n**4. Determine f so that g(f) = 0.
-1, -2/5, 0
Suppose 2*f - 16 = 3*g, 2*g = 3*f + 4*g + 2. Factor 2/7 - 1/7*w - 1/7*w**f.
-(w - 1)*(w + 2)/7
Let g be (-9)/21 + 117/126. Find m, given that 0 - g*m - 3/4*m**2 - 1/4*m**3 = 0.
-2, -1, 0
Determine u, given that -16/9*u**5 - 4/9 + 32/9*u**2 + 8/9*u - 28/9*u**4 + 8/9*u**3 = 0.
-1, 1/4, 1
Let d(h) be the first derivative of -1/10*h**2 + 1/20*h**4 + 0*h + 0*h**3 + 4. What is n in d(n) = 0?
-1, 0, 1
Let g = 3 - 3. Let m(x) = -x**3 - x + 3. Let t be m(g). Solve -j**5 + 2*j**4 + t - j**3 - 3 = 0.
0, 1
Let d(u) be the first derivative of 4 - 2/3*u**2 + 0*u - 5/12*u**4 + 1/15*u**5 + 8/9*u**3. Factor d(b).
b*(b - 2)**2*(b - 1)/3
Let q(o) be the second derivative of 5*o**7/126 - 2*o**6/45 - o**5/10 + o**4/9 + o**3/18 + 26*o. Solve q(z) = 0.
-1, -1/5, 0, 1
Let d be (-49)/(-14)*(-2 + 0). Let u = 7 + d. Factor 2/7*i**3 - 2/7*i**5 + 0*i**4 + u + 0*i**2 + 0*i.
-2*i**3*(i - 1)*(i + 1)/7
Let p = -11 - -13. Let i(b) be the first derivative of -1/2*b**4 - 2 - p*b - 3*b**2 - 2*b**3. Solve i(k) = 0.
-1
Let b be 12/(-16) + -2*15/(-36). Let i(f) be the second derivative of -3/40*f**5 + 0 - f + 0*f**2 - b*f**4 + 0*f**3. Suppose i(g) = 0. Calculate g.
-2/3, 0
Let h(k) be the third derivative of 1/3*k**3 + 0 + 0*k - 5*k**2 - 1/8*k**4 + 1/60*k**5. Find b such that h(b) = 0.
1, 2
Let n(l) be the second derivative of -l**6/1440 + l**5/240 + l**4/32 + l**3/6 + 5*l. Let p(y) be the second derivative of n(y). Factor p(b).
-(b - 3)*(b + 1)/4
Let a(u) = -u**2 - 4*u + 4. Let l(j) = 4*j**2 + 11*j - 11. Let i(n) = -11*a(n) - 4*l(n). Factor i(m).
-5*m**2
Let v = 5 + -3. Determine r, given that -4*r**3 - 8*r**v + 6*r**2 + 6*r**2 = 0.
0, 1
Let y = 64 - 444/7. Solve -y - 6/7*m - 2/7*m**2 = 0 for m.
-2, -1
Determine w so that 72/11*w**2 + 20/11*w**3 + 54/11 + 108/11*w + 2/11*w**4 = 0.
-3, -1
Factor -77 + 5*k + 5*k**3 + 77 + 10*k**2.
5*k*(k + 1)**2
Let x(f) be the second derivative of -f**6/90 + f**5/5 - 3*f**4/2 - 5*f**3/6 - 4*f. Let g(p) be the second derivative of x(p). What is a in g(a) = 0?
3
Factor 3*v**2 + 3*v - 2 + 5*v**3 + 11 - 8 - 4*v**3.
(v + 1)**3
Let o(i) be the first derivative of -i**6/14 + 6*i**5/35 - 42. Factor o(w).
-3*w**4*(w - 2)/7
Let g be (3/(-12))/((-14)/8). Find z such that 3/7*z**3 + z**2 + g + 5/7*z = 0.
-1, -1/3
Let h(z) be the second derivative of 2*z**6/15 - 7*z**5/5 + 5*z**4 - 6*z**3 - 49*z. What is s in h(s) = 0?
0, 1, 3
Let d be 3*(-2)/(-30) - (-68)/10. Let o(t) be the third derivative of 0*t**5 + 0*t**3 - 1/840*t**8 + t**2 + 0*t**d + 0 + 1/300*t**6 + 0*t + 0*t**4. Factor o(b).
-2*b**3*(b - 1)*(b + 1)/5
Let u(o) be the first derivative of o**4/8 - 2*o**3 + 9*o**2 - 22. Factor u(v).
v*(v - 6)**2/2
Let f be (-20)/(-15)*(-6)/(-4). Factor -2*k**4 + 0*k**3 - 2*k + k**2 - 3*k**f + 4*k**4 + 2*k**3.
