
47
Let r(u) = 2*u**2 + 21*u - 8. Let t be r(-11). Solve -6*h**3 - 19*h - 12*h + 46*h - 12*h + t*h**5 = 0 for h.
-1, 0, 1
Let u(h) be the second derivative of h**5/30 + 2*h**4/9 + 4*h**3/9 - 28*h + 3. Let u(k) = 0. Calculate k.
-2, 0
Let t(f) be the first derivative of 2/27*f**3 + 0*f - 1/9*f**2 + 9. Suppose t(u) = 0. Calculate u.
0, 1
Let n = 5 + -5. Let p = 26445/4 + -6611. Let 0*r + n + p*r**2 = 0. Calculate r.
0
Suppose -25/3*h - 410/3*h**2 - 5/3*h**5 + 35/3*h**4 + 125 + 10*h**3 = 0. What is h?
-3, -1, 1, 5
Suppose 15*c**2 - 15*c**3 - 13*c**4 + 20*c - 119*c**5 - 2*c - 2*c**4 + 116*c**5 = 0. What is c?
-3, -2, -1, 0, 1
Let b(k) = 3*k**2 - 2*k - 2. Let o(p) = 16*p**2 - 10*p - 11. Suppose -101*m + 103*m = -12. Let t(v) = m*o(v) + 33*b(v). Factor t(f).
3*f*(f - 2)
Let q be ((-6)/(-10))/(90/900) - 2. Solve q*v**4 - v - 8/3*v**2 + 0 + v**3 - 4/3*v**5 = 0 for v.
-1/2, 0, 1, 3
Let u(z) be the third derivative of -z**6/30 - 2*z**5/3 + 23*z**4/6 - 8*z**3 - 245*z**2 + 3. Suppose u(f) = 0. Calculate f.
-12, 1
Let o = -3 + 15. Find s, given that 2*s**3 - o - s**2 - s + 5 + 8 - s**3 = 0.
-1, 1
Suppose 2/5 + 82/5*k**2 - 44/5*k - 8*k**3 = 0. Calculate k.
1/20, 1
Find c, given that 57*c - 2*c**3 - 2*c**3 + 164*c**2 - 1500*c + 154*c - 1764 - 307*c = 0.
-1, 21
Factor 10 - 28*i - 32*i**3 + 32*i**2 + 20*i**3 - 2.
-4*(i - 1)**2*(3*i - 2)
Let d be 0/2*((-12)/2 - (2 - 9)). Factor -1/5*j**3 + 1/5*j**5 + 0*j + 0*j**2 + d*j**4 + 0.
j**3*(j - 1)*(j + 1)/5
Suppose 4*y - 3*s = 35, -y = -2*s - s - 20. Suppose -3*p - o + 3 = 0, p + 3*p = y*o + 23. Let 3*b + 0*b**2 - 3*b**5 + b**p + 6*b**4 - 7*b**2 = 0. What is b?
-1, 0, 1
Let z(g) be the third derivative of 0*g**4 + 0*g + 1/270*g**6 + 0*g**5 - 1/945*g**7 + 0*g**3 + 42*g**2 - 1/1512*g**8 + 0. Factor z(d).
-2*d**3*(d - 1)*(d + 2)/9
Let m(i) be the second derivative of -18*i**5/5 + 145*i**4/6 - 2*i**3/3 - 8*i**2 + 6*i - 7. Solve m(u) = 0.
-2/9, 1/4, 4
Let x(s) be the first derivative of 8*s**6 + 312*s**5/5 + 387*s**4/4 - 146*s**3 - 273*s**2/2 - 36*s + 127. Find z such that x(z) = 0.
-4, -3, -1/4, 1
Let k = -2355 - -7067/3. Factor 2/3*g**4 + k*g**2 + 2*g**3 - 4/3 - 2*g.
2*(g - 1)*(g + 1)**2*(g + 2)/3
Let x be ((7 - 5)/(1 + 0))/8. Determine a so that -1/4 + x*a + 1/2*a**2 = 0.
-1, 1/2
Let o(r) = r**3 - 7*r**2 + 9*r - 8. Let l be o(6). Factor -65*n**2 + 14*n + 20*n**3 + 26*n - l + 15*n.
5*(n - 2)*(n - 1)*(4*n - 1)
Let k(o) = -o**3. Let f(h) = -21*h**3 + 3*h**2 + 3*h - 3. Let d = 5 - -13. Let w(n) = d*k(n) - f(n). Let w(j) = 0. What is j?
-1, 1
Suppose 3*s - 41 = -26. Factor -5*l - l**5 + 5*l**4 - 3*l - 8*l**2 - l**4 + 6*l**3 - l**s.
-2*l*(l - 2)**2*(l + 1)**2
Let k(v) be the second derivative of v**7/3 + 46*v**6/15 + 613*v**5/70 + 46*v**4/7 + 12*v**3/7 + 522*v. Factor k(d).
