. Find f such that d(f) = 0.
-1, 15
Suppose 0 + 0*b - 1/5*b**5 - 2/5*b**4 - 1/5*b**3 + 0*b**2 = 0. Calculate b.
-1, 0
Factor -1/2*v**3 - 3/2*v**2 - 3/2*v - 1/2.
-(v + 1)**3/2
Let u(p) be the first derivative of 32*p + 18 - 7 + 24*p**2 + 4*p**4 + 8*p**3 - 3*p**4 + 0*p**3. Factor u(y).
4*(y + 2)**3
Suppose -3*w + 11*w = 16. Suppose -2*s - 3 = -w*u + 1, 2*s + 19 = 5*u. Let 3/5*j**s + 0*j + 0*j**2 + 0 + 3/5*j**5 + 6/5*j**4 = 0. What is j?
-1, 0
Let f(h) be the first derivative of 12/5*h**5 - 10/3*h**6 - 4*h**2 + 7*h**4 + 0*h - 4*h**3 + 5. Determine k so that f(k) = 0.
-1, -2/5, 0, 1
Let y(f) be the third derivative of -f**8/840 - 4*f**7/525 + f**6/60 + 6*f**5/25 + 3*f**4/5 - 378*f**2. Find t, given that y(t) = 0.
-3, -2, 0, 3
Let b be ((-8)/30)/((-7)/(-5)) - (-84)/252. Factor b*y**2 + 2/7*y - 3/7.
(y - 1)*(y + 3)/7
Factor 2/9*h**2 + 8/3*h + 22/9.
2*(h + 1)*(h + 11)/9
Suppose -k = -4*v + v + 11, -3*k = v + 13. Factor 8*t**4 + 1 + v*t**5 + 25*t**3 - 1 - 15*t**3 + 4*t**2.
2*t**2*(t + 1)**2*(t + 2)
Let s(n) be the third derivative of -n**5/20 - 17*n**4/8 - 15*n**3 - 73*n**2. Let s(z) = 0. Calculate z.
-15, -2
Let m be 7 + -5 + 1*3. Let z be (-2)/m - 27/(-5). Suppose -2*j - z + 3*j**2 - 3*j**3 + 2 + 4*j + j = 0. What is j?
-1, 1
Let t(c) be the second derivative of c**7/105 + c**6/15 + 3*c**5/50 - c**4/6 - 4*c**3/15 - 36*c. Solve t(r) = 0 for r.
-4, -1, 0, 1
Let b(x) be the second derivative of -x**5/5 - 5*x**4 - 48*x**3 - 224*x**2 + 186*x. Let b(i) = 0. What is i?
-7, -4
Suppose 14 = u - 34*t + 37*t, t = 4. Let a(z) be the third derivative of 1/84*z**4 + 0*z**3 + 1/420*z**5 + 0*z + z**u + 0. Find n, given that a(n) = 0.
-2, 0
Let t(j) = 8*j**4 - 3*j**3 + 28*j**2. Let o(x) = 9*x**4 - 2*x**3 + 29*x**2. Let g(u) = -7*o(u) + 8*t(u). Factor g(r).
r**2*(r - 7)*(r - 3)
Let k(l) be the first derivative of -l**4/18 - 104*l**3/27 + 53*l**2/9 - 571. Determine q so that k(q) = 0.
-53, 0, 1
Let v = -62 + 48. Let p be 21/30 - (v/(-4))/7. Factor 1/5*o**2 + 0 + p*o.
o*(o + 1)/5
Let s(l) be the second derivative of -l**7/294 + 2*l**6/105 - l**5/140 - l**4/6 + 10*l**3/21 - 4*l**2/7 - l - 2. Find k, given that s(k) = 0.
-2, 1, 2
Suppose -3*z + 15 = 4*s - 7*s, -3*s = z - 5. Suppose 4*y**4 - 3*y**2 - y**4 + s*y**4 + 3*y - 3*y**3 = 0. Calculate y.
-1, 0, 1
Suppose -4*m + 13 = -2*m - 3*v, 4 = 5*m + 2*v. Factor 3*p**2 + 13 - 14 - m*p**2.
(p - 1)*(p + 1)
Let k(t) be the second derivative of -5/3*t**3 - 7/24*t**4 - 1/60*t**5 - 25/12*t**2 + 17*t + 0. Factor k(z).
-(z + 5)**2*(2*z + 1)/6
Let b(u) be the second derivative of -u**4/48 + u**3/6 - 3*u**2/8 - 8*u - 3. Solve b(s) = 0.
1, 3
Let p(v) = 26*v**2 - 400*v + 310. Let c(k) = -5*k**2 + 80*k - 63. Let q(b) = -16*c(b) - 3*p(b). Factor q(t).
2*(t - 39)*(t - 1)
Let m(b) = 1 - 2*b + 3*b - 1. Let u be m(2). Solve 0 - 4/3*w**3 + 10/3*w**u - 10/3*w**4 + 4/3*w = 0.
