Factor g(t).
2*(5*t - 3)**2/7
Let n(j) = j. Let x(a) = -5*a**3 + 65*a**2 - 6*a. Let o(f) = 6*n(f) + x(f). Factor o(w).
-5*w**2*(w - 13)
Let f(m) be the first derivative of -5*m**4 + 28*m**3 - 441*m**2/10 + 171. Find d, given that f(d) = 0.
0, 21/10
Let i = -733 + 736. Let q(b) be the second derivative of 1/140*b**5 + 1/210*b**6 + 0 - 6*b + 0*b**2 - 1/84*b**4 - 1/42*b**i. Factor q(t).
t*(t - 1)*(t + 1)**2/7
Suppose -o - v + 2 = 0, 4*o - 7*o = -3*v - 12. Let h be 8/(-6) + 1 + 2. Determine a so that -1/3*a**2 - 4/3 - 8/3*a + h*a**o - 1/3*a**5 + 1/3*a**4 = 0.
-1, 2
Let v(x) = x**3 - 3*x**2 - 3 - 2 - 2*x - x**2 - 2*x**3. Let c be v(-4). Factor -f**5 + 6*f**4 - 3*f**3 + 0*f**5 + f**2 - c*f**4 + 0*f**5.
-f**2*(f - 1)**3
Solve 26/11*g**2 - 98/11 + 2/11*g**3 + 70/11*g = 0.
-7, 1
Let h(a) be the second derivative of 22*a**6/75 + 2*a**5/5 - a**4/15 + 353*a. Factor h(n).
4*n**2*(n + 1)*(11*n - 1)/5
Let v(r) be the second derivative of -r**5/40 + r**4/16 + 19*r**2/2 - 18*r. Let f(a) be the first derivative of v(a). Suppose f(s) = 0. What is s?
0, 1
Suppose 0 = -2*k + 8*k - 120. Determine m, given that 16*m + 6*m**2 + k - m**2 - 9*m**2 = 0.
-1, 5
Let w(h) be the second derivative of 1/18*h**4 + 0 + 2/9*h**3 - h**2 - 4*h. Solve w(r) = 0 for r.
-3, 1
Let v(d) be the second derivative of 22*d**6/75 - 371*d**5/100 - 121*d**4/30 + 31*d**3/6 - 9*d**2/5 - d + 104. Suppose v(o) = 0. Calculate o.
-1, 2/11, 1/4, 9
Let k(i) be the first derivative of 25/3*i**3 + 5 - 30*i + 65/2*i**2. Factor k(v).
5*(v + 3)*(5*v - 2)
Let l be -3*4/6 - -17. Suppose -l = 2*d - 5*d. Let -2*y**3 + d*y**3 + 1 - 2*y**3 - y**2 - y = 0. Calculate y.
-1, 1
Determine k, given that -8*k + 4/5*k**3 - 4/5*k**2 - 32/5 = 0.
-2, -1, 4
Let j be 40/6 + -6 + (-228)/(-36) + -4. Factor 0*k**2 - 4/19*k**j - 2/19*k**4 + 0 + 0*k.
-2*k**3*(k + 2)/19
Let j be (139/28 - 2) + -1 + 5/(-20). Let -2/7*i**2 + 2*i - j = 0. Calculate i.
1, 6
Let a(h) = -h**3 - 2*h**2 - h - 9. Let m be a(-3). Let l be 16/7 - 6/21. Suppose -1/5*x - 3/5*x**m - 3/5*x**l + 0 - 1/5*x**4 = 0. What is x?
-1, 0
Let p(o) be the first derivative of 6*o**7/35 - 2*o**6/5 - o**5/3 + 2*o**4 - 8*o**3/3 - 5*o**2/2 + 4. Let y(t) be the second derivative of p(t). Factor y(r).
4*(r - 1)*(r + 1)*(3*r - 2)**2
Let s(h) = -4*h**4 + 5*h**3 - h**2 + 3*h - 3. Let o(g) = g**4 - g**3 - g + 1. Let q = -3 + 1. Let c(y) = q*s(y) - 6*o(y). Let c(i) = 0. Calculate i.
0, 1
Let t(d) = 45*d**3 + 4*d**2 - 11*d + 11. Let c(x) = 15*x**3 + x**2 - 4*x + 4. Let k = -1 - -5. Let a(q) = k*t(q) - 11*c(q). Suppose a(y) = 0. What is y?
-1/3, 0
Suppose f - z - 149 = 0, z = 4*f - f - 447. Factor -f*v**3 + 2*v - v**5 + 3 + 148*v**3 - 3*v**4 - 3 + 3*v**2.
-v*(v - 1)*(v + 1)**2*(v + 2)
Determine l so that -8/7*l - 2/7*l**2 + 0 - 1/7*l**4 + 5/7*l**3 = 0.