2*d*(d + 3)**2*(7*d + 2)**2/7
Suppose -372*p**3 + 747*p**3 - 374*p**3 = 0. Calculate p.
0
Suppose -16 = -j + 4*o, -23*j + 5*o + 23 = -21*j. Solve -55/3*f**3 + 1/2 + 58/3*f**2 - 17/3*f + 25/6*f**j = 0 for f.
1/5, 1, 3
Let k(t) = 2*t**3 + 27*t**2 - 57*t - 31. Let g(b) = -b**3 - 27*b**2 + 56*b + 32. Let u(s) = -3*g(s) - 4*k(s). Factor u(w).
-(w - 2)*(w + 7)*(5*w + 2)
Let u(q) = -q**3 - q. Let a(f) = -f**3 + 10*f**2 - 13*f. Let l(p) = a(p) - 2*u(p). Factor l(c).
c*(c - 1)*(c + 11)
Let z(t) be the third derivative of 0*t**3 + 0 + 1/144*t**4 + 0*t**5 - 1/720*t**6 - 16*t**2 + 0*t. Find l, given that z(l) = 0.
-1, 0, 1
Let q(n) = n**2 + 1. Let z be 4/(-14) - 132/(-21). Let v(s) = z + 2*s**2 + 4 - s + 0*s - 3. Let b(w) = -5*q(w) + v(w). Suppose b(r) = 0. What is r?
-1, 2/3
Let i(d) = d + 8. Let x be i(-3). Suppose x*t - 32 = -4*u + u, -u + 8 = t. Determine v, given that 0*v + 4/13*v**3 - 2/13*v**t - 2/13*v**2 + 0 = 0.
0, 1
Let b(k) = -k + 6. Let h be b(1). Determine x so that 9*x**3 - 6*x**2 + 2*x**2 + 6*x**2 + 12*x**4 + h*x**5 = 0.
-1, -2/5, 0
Let t be ((-12)/22)/(-8 - (2 + -7)). Solve -8/11*x**5 - t + 14/11*x**3 + 0*x**4 - 6/11*x + 2/11*x**2 = 0 for x.
-1, -1/2, 1
Determine v, given that -2304/5 + 96/5*v - 1/5*v**2 = 0.
48
Suppose 0 = -5*p - 2*y + 9 + 3, 8 = 3*p + y. Factor -70*z**p + 65*z**4 - 8*z**2 - 10*z**3 + 3*z**2.
-5*z**2*(z + 1)**2
Let n(o) be the third derivative of -o**8/560 + o**7/280 + o**6/120 - o**5/40 + 2*o**3/3 + 2*o**2. Let q(c) be the first derivative of n(c). Factor q(h).
-3*h*(h - 1)**2*(h + 1)
Let d(k) = 5*k**2 - 3155*k + 84345. Let n(m) = m**2 - 526*m + 14057. Let w(u) = -4*d(u) + 25*n(u). Factor w(c).
5*(c - 53)**2
Let j(t) = -t**2 - 2. Let d(g) = 12*g**2 + 40*g - 28. Let o(s) = -d(s) - 8*j(s). What is f in o(f) = 0?
-11, 1
Let k(t) be the third derivative of -t**8/112 - 3*t**7/70 - t**6/20 + t**5/10 + 3*t**4/8 + t**3/2 + 46*t**2. Find s, given that k(s) = 0.
-1, 1
Let k(j) be the first derivative of 2*j**3/3 + 17*j**2 + 32*j - 52. Suppose k(n) = 0. What is n?
-16, -1
Let t = -7 - -21. What is i in -t*i + 11*i + i**3 + 2*i**3 = 0?
-1, 0, 1
Let 1/5*m**2 - 1 + 4/5*m = 0. What is m?
-5, 1
Suppose -50*z + 49*z = -5. Factor -5/2 + 5/2*u**4 - 5*u + z*u**3 + 0*u**2.
5*(u - 1)*(u + 1)**3/2
Let c = -3 - -24/7. Suppose -2*v - 2*w = -10, 1 = 4*v - 2*w - 7. Factor -6/7*m**2 + 6/7 + c*m - 3/7*m**v.
-3*(m - 1)*(m + 1)*(m + 2)/7
Let r(t) be the first derivative of 36 + 1/16*t**4 - 1/4*t**3 - 1/8*t**2 + 1/20*t**5 + 1/2*t. Factor r(s).
(s - 1)**2*(s + 1)*(s + 2)/4
Let l = -40367/69 + 585. Let a = l - -62/23. Solve 6*b - 10/3*b**5 - 20/3*b**2 + 8*b**4 - 4/3 - a*b**3 = 0 for b.
-1, 2/5, 1
Suppose 15*o - 46 = -8*o. Let p(j) be the second derivative of 0*j**o - 1/10*j**5 + 11*j + 2/3*j**3 + 0 + 1/6*j**4. What is c in p(c) = 0?
