) be the third derivative of 3*n**2 + 1/20*n**4 + 0*n**3 + j*n + 1/100*n**5 + 0. Suppose a(o) = 0. Calculate o.
-2, 0
Factor 0*g**3 - 6/11*g**4 - 2/11*g**5 + 8/11*g**2 + 0 + 0*g.
-2*g**2*(g - 1)*(g + 2)**2/11
Let b = 61/5 + -173/15. Factor -b*j + 0 - 2/3*j**2.
-2*j*(j + 1)/3
Let j(z) be the first derivative of 1/3*z**3 + 0*z - z**2 - 1/12*z**4 + 3 - 1/15*z**5. Let m(q) be the second derivative of j(q). Suppose m(c) = 0. What is c?
-1, 1/2
Let w = 4 - 2. Factor -4*f**5 - f + 0*f**5 + 2*f**2 - 2*f**3 + 2*f**w - 4*f**4 + 7*f**5.
f*(f - 1)**2*(f + 1)*(3*f - 1)
Let s(w) be the third derivative of w**6/540 + 11*w**5/270 + 19*w**4/108 + w**3/3 + 5*w**2 + 2*w. Solve s(z) = 0 for z.
-9, -1
Let n be (1 + -4)*18/(-648). Let z(v) be the first derivative of 0*v + n*v**3 - 4 - 1/8*v**2. Factor z(u).
u*(u - 1)/4
Let m(r) = -r**5 - r**4 + r**3 + 3*r**2 - 2*r + 2. Let p(c) = -3*c**5 - 2*c**4 + 3*c**3 + 7*c**2 - 5*c + 5. Let o(f) = 5*m(f) - 2*p(f). Factor o(q).
q**2*(q - 1)**2*(q + 1)
Factor -128/7 - 2/7*c**2 + 32/7*c.
-2*(c - 8)**2/7
Let 18*t**2 + 5*t**3 + 19*t - 8 - 31*t + 24*t = 0. What is t?
-2, 2/5
Let r(g) be the first derivative of -1/2*g - 7/16*g**4 + 3/8*g**2 + 2 + 3/20*g**5 + 1/4*g**3. Solve r(h) = 0.
-2/3, 1
Let p(g) be the third derivative of g**7/70 + 5*g**2. Find k such that p(k) = 0.
0
Suppose -3*u = -5*q + 1, 0 = u + 3*u + 4*q - 20. Let l(c) be the third derivative of -1/420*c**6 + 2*c**2 - 1/210*c**5 + 0*c + 0*c**u + 0 + 0*c**4. Factor l(p).
-2*p**2*(p + 1)/7
Let p(t) be the third derivative of t**9/362880 - t**7/10080 - t**6/2160 + t**5/10 - 5*t**2. Let r(c) be the third derivative of p(c). Factor r(a).
(a - 2)*(a + 1)**2/6
Let g = -125 - -125. Factor 2*k**2 - 2/3*k**3 - 4/3*k + g.
-2*k*(k - 2)*(k - 1)/3
Let v(o) = o**3 - o**2 + o + 1. Let b(f) = -3*f**3 + f - 2. Let w(a) = b(a) + 2*v(a). Let w(y) = 0. Calculate y.
-3, 0, 1
Suppose -2*x - 4*t - 4 = 0, 0 = -4*x - 4*t + 1 + 11. Suppose 7*v = 3*v + x. Factor 0 + 2/7*a - 2/7*a**v.
-2*a*(a - 1)/7
Let r(b) be the first derivative of b**5/5 - b**4/3 + b**3/6 + 6*b + 1. Let d(u) be the first derivative of r(u). Let d(f) = 0. What is f?
0, 1/2
Let z(v) be the second derivative of v**2 - 1/420*v**6 - 3*v + 0 + 0*v**3 + 1/210*v**5 + 1/42*v**4. Let q(g) be the first derivative of z(g). Factor q(m).
-2*m*(m - 2)*(m + 1)/7
Let x(v) = v - v**3 + v + 6 + 2*v**2 + v**5 - 6. Let w(j) = -15*j**5 + 15*j**3 - 33*j**2 - 33*j. Let d(k) = 2*w(k) + 33*x(k). Find r such that d(r) = 0.
-1, 0, 1
Let c(j) = -13*j**2 - 1. Let w be c(-1). Let z = 16 + w. Factor 1/6*n**4 + 0*n**z + 1/6*n**3 + 0 + 0*n.
n**3*(n + 1)/6
Let t(c) be the second derivative of -c**9/45360 - c**8/20160 - c**4/12 + 2*c. Let n(i) be the third derivative of t(i). Let n(u) = 0. Calculate u.
-1, 0
Suppose 12 = 2*n - 4*a, 8*n - 2 = 3*n - 4*a. Let r(t) be the second derivative of 0 + 1/2*t**n + 1/20*t**5 - 1/6*t**3 - 1/12*t**4 + 2*t. Factor r(h).
