6)*(v + 4)/10
Let f = 657 - 654. Factor 0*u + 0*u**f + 0 + 0*u**2 - 2/13*u**4.
-2*u**4/13
Determine v, given that 0 - 32/5*v + 2/5*v**2 = 0.
0, 16
Let a(n) be the second derivative of 2/21*n**4 + 2/7*n**2 - 3/7*n**3 + 0 - 8*n. Factor a(f).
2*(f - 2)*(4*f - 1)/7
Let w = -52261 - -8361827/160. Let l = -7/32 + w. What is u in u**3 - u - l*u**2 - 2/5 + 3/5*u**4 = 0?
-1, -2/3, 1
Let h(c) be the first derivative of -4/3*c**3 + 0*c**2 + 0*c + 2/5*c**5 + 3 + 1/2*c**4. Suppose h(q) = 0. What is q?
-2, 0, 1
Let z(l) = l**3 + l**2 - l. Let d(p) = -p**4 + 4*p**3 - 3*p**2 - 134*p - 196. Let u(o) = d(o) + 6*z(o). Suppose u(g) = 0. What is g?
-2, 7
Factor 11/8*u + 10 - 1/8*u**2.
-(u - 16)*(u + 5)/8
Let n be -1 + 3 - 3/2*50/(-75). Factor 2/9*r**n - 2/9*r**5 - 2/9*r**4 + 0 + 2/9*r**2 + 0*r.
-2*r**2*(r - 1)*(r + 1)**2/9
Let t(c) be the second derivative of -1/20*c**6 - 11/12*c**3 + 0 - 1/2*c**2 - 13/40*c**5 - 19/24*c**4 - 16*c. Solve t(l) = 0.
-2, -1, -1/3
Let d(x) be the second derivative of 4*x**6/15 - 3*x**5/5 - x**4 + 14*x**3/3 - 6*x**2 + 54*x - 2. Find r, given that d(r) = 0.
-3/2, 1
Let p be (-111)/(-18) + 36/27. Let z be (6/42*3)/(2/21). Factor z*v + 3/2*v**3 + 27/2 - p*v**2.
3*(v - 3)**2*(v + 1)/2
Let u(f) be the third derivative of -4/3*f**3 - 40*f**2 + 1/60*f**6 + 0 + 0*f + 1/10*f**5 + 0*f**4. Factor u(r).
2*(r - 1)*(r + 2)**2
Let 28/19*f**4 - 120/19*f + 2/19*f**5 + 118/19*f**3 + 116/19*f**2 - 144/19 = 0. Calculate f.
-6, -2, -1, 1
Let f(b) = 2*b**3 - 16*b**2 + b + 10. Let h(s) = 4*s**3 - 32*s**2 + s + 22. Let l(y) = 5*f(y) - 3*h(y). Factor l(q).
-2*(q - 8)*(q - 1)*(q + 1)
Let f(t) be the first derivative of 45/16*t**4 + 1/2*t**6 + 0*t - 39/20*t**5 + 3/8*t**2 - 7/4*t**3 + 16. Suppose f(g) = 0. Calculate g.
0, 1/4, 1
Suppose 13*i = 16*i - 21. Let -2*c**4 - 15*c**2 - 24*c + 26*c**2 - 18 + 8*c**3 - i*c**2 = 0. What is c?
-1, 3
Let y(v) be the second derivative of -121*v**5/30 - 118*v**4/27 + 125*v**3/27 - 2*v**2/9 + 65*v. Determine c so that y(c) = 0.
-1, 2/121, 1/3
Let x(v) = 15*v**2 - 325*v - 315. Let h(o) = -4*o**2 - 1. Let j(k) = -5*h(k) - x(k). Factor j(n).
5*(n + 1)*(n + 64)
Let f(g) be the third derivative of g**8/196 + g**7/105 - 17*g**6/210 + g**5/70 + 3*g**4/14 - 81*g**2. Suppose f(n) = 0. What is n?
-3, -2/3, 0, 1, 3/2
Solve -1 + h**2 - 1/4*h**3 + 1/4*h = 0 for h.
-1, 1, 4
Let r(y) be the third derivative of -y**8/168 + y**7/105 + y**6/30 - 120*y**2. Factor r(h).
-2*h**3*(h - 2)*(h + 1)
Let y(z) be the second derivative of 2/15*z**5 + 0 - 2/45*z**6 + 13*z + 0*z**4 + 0*z**3 + 0*z**2. Factor y(a).
-4*a**3*(a - 2)/3
Let q = -139 + 143. Let p(g) be the first derivative of 9*g**q + 3/5*g**5 - 4 + 54*g**3 + 162*g**2 + 243*g. Factor p(f).