2*k*(k - 1)*(k + 1)**2
Let h(k) be the second derivative of k**8/168 + 2*k**7/105 + k**6/60 - k**2/2 - k. Let l(b) be the first derivative of h(b). Factor l(c).
2*c**3*(c + 1)**2
Suppose -2*w + 4*w = 0. Factor -2/7*h**3 + 0 - 2/7*h**5 + 0*h + 4/7*h**4 + w*h**2.
-2*h**3*(h - 1)**2/7
Suppose 0 + 0*w + 6/5*w**2 + 3/5*w**4 - 9/5*w**3 = 0. Calculate w.
0, 1, 2
Let h(d) be the third derivative of -d**2 + 0*d**7 - 1/112*d**8 - 1/8*d**4 + 1/20*d**6 + 0*d + 0*d**3 + 0*d**5 + 0. Let h(b) = 0. Calculate b.
-1, 0, 1
Factor 12/5*p**3 + 8/5 - 8/5*p**2 - 12/5*p.
4*(p - 1)*(p + 1)*(3*p - 2)/5
Let b(f) = 2*f - 3. Let m be b(2). Factor 2*s**2 + m + 2*s**2 + 3 - 2*s - 6*s**2.
-2*(s - 1)*(s + 2)
Let a(z) be the third derivative of -3*z**2 + 0*z + 0*z**3 + 1/60*z**5 + 0 - 1/12*z**4 + 1/120*z**6. Factor a(w).
w*(w - 1)*(w + 2)
Suppose 2/11*b**2 + 22 + 4*b = 0. What is b?
-11
Let r(p) be the second derivative of -p**6/105 - p**5/14 - p**4/7 + 35*p. What is h in r(h) = 0?
-3, -2, 0
Suppose 0 = -4*n + 2*n. Suppose -4*h + 6*h - 4 = n. Factor -2*l + 0*l**2 + 5*l**3 - 3*l**3 + 0*l - 2 + 2*l**h.
2*(l - 1)*(l + 1)**2
Let n(w) be the first derivative of -2*w**5/5 + 3*w**4/2 + 2*w**3/3 - 3*w**2 - 10. Factor n(p).
-2*p*(p - 3)*(p - 1)*(p + 1)
Let z = -873/7 - -125. Suppose 2/7*x**4 + 2/7*x**5 + z*x - 4/7*x**3 + 2/7 - 4/7*x**2 = 0. Calculate x.
-1, 1
Let n(z) = -8*z**2 + 24*z - 43. Suppose -4*y + i + 89 = 0, -3*y + 3*i + 120 = 2*y. Let v(h) = -33*h**2 + 96*h - 171. Let o(k) = y*n(k) - 5*v(k). Factor o(a).
-3*(a - 4)**2
Let p be 20/(-3) + 3 - -4. Solve 1/3*j**3 - 1/3 - p*j + 1/3*j**2 = 0.
-1, 1
Let n = 42 + -40. Determine c so that 3/2 + n*c + 1/2*c**2 = 0.
-3, -1
Factor -5 + 5*y**2 + 0*y**2 - 4*y - 4*y**2.
(y - 5)*(y + 1)
Let l(p) be the third derivative of -4*p**2 - 1/30*p**5 + 0*p**4 + 0 + 1/3*p**3 + 0*p. Factor l(x).
-2*(x - 1)*(x + 1)
Let m(p) be the first derivative of -p**4/22 + 4*p**3/33 - p**2/11 - 5. Determine i, given that m(i) = 0.
0, 1
Let g be 1/3 + (-6)/(-90). Let k(x) be the first derivative of -4/15*x**3 + 0*x**4 + g*x + 0*x**2 + 2/25*x**5 - 2. Factor k(f).
2*(f - 1)**2*(f + 1)**2/5
Let q(v) be the second derivative of v**5/10 + 5*v**4/24 - 7*v**3/12 - v**2/2 + 4*v. Factor q(n).
(n - 1)*(n + 2)*(4*n + 1)/2
Let g(i) be the third derivative of i**6/420 + i**5/70 + i**4/42 - 4*i**2. Factor g(f).
2*f*(f + 1)*(f + 2)/7
Factor 1/6 + 1/2*w**2 + 1/6*w**3 + 1/2*w.
(w + 1)**3/6
Let j(c) be the first derivative of -8 + 4/3*c + c**2 - 4/9*c**3. Determine i, given that j(i) = 0.
-1/2, 2
Let v(j) be the second derivative of -j**7/56 + 3*j**6/40 - 9*j**5/80 + j**4/16 - 23*j. Let v(g) = 0. Calculate g.