(h - 1)**2*(h + 1)
Let x be 11/(-54)*-5 + -1. Let t = x + 25/108. Factor -n**3 + 3/4*n**2 + 0 + t*n.
-n*(n - 1)*(4*n + 1)/4
Let p(y) be the first derivative of -3/7*y + 0*y**2 - 5 + 1/7*y**3. Suppose p(v) = 0. What is v?
-1, 1
Let 0 + 3/7*f**3 + 0*f + 6/7*f**2 = 0. Calculate f.
-2, 0
Let v(m) = m**2 + 6*m + 8. Let a be v(-6). Let x = 14 - a. Solve 0*z - 3*z + 9*z**3 + x*z**2 + 4*z = 0 for z.
-1/3, 0
Let b(h) be the third derivative of h**3 - 1/40*h**6 - 9*h**2 + 0 + 1/5*h**5 - 5/8*h**4 + 0*h. Determine d so that b(d) = 0.
1, 2
Let f = 166/129 + 2/43. Factor 10/3*q**5 + 0*q**2 + 0 + 0*q + 14/3*q**4 + f*q**3.
2*q**3*(q + 1)*(5*q + 2)/3
Let h(f) = f**4 - 4*f**3 + 17*f**2 - 6*f. Let n(x) = x**4 + x**2. Let m(l) = 3*h(l) - 12*n(l). Find w such that m(w) = 0.
-3, 0, 2/3, 1
Let x(y) be the first derivative of -y**5/100 - y**4/10 - 2*y**3/5 + 2*y**2 + 3. Let f(t) be the second derivative of x(t). Factor f(p).
-3*(p + 2)**2/5
Let v(c) be the first derivative of -c**8/840 - c**7/105 - c**6/36 - c**5/30 + c**3/3 - 3. Let g(f) be the third derivative of v(f). Factor g(u).
-2*u*(u + 1)**2*(u + 2)
What is j in 4*j**2 - 17*j**5 + 4*j**2 + 10*j**4 + j**5 - 34*j**5 + 32*j**3 = 0?
-2/5, 0, 1
Let l(q) = -q + 0*q - q**2 + 2*q**2 - 4. Let o be l(3). Factor 5*y + 4*y**3 - o*y**4 - 5*y.
-2*y**3*(y - 2)
Suppose 0*g - g - 12 = 0. Let i = -12 - g. Suppose -o**3 + 0 + 1/2*o**4 + i*o + 1/2*o**2 = 0. What is o?
0, 1
Let a be (2/(-21))/(72/(-168)). Find z, given that a*z**2 - 2/9*z - 2/9 + 2/9*z**3 = 0.
-1, 1
Let o be 10*((-12)/(-18) - (-1)/(-15)). Let 21*v**3 - 21/2*v + 3*v**4 + 3 - o*v**2 - 21/2*v**5 = 0. Calculate v.
-1, 2/7, 1
Let j = -31 + 31. Suppose j = y + y - 4. Determine t so that 2/3*t**5 + 0 + 0*t + 2/3*t**4 + 0*t**3 + 0*t**y = 0.
-1, 0
Let g(h) be the third derivative of h**5/30 - 7*h**4/12 - 5*h**2 - 3*h. Factor g(p).
2*p*(p - 7)
Let v(p) be the first derivative of 2*p**5/105 + 4*p**4/21 + 2*p**3/3 + 22*p**2/21 + 16*p/21 + 39. Determine t so that v(t) = 0.
-4, -2, -1
Let g = -15 + 9. Let a = g + 9. Suppose 0*s**4 - 3*s**a + 3*s**2 - s + s**4 - 5 + 5 = 0. What is s?
0, 1
Let k be ((-18)/10)/(21/(-70)). Let p be (-6 + k)*(-1)/(-3). Factor -8/5*g**2 - 2/5*g**3 - 8/5*g + p.
-2*g*(g + 2)**2/5
Let w(p) be the second derivative of -p**4/9 + 4*p**3/9 - 2*p**2/3 - 2*p. Determine g, given that w(g) = 0.
1
Suppose 2*d = d - 5*i - 22, 0 = -3*d + 3*i + 24. Factor -3*l**2 - 5*l**2 + 12*l**4 - l**2 + 3*l**3 - d*l - 3*l**4.
3*l*(l - 1)*(l + 1)*(3*l + 1)
Let i(b) be the second derivative of b**6/165 - b**4/22 - 2*b**3/33 + 9*b. Determine j so that i(j) = 0.
-1, 0, 2
Suppose -9 = -6*j + 3*j. Suppose 8 = g + j*g. Factor 2/9*u**g + 2/9*u - 4/9.