-1, -2/5, 0, 1
Let m be 63/12*3/(-18)*16. Let q(d) = -d**3 - 16*d**2 - 30*d - 24. Let r be q(m). Factor -8 - 1/2*i**2 - r*i.
-(i + 4)**2/2
Suppose 2*i = -0*i + 6. Let n(q) = q**3 - q**2 - 3*q - 3. Let s be n(i). Suppose -6*t - s*t**2 + 0 + 3*t**2 + 0 - 3 = 0. Calculate t.
-1
Let -8/5*x**2 - 1/5*x**4 - 4/5*x + 0 - x**3 = 0. Calculate x.
-2, -1, 0
Let r(v) = -v**2 - 3*v + 9. Let j be r(-6). Let k be ((-8)/36 + (-2)/j)/(-2). Factor -10*w**4 - 50/9*w**5 - 16/3*w**3 + 0*w + k - 8/9*w**2.
-2*w**2*(w + 1)*(5*w + 2)**2/9
Suppose 3*u - 62 = -2*a + 4*u, -4*a + 130 = u. Suppose -6*z + 4 = -a. Factor -27/2*y**2 - z + 18*y.
-3*(3*y - 2)**2/2
Suppose 4*r + 2*q = -8, -121*q - 4 = 5*r - 120*q. Suppose 0 + r*d + 2/7*d**2 + 2/7*d**3 = 0. What is d?
-1, 0
Let z(a) = 2*a + 28. Let o be z(-14). Suppose -12 = -3*d - 3. Factor o - 14/11*r**d - 10/11*r**2 + 4/11*r.
-2*r*(r + 1)*(7*r - 2)/11
Let c be 6/21 + (-288)/(-21). Factor -8*i + c + 2*i**2 + 5 + 10 - 23.
2*(i - 3)*(i - 1)
Let w(d) be the second derivative of 5*d**4/12 + 55*d**3/6 + 45*d**2 - 17*d. Solve w(x) = 0 for x.
-9, -2
Let i(r) = -r**3 + 1. Let k(t) be the second derivative of 1/5*t**6 + 0 + 5*t + 4/3*t**3 - 4*t**2 - 1/3*t**4 - 1/10*t**5. Let g(p) = 6*i(p) + k(p). Factor g(y).
2*(y - 1)**2*(y + 1)*(3*y - 1)
Let d(m) be the third derivative of -m**5/12 + 5*m**4/4 - 15*m**3/2 - 68*m**2. Suppose d(g) = 0. Calculate g.
3
Let d(y) = 3*y**2 + 6*y - 13. Let u be d(3). Factor u + 14*b - 14*b - 24*b + 4*b**2.
4*(b - 4)*(b - 2)
Let r(w) = w**2 - 6*w + 1. Let n = 25 - 3. Let t be (-9 - -11) + (-1 - -3). Let h(u) = -5*u**2 + 31*u - 4. Let c(i) = n*r(i) + t*h(i). Solve c(g) = 0 for g.
1, 3
Let i = -27609/2 + 13817. Factor 5/2*z**3 + i*z**2 + 15*z + 0.
5*z*(z + 2)*(z + 3)/2
Let t(n) be the second derivative of -1/100*n**5 + 5/2*n**2 - 15*n - 3/20*n**4 + 0 - 1/2*n**3. Let t(c) = 0. What is c?
-5, 1
Let j(o) be the third derivative of 1 + 1/12*o**4 - 2*o**2 + 5/18*o**3 + 0*o + 1/180*o**5. Factor j(f).
(f + 1)*(f + 5)/3
Let s(n) be the first derivative of 2*n**3/27 - 14*n**2 + 250*n/9 - 163. Factor s(i).
2*(i - 125)*(i - 1)/9
Suppose -u - 222 = -7*u. Factor -u - c + 37 - c**3 + 0*c - 2*c**2.
-c*(c + 1)**2
Let u(x) be the second derivative of -x**5/110 + 8*x**4/33 + 35*x**3/33 + 18*x**2/11 + 4*x - 48. Suppose u(o) = 0. What is o?
-1, 18
Suppose 0 = -2*m + 5*i + 33, 2*m + 2*i = -1 - 1. Factor -7*g**3 + 10*g**m + 5*g**2 - 7*g**2 - g**3.
2*g**2*(g - 1)*(5*g + 1)
Suppose -7*b = -2*b - 25. Let j(f) be the first derivative of -f**3 - b + 0 - 3 + 3*f**2. Factor j(o).
-3*o*(o - 2)
Suppose 3*q - 5*n - 64 = q, 0 = -2*q - 4*n + 64. Let j = -32 + q. Factor -3/2*t**4 - 3/2*t**3 + 0*t + j + 0*t**2.