3*(f + 3)**4
Let q(i) = i**3 + 5*i**2 + 8*i - 14. Let u(b) = -b**2 + 1. Suppose 48 = -3*t + 3*g, 2*g = -t - 5 - 5. Let k = t - -12. Let n(s) = k*u(s) + q(s). Factor n(x).
(x - 1)*(x + 4)**2
What is f in 3/2*f**2 - 393/2*f - 198 = 0?
-1, 132
Suppose 12 = -5*o - 8, -8 = 4*f + 4*o. Suppose 5*y**3 - y**3 - 4*y**f + 6 - 22 + 16*y**2 = 0. What is y?
-2, 1
Suppose -38*b = -36*b - 140. Let v be (-28)/b*(-6)/4. Factor -6/5*n + 6/5*n**3 + 3/5*n**2 + 0 - v*n**4.
-3*n*(n - 2)*(n - 1)*(n + 1)/5
Let g(z) be the first derivative of 4*z**3/21 - 30*z**2/7 + 176*z/7 - 243. Factor g(p).
4*(p - 11)*(p - 4)/7
Solve -27*d**5 - d**4 - d + 6*d**3 + 12*d**2 - 21*d**4 - 2*d - 14*d**4 = 0.
-1, 0, 1/3
Solve -6*o**2 + 6*o + 0 - 57/2*o**3 - 21*o**4 - 9/2*o**5 = 0 for o.
-2, -1, 0, 1/3
Let r(v) = v**2 + 3*v - 2. Let g be r(-2). Let n(p) = 24*p - 32. Let s(l) = l**2 + 49*l - 64. Let c(k) = g*s(k) + 7*n(k). Determine q so that c(q) = 0.
-8, 1
Solve 3876*i**3 - 3880*i**3 - 16*i - 40*i**2 - 48*i = 0 for i.
-8, -2, 0
Let u(b) be the third derivative of -b**8/6720 + b**7/630 - b**6/240 + 5*b**4/6 + 22*b**2. Let h(m) be the second derivative of u(m). Factor h(z).
-z*(z - 3)*(z - 1)
Let q = 2780048/35 + -79422. Let t = -39/5 + q. Determine a, given that -3/7*a**2 + 0 + 4/7*a**3 - t*a = 0.
-1/4, 0, 1
Let q(v) be the second derivative of 121*v**5/80 - 11*v**4 + 15*v**3/2 - 2*v**2 - 2*v + 3. Suppose q(p) = 0. Calculate p.
2/11, 4
Factor -140 + 160*d - 90*d**3 + 43*d**3 - 55*d**2 + 52*d**3.
5*(d - 7)*(d - 2)**2
Factor 47*o - 3*o**3 + 3*o**3 + 28*o**2 + 23 + o**3 - 3*o**2.
(o + 1)**2*(o + 23)
Let h be -3 - (-6)/60*46. Let x(z) be the first derivative of 4 - 12/5*z**3 + 14/5*z**2 + z**4 - h*z - 4/25*z**5. Factor x(d).
-4*(d - 2)*(d - 1)**3/5
Solve 8234*q - 30*q**2 - 5*q**4 - 8234*q - 25*q**3 = 0.
-3, -2, 0
Let s(f) be the first derivative of -f**3/7 - 156*f**2/7 - 612*f/7 + 584. Find x, given that s(x) = 0.
-102, -2
Let k = 2558 - 12766/5. Factor -12/5*a**2 + 6/5*a**5 + 18/5*a - k*a**3 + 0*a**4 + 12/5.
6*(a - 2)*(a - 1)*(a + 1)**3/5
Determine s so that -41*s + 1/4*s**2 + 1681 = 0.
82
Let p(n) = -4*n - 5. Let y be p(4). Let m be (6/(-21))/(3/y). Suppose 4*f**3 - f - f**3 + 12*f**m + 13*f = 0. Calculate f.
-2, 0
Factor 8/3*r**2 + 0 - 7/3*r - 1/3*r**3.
-r*(r - 7)*(r - 1)/3
Suppose -2/21*q**3 - 4/7*q**2 + 0 + 18/7*q = 0. Calculate q.
-9, 0, 3
Solve -2*g - 1030 - g**3 + 1030 - 8*g**2 + 5*g**2 = 0 for g.
-2, -1, 0
Let p(f) = -f. Let u(l) = 6*l**2 - 35*l + 27. Let s(y) = 5*p(y) - u(y). Let t(v) = -7*v**2 + 31*v - 28. Let r(i) = -4*s(i) + 3*t(i). Factor r(x).
3*(x - 8)*(x - 1)
Let x(z) be the third derivative of -z**8/131040 - z**7/10920 - 11*z**5/60 + 2*z**2. Let i(d) be the third derivative of x(d). Factor i(q).
