). Find h, given that w(h) = 0.
0, 1
Find g, given that 14/5*g - 4/5 + 14/5*g**2 + 8/5*g**5 - 2*g**4 - 22/5*g**3 = 0.
-1, 1/4, 1, 2
Let w = 9 - 4. Find o, given that 12*o**3 + 2*o - 4*o**5 + 2*o**w - 6*o**4 + 4*o**5 + 14*o**4 + 8*o**2 = 0.
-1, 0
Let f(m) = 7*m**2 + 5*m - 6. Let z(b) = b**2 - 1. Let k(x) = -5*f(x) + 20*z(x). Suppose k(d) = 0. Calculate d.
-2, 1/3
Let -2*j - j**3 + 2*j**2 - 3*j + 4*j = 0. What is j?
0, 1
Let h(z) be the third derivative of 0*z**3 + z**2 + 1/2016*z**8 + 1/36*z**5 + 1/48*z**4 + 0*z + 0 + 1/60*z**6 + 1/210*z**7. Factor h(r).
r*(r + 1)**3*(r + 3)/6
Let w = -92/15 - -39/5. Factor -4/3*u + w*u**3 - 1/3*u**4 + 8/3 - 2*u**2.
-(u - 2)**3*(u + 1)/3
Factor 0*x - 1/2*x**3 + 1/2*x**5 - 1/2*x**4 + 1/2*x**2 + 0.
x**2*(x - 1)**2*(x + 1)/2
Let v be (-82)/(-456) - (-24)/32. Let n = v + -5/19. Determine w, given that 0*w - n*w**2 + 2/3 = 0.
-1, 1
Let q(h) = h**2 - 11*h - 26. Let i be q(13). Let d(u) be the second derivative of -1/3*u**2 + i - 11/18*u**3 - 4/9*u**4 - 4*u - 7/60*u**5. Factor d(o).
-(o + 1)**2*(7*o + 2)/3
Suppose 2/3 + 4*r**3 + 2/3*r**4 - 2*r - 4/3*r**2 - 2*r**5 = 0. Calculate r.
-1, 1/3, 1
Let r(s) be the third derivative of s**6/660 - s**5/165 + 2*s**2. Factor r(m).
2*m**2*(m - 2)/11
Suppose -18*p = -20*p + 4. Determine h, given that 0 - 2/9*h + 4/9*h**p - 2/9*h**3 = 0.
0, 1
Let k(d) = d**2 - 5. Let t(x) = 12. Let a(c) = -1. Let o(r) = -27*a(r) - 2*t(r). Let z(i) = -3*k(i) - 5*o(i). Let z(w) = 0. Calculate w.
0
Let j(y) = -y**2 - y + 1. Let i(t) = -8*t**2 + 2*t + 2. Let z(m) = i(m) - 4*j(m). Factor z(f).
-2*(f - 1)*(2*f - 1)
Let x(d) = 12*d**4 - 20*d**3 + 30*d**2 - 20*d + 5. Let z(h) = 11*h**4 - 20*h**3 + 30*h**2 - 20*h + 5. Let f(w) = 6*x(w) - 7*z(w). Factor f(n).
-5*(n - 1)**4
Suppose 4*c + 32 + 64 = 0. Let u be c/42*14/(-4). Determine w so that 8*w**u - 1 - 2*w**2 + 2*w**3 - 7 = 0.
-2, 1
Let 50 - 7*w - 38 - 4*w**2 + 0*w - w = 0. Calculate w.
-3, 1
Let p(m) = -4*m**2 + 12*m - 6. Suppose -2*q + 21 = 17. Let h(j) = 16*j**2 - 48*j + 23. Let u(v) = q*h(v) + 9*p(v). Factor u(g).
-4*(g - 2)*(g - 1)
Let j = 39/8 + -101/24. Let v(q) be the first derivative of 2*q - 3 + j*q**3 + 2*q**2. Determine u so that v(u) = 0.
-1
Let z(k) = -3*k**2 + k - 4. Let y(d) = 5*d**2 + 5. Let x(l) = -l**2 - 1. Let a(r) = 6*x(r) + y(r). Let b = -13 + 9. Let m(t) = b*a(t) + z(t). Factor m(q).
q*(q + 1)
Let k(v) be the first derivative of -2/3*v**3 - 3 + 0*v + 0*v**2. Let k(h) = 0. Calculate h.
0
Let g(f) be the first derivative of 0*f**2 - 5 - f**3 + 0*f**4 + 0*f + 3/5*f**5. Factor g(v).
3*v**2*(v - 1)*(v + 1)
Factor -22*i - 3 - 49/4*i**3 - 175/4*i**2.
-(i + 3)*(7*i + 2)**2/4
Let g(k) = -4*k**3 + 7*k**2 - 5*k - 4. Let s(p) = -4*p**3 + 7*p**2 - 6*p - 5. Let y(m) = 4*g(m) - 3*s(m). Factor y(l).