-1, 0, 2, 4
Find l, given that 60*l + 21*l**2 + 0 + 3/2*l**3 = 0.
-10, -4, 0
Factor 14/9 + 6*a - 2/9*a**5 + 76/9*a**2 + 2/3*a**4 + 44/9*a**3.
-2*(a - 7)*(a + 1)**4/9
Let -8/3*m**4 + 14*m**3 - 17/3*m + 13*m**2 - 2 = 0. What is m?
-1, -1/4, 1/2, 6
Factor 8277*b**5 - 229*b**4 + 28*b**4 - 8280*b**5.
-3*b**4*(b + 67)
Let w(q) = q**3 + 2*q**2 - 2*q - 2. Suppose -2*n = -3*n - 2. Let l be w(n). Factor 0*p**2 + 20*p - 20*p + 2*p**l.
2*p**2
Let n(q) be the second derivative of -q**5/4 - 25*q**4/12 - 5*q**3 + 66*q. Suppose n(k) = 0. What is k?
-3, -2, 0
Let v(g) be the third derivative of -1/630*g**7 - 1/180*g**5 + 0*g**4 + 0*g**3 + 11*g**2 + 1/180*g**6 + 0*g + 0. Determine a, given that v(a) = 0.
0, 1
Let b(u) be the first derivative of u**7/21 - 3*u**6/35 + u**5/35 + 4*u - 13. Let o(r) be the first derivative of b(r). Factor o(j).
2*j**3*(j - 1)*(7*j - 2)/7
Let g(r) = r**2 - 6*r + 6. Let w be g(5). Let q be (60/9)/(w/2). Factor 20/3*b**3 - 5*b + 15 - q*b**2.
5*(b + 1)*(2*b - 3)**2/3
Determine q so that -192 + 3*q**3 - 106*q - 279*q**2 + 346*q + 228*q**2 = 0.
1, 8
Let v(t) be the first derivative of -1/4*t**4 + 1/6*t**6 + 0*t + 0*t**2 + 1/3*t**3 - 1/5*t**5 + 3. Suppose v(p) = 0. What is p?
-1, 0, 1
Factor 41*a**2 - 4 - 15*a + 44*a**2 - 11*a**2 - 55*a.
2*(a - 1)*(37*a + 2)
Let i = 6587 - 6585. Factor 0 + 1/2*s**4 + 0*s**i - 1/2*s**5 + 0*s + 0*s**3.
-s**4*(s - 1)/2
Let g(q) = q**3 - 6*q**2 - 8*q + 10. Let j be g(7). Let s be (-45)/(-60) + (-2)/(-16)*10. Factor -f + f**2 + s + 1 - j.
f*(f - 1)
Let o be (-384)/(-54) + (-3)/27. Let q be (3 - (-72)/(-30))/(o/10). Let -1/7*s**5 + 8/7*s**2 - 12/7*s**3 + q*s**4 + 0 + 0*s = 0. Calculate s.
0, 2
Let x(a) = 3*a**2 - 2*a + 4. Suppose -4*q - q = -25. Let z(f) = 3*f + 14 + 15 - 5*f**2 - 35. Let o(k) = q*z(k) + 8*x(k). Suppose o(m) = 0. Calculate m.
-2, 1
Suppose -5*z = m - 286, 0*z + z - 62 = -5*m. Let n = z - 41. Suppose -8*x**3 + 3*x**2 - 2*x**4 + n*x**3 + 4*x - 13*x**2 = 0. What is x?
0, 1, 2
Let c be -15*4/(-12) - -2. Factor 4 - 32*y + 30*y**2 - c + 14 - 8*y**3 - y**4.
-(y - 1)**3*(y + 11)
Let j(b) be the second derivative of -b**6/40 - b**5/60 + b**4/9 + 2*b**3/9 + 2*b**2 + 6*b. Let k(s) be the first derivative of j(s). Solve k(o) = 0.
-2/3, 1
Let x = 1/2249 + 49475/6747. Factor -2/3*k**4 - 38/3*k**2 + 0 - x*k**3 - 6*k.
-2*k*(k + 1)**2*(k + 9)/3
Find j such that 42/11*j + 20/11 - 6/11*j**3 - 56/11*j**2 = 0.
-10, -1/3, 1
Factor c + 45*c**2 + 8662*c**4 - 7*c + c**3 - 8683*c**4 - 19*c**3.
-3*c*(c - 1)*(c + 2)*(7*c - 1)
Let v(g) be the third derivative of 1/30*g**5 - 8/3*g**3 + 0 - 2*g**2 - 1/6*g**4 + 0*g. Factor v(b).
2*(b - 4)*(b + 2)
Let s(p) = p**2 + 2*p + 2. Let d be s(0). Factor 4*w - 14*w**2 + 10 + 2 - 4*w**3 + d*w**2.