2*(u - 1)*(u + 2)/9
Solve 5/3*d**4 - 7/3*d**3 - d**2 + 7/3*d - 2/3 = 0 for d.
-1, 2/5, 1
Factor m**2 - 36*m + 32 + 26*m - 7.
(m - 5)**2
Factor 10*k**2 + 1 - 2 - 2*k**3 - 16*k + 9.
-2*(k - 2)**2*(k - 1)
Find m, given that -2/11*m + 2/11*m**2 + 0 = 0.
0, 1
Suppose -6*m = -2*d - m + 6, -4*m - 12 = -4*d. Find f such that -5*f**3 - d - f + 9*f**2 - 6*f + 2 + 3 + f**4 = 0.
1, 2
Let n(o) be the third derivative of o**7/140 - 7*o**6/80 + o**5/5 + o**4 + 7*o**2. Factor n(w).
3*w*(w - 4)**2*(w + 1)/2
Let o(k) be the second derivative of -k**6/10 - 9*k**5/20 - 3*k**4/4 - k**3/2 + 8*k. Determine j so that o(j) = 0.
-1, 0
Suppose 0*a + 42 = 3*a. Let n = a + -11. Factor -1/3 + 1/3*h**4 + 2/3*h - 2/3*h**n + 0*h**2.
(h - 1)**3*(h + 1)/3
Factor 7*u**4 - 4 + 5*u**4 - 70*u**2 - 12*u + 8*u**3 + 62*u**2 + 4*u**5.
4*(u - 1)*(u + 1)**4
Suppose b + 2*b = -3. Let f = 4 + b. What is m in 0 + 0*m - 2/5*m**2 - 2/5*m**f = 0?
-1, 0
Let d(f) be the second derivative of f**6/10 + 3*f**5/5 + 5*f**4/4 + f**3 - 7*f. What is g in d(g) = 0?
-2, -1, 0
Factor -21/5*o**3 - 6/5 - 33/5*o - 48/5*o**2.
-3*(o + 1)**2*(7*o + 2)/5
Let j(i) = -4*i**3 - 4*i**2 + 2*i. Let z(u) = -7*u**3 - 7*u**2 + 4*u. Let r(s) = -5*j(s) + 3*z(s). Factor r(k).
-k*(k - 1)*(k + 2)
Let n(o) = -o**5 + o**4 - o**3 + o**2 + 2*o. Let i(t) = -3*t**5 + 2*t**4 - 2*t**3 + 3*t**2 + 7*t. Let a(v) = -6*i(v) + 21*n(v). Let a(g) = 0. Calculate g.
0, 1
Let z be 14/24 - (-2)/(-8). Suppose 29*h + 16*h = 6*h. Solve -z*n**2 + h + 1/3*n = 0.
0, 1
Factor 40*p**3 + 107*p**2 + 107*p**2 + 2*p**5 + 16*p**4 - 182*p**2.
2*p**2*(p + 2)**2*(p + 4)
Let d(x) be the third derivative of 4*x**2 + 0*x - 1/30*x**5 + 0 + 5/12*x**4 - 7/60*x**6 + 2/3*x**3 - 1/105*x**7 + 1/84*x**8. Solve d(l) = 0.
-1, -1/2, 1, 2
Suppose -4*y + 0 - 8 = -5*s, 0 = -3*y - s + 13. Factor -2*v**3 - v**5 + v**3 + y*v**3 - v.
-v*(v - 1)**2*(v + 1)**2
Let 3*q**3 + 4*q + 1 + q**3 - 8*q**2 - 1 = 0. Calculate q.
0, 1
Let v(r) = -r**3 - r**2 - r + 3. Let z be v(0). Let u be (2 - 1)*3/6. Find f such that u*f**4 + 0*f**2 + 0*f + 0 + 0*f**z = 0.
0
Let x = -3 + 3. Suppose -2*d + 6 + x = 0. Factor -6*y + 6*y**d + 0 + 2*y**4 + 2*y**2 - 3 - 1.
2*(y - 1)*(y + 1)**2*(y + 2)
Let b(g) be the third derivative of g**6/540 - g**5/135 - g**4/27 + 8*g**3/27 - 9*g**2. Factor b(y).
2*(y - 2)**2*(y + 2)/9
Suppose 0 = 5*s + 2*q - 47, -5*s + 3*s + 4*q = -14. Let o = 9 - s. Determine g so that 4*g**3 + 8*g**2 + o + 2/3*g**4 + 16/3*g = 0.
-2, 0
Let p be (9/(-12))/((-6)/16). Let o(t) be the second derivative of -21/10*t**6 - 3/5*t**5 + 14/3*t**7 + 2*t + 0*t**p + 0*t**3 + 1/3*t**4 + 0. Factor o(u).
u**2*(4*u + 1)*(7*u - 2)**2
Factor -10*q + 4*q - 4*q**2 + 10*q.
-4*q