-(l - 1)**2*(4*l + 1)
Let -26*j**3 + 23*j + 8*j**4 - 20*j**2 + 17*j**4 - 4*j**3 + 17*j - 5*j**5 = 0. Calculate j.
-1, 0, 2
Let i(j) be the third derivative of 0*j + 0 + 5/12*j**4 - 2/3*j**3 - 2/15*j**5 - 3*j**2 + 1/60*j**6. Solve i(n) = 0 for n.
1, 2
Let q(i) be the first derivative of i**5/10 - i**4/2 + i**3/2 + i**2 - 2*i - 3. Factor q(o).
(o - 2)**2*(o - 1)*(o + 1)/2
Let g(m) be the third derivative of m**8/560 + m**7/70 + 3*m**6/200 - m**5/20 - m**4/10 + 12*m**2 - 3. Determine r so that g(r) = 0.
-4, -1, 0, 1
Suppose -3 - 7 = -5*s. Suppose 0 = -5*k - u + 8 - 2, 5*k - 30 = 5*u. Let k*q**4 - q**2 + 3*q**s - 4*q**4 = 0. Calculate q.
-1, 0, 1
Let i(x) = -17*x**2 - 5*x + 13. Let z = -34 + 60. Let d(u) = -4*u**2 - u + 3. Let b(j) = z*d(j) - 6*i(j). Solve b(y) = 0.
0, 2
Let u(y) be the second derivative of 1/6*y**4 - 4*y + 1/6*y**3 + 0 + 0*y**2. Factor u(t).
t*(2*t + 1)
Let b(f) be the first derivative of f**5/20 + f**4/4 + 5*f**3/12 + f**2/4 + 5. Find l, given that b(l) = 0.
-2, -1, 0
Suppose -h - 4*g = 6, g - 4 = -4*h + 2. Let p be h - 1*8/12. Factor 4/3 - 2/3*d**3 - p*d**2 + 2/3*d.
-2*(d - 1)*(d + 1)*(d + 2)/3
Let s(a) be the first derivative of -3*a**4/4 + 5*a**3 - 9*a**2/2 - 27*a + 4. Let s(w) = 0. Calculate w.
-1, 3
Let c be (-1)/2*-1*2. Suppose 0 = -m + 3*a + c, 1 = -m + a + 4. Let w - 2*w**2 - 14 - m - 13*w = 0. Calculate w.
-3
Let j(o) be the second derivative of o**4/72 - 7*o**3/18 + 49*o**2/12 + 4*o. Factor j(t).
(t - 7)**2/6
Let c = 948 - 3787/4. Determine u so that -1/4 - 5/4*u - 5/2*u**2 - 5/2*u**3 - 1/4*u**5 - c*u**4 = 0.
-1
Let m be (-2)/(-6)*(-2 - 1). Let h = -2 - m. Let u(z) = z**3 + 1. Let g(j) = -4*j**3 - 2*j**2 + j - 5. Let c(x) = h*g(x) - 5*u(x). Suppose c(v) = 0. What is v?
0, 1
Let u(a) be the third derivative of a**8/6720 + a**7/840 + a**6/360 + a**3/6 - 2*a**2. Let z(d) be the first derivative of u(d). What is q in z(q) = 0?
-2, 0
Find q such that -2/5*q**3 + 0 - 2/5*q**5 + 4/5*q - 6/5*q**4 + 6/5*q**2 = 0.
-2, -1, 0, 1
Let w(c) be the first derivative of -2*c**3/15 - 2*c**2/5 - 2*c/5 + 6. Factor w(h).
-2*(h + 1)**2/5
Let w(s) be the first derivative of -3*s**4/4 - s**3 + 3*s**2/2 + 3*s + 4. Factor w(t).
-3*(t - 1)*(t + 1)**2
Let c(q) be the first derivative of 2/65*q**5 + 4 + 1/13*q**2 + 0*q - 2/39*q**3 - 1/26*q**4. Suppose c(a) = 0. Calculate a.
-1, 0, 1
Let g be ((-6)/(-4))/(-3) - (-105)/50. Factor -2/5*z**2 + 4/5*z**3 + 0*z + g*z**5 + 0 + 14/5*z**4.
2*z**2*(z + 1)**2*(4*z - 1)/5
Suppose -2*w = 2*y, -3*y - 2*y + 4*w + 36 = 0. Suppose -z - 1 = f + y, 15 = -3*z. Factor 4/3*j**4 - 2/3*j**5 - 4/3*j**2 + 2/3*j + 0 + f*j**3.
-2*j*(j - 1)**3*(j + 1)/3
Let g = -112/15 - -39/5. Factor -2/3*u + g + 1/3*u**2.