-1, 0, 2
Let h(n) be the third derivative of 0*n - 1/4*n**5 + 5/12*n**4 + 0 + 22*n**2 + 5/6*n**3. What is m in h(m) = 0?
-1/3, 1
Let a(t) be the first derivative of t**5/5 - t**3/3 + 54. Determine c, given that a(c) = 0.
-1, 0, 1
Factor -18 + 15*f + 16*f**2 + 6*f**3 + 0*f**3 - 10*f**2 - 9*f**3.
-3*(f - 3)*(f - 1)*(f + 2)
Solve -1690 + 1560*f - 255/2*f**4 - 3115/2*f**3 - 5/2*f**5 + 3635/2*f**2 = 0 for f.
-26, -1, 1
Let b(r) be the first derivative of -9 - 4/3*r + 0*r**3 + 1/6*r**4 - r**2. Factor b(w).
2*(w - 2)*(w + 1)**2/3
Let l be -1*(5 + -3) - (9 - 4). Let y(t) = -t**2 - 17*t - 68. Let f be y(l). Determine c, given that -2/5*c**f - 2/5 - 4/5*c = 0.
-1
Let j be (-4 + 2 + -1)/((-36)/(-24)*-1). Let 0*i + 9/8*i**j - 3/8 - 3/4*i**3 = 0. What is i?
-1/2, 1
Suppose -5*x + 13 = -7. Let s be (0/(-5 + 4))/x. Factor -2*j**3 + 0*j + s*j + 10*j**3 - 8*j**2 - 2*j**4.
-2*j**2*(j - 2)**2
Let g(c) be the third derivative of 0*c**4 - 1/945*c**7 + 54*c**2 - 1/270*c**6 + 0 + 0*c**3 + 1/90*c**5 + 0*c. Factor g(s).
-2*s**2*(s - 1)*(s + 3)/9
Suppose -104 = 3*o - 110. Let t(w) be the first derivative of 0*w - 3/2*w**2 + o + 3/4*w**4 + 0*w**3. What is x in t(x) = 0?
-1, 0, 1
Let l(t) be the third derivative of t**5/75 + 11*t**4/30 + 16*t**3/5 - 22*t**2 + 4*t. Suppose l(p) = 0. What is p?
-8, -3
Let z(a) = 8*a**2 + 6*a - 1. Let p be z(-2). Let c(j) = j**3 - 18*j**2 - 20*j + 19. Let q be c(p). Factor 2/3*u**2 + 0 + q*u + 1/3*u**3.
u**2*(u + 2)/3
Let x(y) = -3*y**2 - 12*y + 9. Let r(b) = -b**2 - b + 1. Let a(d) = 6*r(d) - x(d). Factor a(i).
-3*(i - 1)**2
Let t = 5 + -1. Factor 0*w**3 + 6*w**2 - 3*w - w + 2*w**2 - t*w**3.
-4*w*(w - 1)**2
Let w(m) = -2*m**2 + 1. Let c be w(1). Let f = c + 3. Solve 1 - 23*z**f - 15*z**3 - 21*z - 4*z**2 - 5 - 2 - 3*z**4 = 0 for z.
-2, -1
Let a(o) = 2*o**2 - o - 4. Let y be a(2). Suppose 0 = l - y*d - 7, l - 4*l + 3*d + 15 = 0. Factor 0 + 2/3*h**2 + 2/3*h - 35/6*h**l.
-h*(5*h - 2)*(7*h + 2)/6
Let c = 849 - 847. Let p(q) be the first derivative of -8/15*q**3 + 0*q + 0*q**c + 1/5*q**4 + 3. Suppose p(u) = 0. Calculate u.
0, 2
Let k(s) be the first derivative of 242/7*s + 2/21*s**3 + 22/7*s**2 - 3. Factor k(p).
2*(p + 11)**2/7
Let y(d) be the first derivative of 2*d**5/65 - 10*d**3/39 + 8*d/13 + 40. Find u such that y(u) = 0.
-2, -1, 1, 2
Let o be -6 + -1 + (-2)/(-8)*29. Factor 3/4*x**3 + 0 + x**4 - o*x**2 + 0*x.
x**2*(x + 1)*(4*x - 1)/4
Factor 57*o**2 - 1/3*o**5 + 36 - 67/3*o**3 - 72*o + 13/3*o**4.
-(o - 3)**3*(o - 2)**2/3
Factor 32/13 + 2/13*l**2 - 16/13*l.
2*(l - 4)**2/13
Let g(m) = m + 5. Let j be g(-3). Factor -12*t**3 + 6*t**4 - t**5 + 634*t**j - 624*t**2 - 5*t + 2*t.
-t*(t - 3)*(t - 1)**3
Suppose 2*a**4 + 41 - 36*a + 15 - 52*a**