-3*t**3*(t + 1)/2
Factor 6/7 + 2/7*x**3 + 2/7*x**2 - 10/7*x.
2*(x - 1)**2*(x + 3)/7
Let d(y) be the second derivative of 4/3*y**3 - 1/30*y**6 + 31*y + 0 + 1/4*y**4 - 1/10*y**5 + 2*y**2. Factor d(o).
-(o - 2)*(o + 1)**2*(o + 2)
Suppose -4*t + 8 = -8. Let h(b) = b**2 + 3*b + 5. Let y be h(-2). Factor f**t - 7*f + f**2 + 2*f**y + 7*f.
f**2*(f + 1)**2
Let p(d) = d**2 + d + 12. Let n be p(0). Suppose n = 4*z - 0*z. Factor 9*b**z - 5*b**2 + 3*b**2 + 0*b**5 - 4*b**2 - 3*b**5.
-3*b**2*(b - 1)**2*(b + 2)
Factor -3/4*p**2 + 0 + 3/4*p.
-3*p*(p - 1)/4
Let f(b) be the third derivative of b**6/280 - 75*b**4/56 + 125*b**3/7 + 92*b**2 + b. What is h in f(h) = 0?
-10, 5
Suppose 5*o + 0*i - 3*i = 8, 3*o + 2*i - 20 = 0. Suppose -5*v + 5*h - 8 = -18, o*h + 8 = 0. Factor -2/7*f**2 + v*f + 2/7*f**3 + 0.
2*f**2*(f - 1)/7
Suppose -82 = 192*c - 190*c. Let i = 44 + c. Factor 1/5*s**2 + 0*s + 0 + 1/5*s**i.
s**2*(s + 1)/5
Let z(g) be the third derivative of g**5/30 - 13*g**4/12 - 14*g**3/3 + 415*g**2. What is n in z(n) = 0?
-1, 14
Factor -2/3*q**3 + 0*q**2 + 0 + 0*q + 1/3*q**4 + 1/3*q**5.
q**3*(q - 1)*(q + 2)/3
Let u(d) be the third derivative of d**6/24 + 3*d**5/2 + 45*d**4/2 + 180*d**3 + 8*d**2. Solve u(r) = 0.
-6
Let m be -13 + 11 - 22/(-9) - 0. Let s(l) be the first derivative of -2/27*l**3 + 5 - 1/3*l**2 - m*l. Factor s(b).
-2*(b + 1)*(b + 2)/9
Let m(z) = -1 - 99*z**2 + 99*z**2 + z**3 + 2 + z. Let k(s) = 120*s**3 + 45*s**2 + 6*s + 9. Let c(a) = -k(a) + 12*m(a). Suppose c(g) = 0. What is g?
-1/3, 1/4
Let r(a) be the second derivative of a**4/6 - 53*a**3/3 - 54*a**2 - 56*a. Determine m so that r(m) = 0.
-1, 54
Suppose -5*b = -2*u, 0 = -2*u - 0*u + 10. Suppose 5*l - 25 = 2*h, -5*l - 2*h + 2 + 3 = 0. Suppose 4*a**2 - a**b + a**2 - l*a**2 + 1 + 2*a = 0. What is a?
-1
Let p be -9 + 10 + -3 + 7. Let z(u) be the first derivative of -5/4*u**4 - 7/5*u**5 + 3*u**3 - 2*u + 5/2*u**2 - p. What is t in z(t) = 0?
-1, 2/7, 1
Let p be 0 + ((-4)/2)/(-1). Determine q so that -p*q**3 + 5*q**3 - 4*q**3 + q - 4*q + 4*q**2 = 0.
0, 1, 3
Suppose 3*n = 2*w - 6, 2*w - 2*n + 1 - 3 = 0. Let m(z) = -4*z + 8 - 2*z - 3 + z**2. Let h(u) = -3*u**2 + 17*u - 14. Let b(r) = w*h(r) - 8*m(r). Factor b(p).
(p - 2)*(p - 1)
Let g = 13224/7 - 1877. Let q = g + -11. Let -q*v**3 + 4/7*v**4 + 4/7*v**2 + 0 + 0*v = 0. Calculate v.
0, 1
Let x(y) be the first derivative of 1/24*y**5 - 1/72*y**4 + 0*y**3 + 0*y - 5/144*y**6 + 2 - 5/2*y**2. Let n(j) be the second derivative of x(j). Factor n(b).
-b*(5*b - 2)*(5*b - 1)/6
Suppose 0 = -5*a + 20, -2*d + 33*a - 28*a - 12 = 0. Factor -4*h**2 - 2/9*h**d + 6 - 16/9*h**3 + 0*h.
-2*(h - 1)*(h + 3)**3/9
Let m(r) be the third derivative of -r**8/840 - 2*r**7/175 - 13*r**6/300 - 2*r**5/25 - r**4/15 + 160*r*