he third derivative of v**7/105 - v**6/20 + v**5/30 + v**4/4 - 2*v**3/3 + v**2. Factor p(o).
2*(o - 2)*(o - 1)**2*(o + 1)
Let w(x) be the first derivative of -x**4/2 - 4*x**3/3 + 7*x**2 - 8*x - 9. Factor w(i).
-2*(i - 1)**2*(i + 4)
Suppose -12 = -2*j + 4*c - 2*c, 2*j = -2*c. Suppose f**j - 1/2*f**4 - 1/2*f**2 + 0*f + 0 = 0. What is f?
0, 1
Let q(l) be the second derivative of l**7/21 + 4*l**6/15 + 3*l**5/5 + 2*l**4/3 + l**3/3 + 3*l. Factor q(w).
2*w*(w + 1)**4
Suppose 2*m = 5 + 1. Let h be ((-3)/15 - 0)*-4. Let -22/5*a**2 + h + 8/5*a**m + 2*a = 0. Calculate a.
-1/4, 1, 2
Let k be 6/(-2) + 3038/450. Let d = -66/25 + k. Solve -8/9*r**3 - 4/9*r - 2/9*r**4 - d*r**2 + 0 = 0.
-2, -1, 0
Let l = -7/794 + -85853/78606. Let q = l + 17/11. Factor -2/9 - 2/9*d**2 - q*d.
-2*(d + 1)**2/9
Suppose -32/9*o**3 + 0 - 4/9*o + 14/9*o**4 + 22/9*o**2 = 0. What is o?
0, 2/7, 1
Let a(k) = k**2 + k - 2. Let s(h) = 3*h**2 + 3*h - 3. Let u(n) = -5*a(n) + 3*s(n). Determine d, given that u(d) = 0.
-1/2
Let o be 4/12*8/4. Suppose -4/3*t**2 + 0 - o*t**5 + 2/3*t + 4/3*t**4 + 0*t**3 = 0. What is t?
-1, 0, 1
Let g(p) be the third derivative of 0*p + 5/36*p**4 - 1/36*p**6 + 0 + 1/3*p**3 - 7*p**2 - 1/30*p**5. Factor g(y).
-2*(y - 1)*(y + 1)*(5*y + 3)/3
Let o(h) = 0 - 3 + h + 2 + 0. Let p(i) = -2*i**2 - 9*i - 7. Let m(q) = o(q) + p(q). Solve m(w) = 0 for w.
-2
Suppose -5*f + 0*f - 10 = 5*a, 0 = -3*f + 4*a - 34. Let q(d) = d**2 + 5*d - 4. Let l be q(f). Determine u so that -3*u**l + 4*u**2 - 2*u**2 = 0.
0
Let x = 154 - 1076/7. Factor 0 + 2/7*j**4 + x*j - 2/7*j**3 - 2/7*j**2.
2*j*(j - 1)**2*(j + 1)/7
Factor 1/3*w**3 + 1/6*w**2 - 1/6*w**4 - 1/3*w + 0.
-w*(w - 2)*(w - 1)*(w + 1)/6
Let a(i) = i**4 + i**2 + i - 1. Let d(b) = 9*b**4 + 13*b**3 + 20*b**2 + 12*b - 4. Let s(k) = 5*a(k) - d(k). Determine g so that s(g) = 0.
-1, -1/4
Suppose -3*w = 4*c - 20, 5*c - w - 2 = 2*c. Find j such that -2/3*j**3 + c*j**2 - 2/3*j + 4/3*j**5 + 0 - 2*j**4 = 0.
-1, 0, 1/2, 1
Let z = 0 - -5. Let o(m) = 10*m**5 - 17*m**4 + 16*m**3 - 16*m**2 + 7*m + 5. Let k(x) = -x**5 + x**3 + x**2 - x - 1. Let w(g) = z*k(g) + o(g). Factor w(a).
a*(a - 1)**3*(5*a - 2)
Let j = 334/9 + -37. Let o = 13/9 - j. Factor o*y**2 + 2/3*y**3 + 2/3*y + 0.
2*y*(y + 1)**2/3
Let j be (42/15 - -2) + 2. Let q = -4 + 6. Suppose j*h**2 + q*h**4 + 0*h - 8/5 - 36/5*h**3 = 0. What is h?
-2/5, 1, 2
Let i be (26/8 - -2) + (-17)/68. Let d(h) be the second derivative of 5/2*h**3 + 3/10*h**6 + 0 + h - 3*h**2 - 1/4*h**4 - 3/4*h**i. Factor d(x).
3*(x - 1)**2*(x + 1)*(3*x - 2)
Let v(s) be the third derivative of s**6/480 - s**5/20 + s**4/2 - 8*s**3/3 + 6*s**2. Find h, given that v(h) = 0.