-4*(w - 1)*(w + 1)*(w + 3)
Let r(v) be the second derivative of 17/4*v**4 - 8*v**3 + 4*v - 21/10*v**6 + 6*v**2 + 21/20*v**5 + 9/14*v**7 + 0. Determine w so that r(w) = 0.
-1, 2/3, 1
Let u be ((-54)/(-45))/((-6)/(-20)). Suppose -16 = -u*h + 16. Factor 3*g**2 + 2*g**2 + 2*g**4 + h*g**3 + 3*g**2.
2*g**2*(g + 2)**2
Let r(k) be the first derivative of -k**6/10 + 18*k**5/25 + 6*k**4/5 - 6*k**3/5 - 21*k**2/10 + 388. Let r(n) = 0. Calculate n.
-1, 0, 1, 7
Factor -11*x + 39*x**3 - 44 + 80*x + 222*x**2 + 188*x + 22*x - 64.
3*(x + 3)**2*(13*x - 4)
Let w(c) be the third derivative of c**8/6720 + c**7/2520 - c**4/3 - 7*c**2. Let g(v) be the second derivative of w(v). Factor g(s).
s**2*(s + 1)
Let w(g) be the second derivative of -12*g**5/5 - 29*g**4/4 + 27*g**3 - 27*g**2/2 - 522*g. Factor w(q).
-3*(q - 1)*(q + 3)*(16*q - 3)
Let d be (-4)/(-36) + 225/162. Let t(k) be the second derivative of -d*k**2 + 5/4*k**4 - 8*k + 1/2*k**3 + 9/20*k**5 + 0. Factor t(w).
3*(w + 1)**2*(3*w - 1)
Let -29/6*b - 2/3*b**2 - 4 + 1/6*b**3 = 0. What is b?
-3, -1, 8
Let v = -209 + 211. Suppose 0 = y - v, y = h - 0*y. Determine d, given that 8/7*d**3 + 0*d + 0 - 4/7*d**h - 4/7*d**4 = 0.
0, 1
Let x(h) = 2*h**4 - 19*h**3 - 29*h**2 - 3*h + 5. Let v(f) = -2*f**4 + 9*f**3 + 15*f**2 + f - 3. Let j(n) = -5*v(n) - 3*x(n). Factor j(c).
4*c*(c + 1)**3
Let u be (79 - -2)/(2/12 - 0). Let o = 3408/7 - u. Solve -4/7 - 2*a - o*a**3 - 16/7*a**2 = 0 for a.
-1, -2/3
Let v(w) = 2*w**4 - 14*w**3 - 6*w**2 + 64*w - 40. Let j(c) = -4*c**4 + 14*c**3 + 6*c**2 - 65*c + 40. Let f(l) = 2*j(l) + 3*v(l). Let f(o) = 0. Calculate o.
-5, -4, 1
Let m(l) be the third derivative of 2*l**7/525 - 7*l**6/150 + 13*l**5/75 + l**4/10 - 12*l**3/5 + l**2 - 3*l. What is o in m(o) = 0?
-1, 2, 3
Let a(d) be the second derivative of 1/9*d**3 + 3/20*d**5 + 0 + 7/36*d**4 + 0*d**2 + d + 1/18*d**6 + 1/126*d**7. Factor a(w).
w*(w + 1)**3*(w + 2)/3
Let 153*v**3 - 129*v**3 - 33*v**2 + 24*v**4 - 93*v**3 + 9 + 69*v = 0. Calculate v.
-1, -1/8, 1, 3
Factor 18/5*c**4 + 2/5*c**2 - 12/5*c**3 + 0 + 0*c - 8/5*c**5.
-2*c**2*(c - 1)**2*(4*c - 1)/5
Factor 16*m - 7*m + 4*m - 2*m + 4 - 3*m**2.
-(m - 4)*(3*m + 1)
Suppose -s - 4*d - 5 = -0, s + 3*d = -4. Let b(z) = z**4 + 1. Let r(l) be the first derivative of -l**4/2 + 6*l + 1. Let a(q) = s*r(q) + 6*b(q). Solve a(i) = 0.
-1/3, 0
Let b be 3*((-140)/12 - -5 - -7)*2. Suppose 30/7*t**b + 0 - 4/7*t = 0. Calculate t.
0, 2/15
Let s be 0/(3 + (75/(-25))/((-6)/(-2))). What is l in 2/7*l**2 + s*l**3 + 0 - 2/7*l**4 + 0*l = 0?
-1, 0, 1
Factor 726 - c**2 + 4*c**2 + 141 + 102*c.
3*(c + 17)**2
Let j(s) be the first derivative of -46 + 12/7*s**4 + 0*s + 0*s**2 - 3/35*s**5 - 64/7*s**3. What is p in j(p) = 0?
0, 8
Let z = -543 - -543. Solve -5/3*q**4 - 5/3*q + 