-2*q*(q + 3)/13
Factor 41 + 35*i**3 - 147 - 31*i**3 - 72*i**2 - 14*i - 134 + 322*i.
4*(i - 12)*(i - 5)*(i - 1)
What is m in -38*m - 23*m + 15*m - 29*m - 2704 - 29*m - m**2 = 0?
-52
Let 1708*r**3 - 1858*r**3 + 38*r**2 - 30*r**2 = 0. What is r?
0, 4/75
Suppose -j + 65 = 8. Let z be 31/j - 7/21. Determine a so that 2/19*a**2 + z*a + 0 = 0.
-2, 0
Suppose -3*f = -4*d - 17 - 3, 0 = -f + 4*d + 20. Let k(m) be the first derivative of 0*m**3 + 3/4*m**4 - 1/2*m**6 + 3 + f*m**5 + 0*m**2 + 0*m. Factor k(n).
-3*n**3*(n - 1)*(n + 1)
Let k(p) be the first derivative of 3*p**4/8 - 11*p**3/2 - 3*p**2/4 + 33*p/2 - 328. Find s, given that k(s) = 0.
-1, 1, 11
Let s(w) be the second derivative of -w**7/1155 + w**5/110 - w**4/66 - 11*w**2/2 + 18*w. Let j(t) be the first derivative of s(t). Factor j(y).
-2*y*(y - 1)**2*(y + 2)/11
Let n(l) be the second derivative of 2401*l**6/195 + 1372*l**5/13 + 4900*l**4/13 + 28000*l**3/39 + 10000*l**2/13 - 8*l + 1. Suppose n(z) = 0. What is z?
-10/7
Let q(i) = i**2 + 150*i + 3*i**2 - 148*i. Let m(f) = -f**2 - f. Let t(s) = 3*m(s) + q(s). Factor t(x).
x*(x - 1)
Let j be 13 - 6/((-4)/(-2)). Suppose -9 = -5*m + 6. Suppose 0*g**m - 2 + j + 4 - 4*g - 12*g**2 + 4*g**3 = 0. Calculate g.
-1, 1, 3
Let h(g) be the first derivative of g**4/6 + 4*g**3/3 + 4*g**2 + 24*g - 17. Let z(k) be the first derivative of h(k). Factor z(n).
2*(n + 2)**2
Solve -290*v - 666*v**2 - 81/2*v**3 - 32 = 0.
-16, -2/9
Let g = 235 - 151. Let 28*i**5 - 134*i**4 - 137*i**2 - 10 + 2 + 64*i + g*i**3 - 45*i**2 + 148*i**3 = 0. What is i?
2/7, 1/2, 1, 2
Let u(p) be the second derivative of -1/56*p**7 - 20*p + 0*p**3 + 1/40*p**6 + 0*p**2 - 1/16*p**4 + 3/80*p**5 + 0. What is g in u(g) = 0?
-1, 0, 1
Let f(u) be the first derivative of 8192/7*u + 28 + 2048/7*u**2 + 16/7*u**4 + 256/7*u**3 + 2/35*u**5. Factor f(k).
2*(k + 8)**4/7
Let f be 2/16 + (-225)/8. Let o be ((-6)/f)/((-9)/(-21)). Factor 1/2*b**5 + 0*b + o*b**4 - 1/2*b**3 + 0 - 1/2*b**2.
b**2*(b - 1)*(b + 1)**2/2
Let p(i) be the first derivative of -i**4/6 - 2*i**3 - 9*i**2 - 7*i - 6. Let k(u) be the first derivative of p(u). Find t, given that k(t) = 0.
-3
Let z(w) = w**2 - 5*w + 7. Let s be z(4). Suppose y = 5*g - 29, 3*g + 3*y - 6 = -s. Factor 0*j - 4/5*j**2 + 0 + 14/5*j**g + 22/5*j**3 - 32/5*j**4.
2*j**2*(j - 1)**2*(7*j - 2)/5
Let i = -17 + 88. Let g = 71 - i. Suppose g + 4/5*f**2 + 2/5*f**3 + 2/5*f = 0. What is f?
-1, 0
Let m(o) = -12 + 37*o + o**2 - 1 - 47*o. Let c be m(12). Factor c*n**3 + 1 - n**2 - 4*n**2 - n + 0*n - 14*n**3.
-(n + 1)**2*(3*n - 1)
Let s be 2*(3/(-4) + (-7)/(-4)). Let r(f) be the first derivative of -1/2*f**4 + f**s - 1 - 22/21*f**3 + 18/35*f**5 + 4/7*f. Solve r(i) = 0 for i.
-1, -2/9, 1
Suppose -2*i - 1/8*i**2 + 17/8 = 0. What is i?
-17, 1
Let n = -196/85 - -46/17. Let r(w) be the first derivative of 0*w*