4
Let l(i) = i**2 - 9*i + 2. Let c be l(8). Let v be (2 + 9/c)*4. Suppose -5/3*m**v + 25/3*m**3 - 16/3*m - 4/3 = 0. What is m?
-2/5, 1
Suppose -l = 2 - 3. Suppose -3*c - l + 7 = 0. Factor 0 - 1/3*m**4 + 2/3*m**3 + 1/3*m**c - 2/3*m.
-m*(m - 2)*(m - 1)*(m + 1)/3
Find o, given that 0*o**3 - 4*o - 6 + 2*o**4 + 4*o**2 + 0*o**2 - 8*o**3 + 12*o = 0.
-1, 1, 3
Solve 72/5*m**2 + 96/5*m + 18/5*m**3 + 128/15 = 0 for m.
-4/3
Let a(t) be the second derivative of -1/12*t**3 - 5*t + 1/24*t**4 + 1/40*t**5 - 1/4*t**2 + 0. Factor a(f).
(f - 1)*(f + 1)**2/2
Let m(o) = o**3 + o**2 + o + 1. Let b be m(0). Suppose -6*i - b = -13. Factor -4/3 + i*h - 2/3*h**2.
-2*(h - 2)*(h - 1)/3
Suppose s + 3*r = -2*r + 5, 0 = -3*s + r + 15. Suppose s*y - 5 + 0 = 0, 4*u = 4*y + 12. Factor 0 + 1/3*x**5 + 2/3*x + 3*x**3 - 5/3*x**u - 7/3*x**2.
x*(x - 2)*(x - 1)**3/3
Let l(c) be the first derivative of -c**6/24 - c**5/10 + c**3/6 + c**2/8 + 7. Let l(k) = 0. Calculate k.
-1, 0, 1
Let v be 1/(-3)*0*4/12. Determine c so that v*c - 2/3*c**2 + 0 = 0.
0
Let n(x) = -6*x**3 + x**2 - 1. Let d be n(1). Let k = -6 - d. Let 1/2*c**4 + 0*c**2 + 0*c**3 + k + 0*c = 0. Calculate c.
0
Let w(j) be the third derivative of -j**7/70 - j**6/12 - j**5/5 - j**4/4 - j**3/6 + 2*j**2. Determine p so that w(p) = 0.
-1, -1/3
Suppose b + 33 + 4 = 4*q, -4*q + 5*b = -57. Suppose 0 = -2*c - q, -5*m + m - 3*c = -12. What is z in 4*z + 0*z**3 + 3*z**3 + m*z**2 + z - 2*z = 0?
-1, 0
Factor 29*x**2 - 12 - 67*x**2 + 35*x**2 + 15*x.
-3*(x - 4)*(x - 1)
Let o be (-4)/(-90) - 4/(-10). Let i be (-2 - (-1 - 2))/((-4)/(-12)). Determine q so that 0 + 0*q**4 + o*q**i - 2/9*q + 0*q**2 - 2/9*q**5 = 0.
-1, 0, 1
Let n(d) be the third derivative of d**5/90 - d**4/36 + 5*d**2. Factor n(w).
2*w*(w - 1)/3
Let n be 128/(-448)*7/(-2). Determine g so that -3/4*g**2 - 2*g - n = 0.
-2, -2/3
Let f(w) be the second derivative of w**9/1008 - w**7/280 + w**3/6 + 3*w. Let p(h) be the second derivative of f(h). Suppose p(x) = 0. Calculate x.
-1, 0, 1
Let o(w) be the first derivative of -2*w**5/15 + 4*w**3/9 - 2*w/3 - 14. Factor o(r).
-2*(r - 1)**2*(r + 1)**2/3
Let -3*d**3 + 6/7*d**4 + 0 + 3*d**5 - 6/7*d**2 + 0*d = 0. Calculate d.
-1, -2/7, 0, 1
Factor -23*r**2 + 11*r**3 + 4*r + r**2 + 12*r**2 - 3*r**3 - 2*r**4.
-2*r*(r - 2)*(r - 1)**2
Let y(h) be the third derivative of h**8/84 + 8*h**7/105 + h**6/5 + 4*h**5/15 + h**4/6 + 6*h**2. Solve y(c) = 0 for c.
-1, 0
Let k = -388/7 - -56. Determine l so that -2/7*l**2 + 6/7*l - k = 0.
1, 2
Let v = -10907/36 + 303. Let i(c) be the third derivative of 0*c - 1/45*c**5 + c**2 - v*c**4 + 0*c**3 - 1/180*c**6 + 0. Factor i(y).
-2*y*(y + 1)**2/3
Let v(x) be the first derivative of -x**6/120 + 3*x**5/40 - x**4/4 + 2*x**3/3 - 3. Let z(u) be the third derivative of v(u). Find j, given that z(j) = 0.
1, 2
Let f = -7 + 11. Let b(o) = o**4 - o**3 + 10*o**2 + 4. Let v(a) = 9*a**2 + 3. Let t(i) = f*v(i) - 3*b(i). Factor t(p).
