 2)*(m + 10)*(3*m + 1)
Let t(i) be the second derivative of -2/15*i**3 + 4/5*i**2 + 15*i - 1/15*i**4 + 0. What is u in t(u) = 0?
-2, 1
Let l(w) be the first derivative of 0*w**2 + 1/10*w**4 + 5 + 0*w + 0*w**3. Suppose l(g) = 0. What is g?
0
Let v(b) be the first derivative of 0*b**5 + 1/8*b**4 + 0*b**3 + 6 + 0*b - 1/12*b**6 + 0*b**2. Factor v(f).
-f**3*(f - 1)*(f + 1)/2
Let w(t) = -8*t**5 + 28*t**4 - 8*t**3 - 12*t**2 - 12. Let f(s) = -3*s**5 + 11*s**4 - 3*s**3 - 5*s**2 - 5. Let q(o) = 12*f(o) - 5*w(o). Factor q(r).
4*r**3*(r - 1)**2
Let w(g) be the third derivative of g**7/280 - g**6/60 - g**5/40 + g**4/4 + 3*g**3/2 + 9*g**2. Let x(q) be the first derivative of w(q). Factor x(p).
3*(p - 2)*(p - 1)*(p + 1)
Suppose l - 27 = -14. Suppose -l*r + 14*r = 0. Solve 4/3*h**2 + r*h + 0*h**3 - 2/3 - 2/3*h**4 = 0.
-1, 1
Let h(k) = k**3 + 1. Let s(f) = -10*f**3 + 15*f**2 - 5. Let d(c) = c**2 - 12*c - 33. Let r be d(14). Let j(m) = r*h(m) - s(m). Solve j(y) = 0.
0, 3
Let v(b) be the third derivative of b**6/24 + b**5/4 - 5*b**4/6 + 12*b**2 + 15*b. Factor v(x).
5*x*(x - 1)*(x + 4)
Let f = 28 - 23. Let o(h) = -13*h**2 + 75*h - 195. Let g(p) = -7*p**2 + 37*p - 97. Let v(w) = f*g(w) - 3*o(w). Determine q, given that v(q) = 0.
5
Suppose 0 = 68*t - 79*t + 33. Factor 2/3*v**t - 8/9*v + 10/9*v**2 - 8/9.
2*(v - 1)*(v + 2)*(3*v + 2)/9
Factor 19*v**4 - v**5 + 20*v**2 + 14*v**4 + 7*v**3 + 12*v - 35*v**4.
-v*(v - 3)*(v + 1)*(v + 2)**2
Let p = 24164 - 24164. Factor -3/7*f**3 + 6/7*f + p - 3/7*f**2.
-3*f*(f - 1)*(f + 2)/7
Factor 2/15*j**2 - 2 - 28/15*j.
2*(j - 15)*(j + 1)/15
Let v = 5 - 7/2. Let y(x) be the second derivative of 0 + 0*x**3 + 3/5*x**5 + x**4 + 4*x + 0*x**2 - v*x**6. What is t in y(t) = 0?
-2/5, 0, 2/3
Solve -3/4*f**2 + 0*f + 3 = 0 for f.
-2, 2
Let w(y) be the second derivative of 2*y**7/147 + 2*y**6/21 - y**5/5 - 5*y**4/21 + 4*y**3/7 - 40*y. Determine o, given that w(o) = 0.
-6, -1, 0, 1
Let x be (4 - 1) + (37 - 156). Let q be (4 + x/28)*-22. Solve -q*p + 96/7*p**4 - 10/7*p**2 + 16*p**3 + 4/7 = 0.
-1, -2/3, 1/4
Suppose 2*s = s. Suppose s = -0*u + u - 9. Find g such that g**3 + g**3 + u - 3*g**2 + g**2 - 12*g + g**4 + 2*g**3 = 0.
-3, 1
Let x = 30299/35 + -6