(u - 1)**2/3
Let q(c) = 36*c**5 - 120*c**4 + 148*c**3 - 78*c**2 + 12*c - 2. Let n(u) = u**2 - 2*u - 1. Let m(p) = -2*n(p) + q(p). Suppose m(b) = 0. Calculate b.
0, 2/3, 1
Factor 4/7*k - 2/7*k**2 - 2/7.
-2*(k - 1)**2/7
Let j be (9 - 10)*(-90)/(-2). Let z be 6*(-5)/j*1. Factor z*q**3 - 2/3*q**2 + 0 + 2/3*q**4 - 2/3*q**5 + 0*q.
-2*q**2*(q - 1)**2*(q + 1)/3
Let n(z) be the first derivative of 18*z**3/7 - 39*z**2/14 + 6*z/7 - 4. Factor n(c).
3*(2*c - 1)*(9*c - 2)/7
Factor 31*v**2 - 28*v**2 + 9 + 27*v - 12*v - 3*v**3.
-3*(v - 3)*(v + 1)**2
Let a(r) = 3*r**3 - 4*r**2 - 7*r. Let n(b) = b**3 - b. Let h(v) = a(v) - 4*n(v). Solve h(k) = 0.
-3, -1, 0
Let z(u) be the third derivative of u**8/546 - u**7/1365 - u**6/260 - 29*u**2. Factor z(q).
2*q**3*(q - 1)*(4*q + 3)/13
Let t(w) be the third derivative of w**8/160 + w**7/35 + 11*w**6/240 + w**5/40 + w**3/6 - 2*w**2. Let i(b) be the first derivative of t(b). Factor i(v).
3*v*(v + 1)**2*(7*v + 2)/2
Let o = -4 + -1. Let s(w) be the first derivative of w**3/3 - 6*w + 1. Let j(c) = c**2 - 5. Let x(k) = o*s(k) + 6*j(k). Solve x(t) = 0.
0
Let a(c) be the first derivative of -4*c + 7/4*c**4 + 1 - 23/3*c**3 + 10*c**2. Solve a(o) = 0 for o.
2/7, 1, 2
Let l = 40/17 + 16/51. Factor -14/3*y**3 - 16/3*y + l - 38/3*y**2.
-2*(y + 1)*(y + 2)*(7*y - 2)/3
Let m(c) = -3*c - 45. Let i be m(-15). Suppose i + 0*j - 2/9*j**2 = 0. What is j?
0
Suppose 4*g = -5*v + 22, v = 4*g - v - 8. Factor -6*b**g + b**2 + b**4 + 0*b**3 + 4*b**3.
b**2*(b - 1)**2
Let u be 10/3*(-2)/(-10). Find v such that -2/3 + 4/3*v - u*v**2 = 0.
1
Let j(y) be the first derivative of y**4/8 + y**3/6 - y**2 - 2*y + 40. Factor j(o).
(o - 2)*(o + 1)*(o + 2)/2
Suppose 5*y - 3*y + 12 = 0. Let m = y - -6. Factor -c**2 + m + 0*c - 1/2*c**3.
-c**2*(c + 2)/2
Let u be 2/(-4) - (-28)/24. Let c = 55/3 + -18. Suppose 0 - u*l**2 - 1/3*l**3 - c*l = 0. Calculate l.
-1, 0
Let w be (-2)/3 + 57/(-9). Let j = w + 7. Let 1/4*x**2 + j + 1/4*x = 0. Calculate x.
-1, 0
Let g(z) = 7*z**3 + 2*z**2 - 5*z. Let c(l) = 2*l - 4*l + 2*l**2 - 4*l + 8*l**3 + 0*l. Let p(h) = 5*c(h) - 6*g(h). Solve p(x) = 0 for x.
-1, 0
Let f = 2 + 0. Suppose 0 = f*n - 4*n + 14. Factor 2 - n*m + m**2 + 5*m**2 - m**2.
(m - 1)*(5*m - 2)
Let d(f) = 9*f**3 + 4*f**2 + 9*f - 7. Let g(x) = 8*x**3 + 4*x**2 + 8*x - 6. Let n(k) = 6*d(k) - 7*g(k). Factor n(a).
-2*a*(a + 1)**2
Let b(n) be the third derivative of 1/180*n**5 + 0*n + 0*n**3 + 0*n**4 - 1/360*n**6 + 0 + 2*n**2. Let b(o) = 0. What is o?
0, 1
Let g be (-5 - -9)*2/1316. Let x = 1326/1645 - g. Factor -2*a**2 - 14/5*a - x.
-2*(a + 1)*(5*a + 2)/5
Let f(v) = -v - 2. Let k be f(-8). Factor 8*n + 3*n**3 - k*n**2 - 6*n - 2*n**4 + 3*n**3.
-2*n*(n - 1)**3
Let b(f) be the second derivative of f**5/40 - f**4/6 + 5*f**3/12 - f**2/2 + 6*f. What is v in b(v) = 0?
1, 2
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