-3*p**2*(p - 2)*(p + 1)
Let o = -12154 + 84863/7. Let k = o - -31. Factor 2/7*g**3 + 4/7 - k*g - 4/7*g**2.
2*(g - 2)*(g - 1)*(g + 1)/7
Let s(p) = 5*p**4 + p**3 - 5*p**2 + 5*p. Let g(q) = -14*q**4 - 2*q**3 + 14*q**2 - 14*q. Let x(r) = -3*g(r) - 8*s(r). Let x(a) = 0. Calculate a.
-1, 0, 1
Let y be ((6/(-7))/(4/(-7)))/3. Factor 1/2*a**2 + y - a.
(a - 1)**2/2
What is p in -1/2*p**3 + 0*p - 1/2*p**2 + 0 = 0?
-1, 0
Let u(f) be the second derivative of f**5/80 + f**4/8 + 3*f**3/8 - 9*f. Factor u(a).
a*(a + 3)**2/4
Let v(s) be the first derivative of 1/2*s**6 - 4*s**3 + 6/5*s**5 + 0*s + 1 - 9/4*s**4 + 6*s**2. Find m, given that v(m) = 0.
-2, 0, 1
Let k(n) be the first derivative of -n**3/21 + 15*n**2/7 - 225*n/7 - 43. Factor k(h).
-(h - 15)**2/7
Let c be (-12)/15*20/(-4). Find h, given that -6*h**3 - 4*h**4 - 2*h**2 - 2*h**c - 2*h**5 + 0*h**2 = 0.
-1, 0
Suppose 20 = 5*r - 0*r. Let w(y) be the second derivative of 1/3*y**3 + 0*y**2 + 0 + 0*y**r - 1/10*y**5 + y. Determine m, given that w(m) = 0.
-1, 0, 1
Let q(w) be the second derivative of -2*w**6/75 - w**5/100 + w**4/15 + w**3/30 + 3*w. Solve q(j) = 0 for j.
-1, -1/4, 0, 1
Let m(y) = -y**2 - 12*y - 18. Let i be m(-10). Suppose 0 = 3*n + i*n - 15. Find w such that 33/4*w**2 + 9/2*w**3 - 27/4*w**4 - 3*w - n = 0.
-2/3, 1
Let x = -2762/9 - -308. Factor -8/9*m**4 + 2/9*m**5 + 8/9*m**3 + 4/9*m**2 + 4/9 - x*m.
2*(m - 2)*(m - 1)**3*(m + 1)/9
Let v(r) = -3*r**2 + 32*r - 15. Let s be v(10). Let d(o) be the third derivative of 0*o**3 + 0 + 1/48*o**4 - o**2 - 1/240*o**6 + 0*o**s + 0*o. Factor d(x).
-x*(x - 1)*(x + 1)/2
Let n be ((-5)/(-3) + -2)*-4. Let p be 14/(-91) + 6/39. Factor 2/3*d**3 - 2*d**2 + p + n*d.
2*d*(d - 2)*(d - 1)/3
Let r(d) = 5*d**2 + 2 - d + d**3 - 4*d**2 - 3. Let a(n) = 12*n**3 + 2*n**2 - 12*n - 2. Let l(v) = a(v) - 4*r(v). Factor l(s).
2*(s - 1)*(s + 1)*(4*s - 1)
Factor 10*g**2 + 9*g**3 - 17*g**3 + 2*g**4 - 4*g + 0*g.
2*g*(g - 2)*(g - 1)**2
Let i be 9/6*40/12. Factor 1/3*c**3 + 0*c**2 - 2/3*c**4 + 0 + 1/3*c**i + 0*c.
c**3*(c - 1)**2/3
Let h(b) = b**3 - 5*b**2 + 4*b + 3. Let a be h(4). Factor -5 + 0*k**3 - k**3 + 3 + k - k**2 + a.
-(k - 1)*(k + 1)**2
Let v(i) be the second derivative of -1/20*i**5 - i + 0*i**2 + 1/6*i**3 - 1/24*i**4 + 1/60*i**6 + 0. Factor v(g).
g*(g - 2)*(g - 1)*(g + 1)/2
Let u = -11 - -16. Suppose -s + a = 0, 4 + 14 = 4*s + u*a. Solve -1 - 2*w + s*w**2 - 3*w**2 + 0*w**2 = 0.
-1
Suppose 4*q - 6 = 2. Let x(j) be the third derivative of j**5/60 - j**4/24 + j**3/6 + j**2. Let v(z) = 6*z. Let r(n) = q*x(n) + v(n). What is w in r(w) = 0?
-1
Suppose 2*k - 2*g = -k + 34, 0 = 4*k + 5*g - 76. What is q in -7*q**3 - 10*q**4 + k*q + 0 + 6*q**2 - q**3 - 6*q**3 + 4 = 0?
-1,