0, 1
Suppose 0 = 4*g - 129 + 101. Let c(z) be the second derivative of 0 + 1/126*z**g + 0*z**3 + 3*z - 1/60*z**5 + 0*z**2 - 1/90*z**6 + 1/36*z**4. Factor c(u).
u**2*(u - 1)**2*(u + 1)/3
Let d(a) = a**3 - 8*a**2 - 9*a + 2. Let m be d(9). Find i such that -8*i**2 + 3*i**3 + m*i**5 + 10*i**4 + 2*i**3 - 16*i + 7*i**3 = 0.
-2, 0, 1
Let y be 16/(-12) - (2 - 4). Let s(j) be the first derivative of y*j**3 + 1 - 2*j + 0*j**2. What is v in s(v) = 0?
-1, 1
Let g = 26 - 22. Let j(l) be the first derivative of 0*l + 0*l**2 - 2/15*l**3 - 1/10*l**g - 4. Solve j(v) = 0 for v.
-1, 0
Determine h so that -13/3*h**2 + h**3 + 16/3*h - 4/3 = 0.
1/3, 2
Let t(a) be the second derivative of 9/80*a**5 + 3/56*a**7 + 0*a**2 - a + 0 - 1/4*a**3 - 7/40*a**6 + 3/16*a**4. Factor t(i).
3*i*(i - 1)**3*(3*i + 2)/4
Let h(v) be the third derivative of v**6/40 - 7*v**5/30 + 3*v**4/2 - 14*v**3/3 + 5*v**2. Let z(a) = -a**2 + 1. Let w(p) = -h(p) - 4*z(p). Factor w(s).
-3*(s - 2)**3
Find f, given that 10/9*f + 1/9*f**2 + 25/9 = 0.
-5
Let r(m) be the third derivative of -1/210*m**5 + 2*m**2 + 0*m**4 + 0*m + 1/735*m**7 + 1/1176*m**8 + 0*m**3 - 1/420*m**6 + 0. Factor r(b).
2*b**2*(b - 1)*(b + 1)**2/7
Let m = -5 + 10. Suppose 20 = m*j - 0*j. Find x such that -4*x**2 + 5*x**2 + 0*x**3 - x**j + x**3 - x = 0.
-1, 0, 1
Let c(k) be the first derivative of 3/8*k**6 - 3 + 33/16*k**4 + 1/4*k**2 + 0*k - 29/20*k**5 - 5/4*k**3. Let c(r) = 0. Calculate r.
0, 2/9, 1
Suppose 3 = y, 3*q - 5*y + 10 = -5. Let k(i) be the third derivative of q - 1/270*i**5 + 0*i - 3*i**2 + 1/108*i**4 - 1/540*i**6 + 1/27*i**3. Factor k(a).
-2*(a - 1)*(a + 1)**2/9
Suppose 2*v = 3*v - 3. Solve -3*w**4 - 4*w**4 + 0*w**3 + v*w**3 + 6*w**4 + w - 3*w**2 = 0.
0, 1
Suppose 0 = -14*w + 8*w + 18. Let t(q) be the first derivative of 1/7*q**6 + 4/21*q**w + 0*q**2 + 0*q + 2 + 1/2*q**4 + 16/35*q**5. Solve t(p) = 0 for p.
-1, -2/3, 0
Factor -9*b**2 + 3*b**4 + 6 - 4*b**3 + 5*b**3 + 3*b - 4*b**3.
3*(b - 2)*(b - 1)*(b + 1)**2
Let p = -4 + 3. Let s(l) = -l**2 - 1. Let u(f) = -12*f**2 - 6*f - 14. Let i(j) = p*u(j) + 10*s(j). Factor i(g).
2*(g + 1)*(g + 2)
Solve 9/2*t**2 - 3*t + 0 = 0.
0, 2/3
Let s be (78/(-20))/(-13)*(-26)/(-18). Let h(p) be the third derivative of -p**4 - 4/3*p**3 - s*p**5 + 0*p + 2*p**2 + 0 - 1/105*p**7 - 1/10*p**6. Factor h(c).
-2*(c + 1)**2*(c + 2)**2
Suppose -12 = -5*b + 8. Suppose 5*c - b*t = 0, 2*c + 2*t = 3*c. Find u, given that -2/9 - 2/9*u**4 + c*u**3 + 0*u + 4/9*u**2 = 0.
-1, 1
Suppose 3*n + 0 + 9 = 0. Let w = 3 + n. Factor 1/2*m + 1/2*m**3 - m**2 + w.
m*(m - 1)**2/2
Let f(j) be the third derivative of -j**4/24 - j**3/2 - j**2. Let i be f(-5). Solve -2*n**2 + 2 - 2 - i*n = 0.
-1, 0
Let i(d) be the third derivative of -d**5/20 - d**4/2 - 3*d**3/2 + 4*d**2. Factor i(k).
-3*(k + 1)*(k + 3)
Factor -4*t - 4*t**4 - 9*t**4 + 15*t**