- 10*d**3 + 2*d**2 + 48*d - 48. Let u(p) = -9*p**4 - 11*p**3 + 3*p**2 + 48*p - 46. Let z(g) = 6*u(g) - 5*x(g). Factor z(q).
-4*(q - 1)**2*(q + 3)**2
Suppose 0 = -563*q + 584*q - 42. Determine i, given that -1/9*i**q + 0*i + 1/9 = 0.
-1, 1
Let i(p) be the third derivative of 0*p + 0*p**3 - 8*p**2 + 0 + 1/12*p**5 - 35/24*p**4. Factor i(o).
5*o*(o - 7)
Let i = -14034 - -126328/9. Determine x, given that 4/9 + 10/9*x - 8/9*x**5 - 2/9*x**3 - 26/9*x**2 + i*x**4 = 0.
-1, -1/4, 1, 2
Let c(k) = -k - 3. Let a be c(-11). Let 6*h**3 + 8*h**2 + 0*h**3 - a - 2*h**3 + 8*h - 12*h = 0. What is h?
-2, -1, 1
Let w(h) = -h**3 - 5*h**2 - 3*h + 4. Let o(l) = l**2 + 10*l + 20. Let r be o(-4). Let i be w(r). Suppose 1/2*t**2 - 3/4*t + 1/4*t**3 + i = 0. Calculate t.
-3, 0, 1
Let a = 18 + -11. Suppose a*b = 4*b + 9. Factor l**3 + 5*l + l**4 + 3*l**b - 2 - 5*l**3 - 3*l**2.
(l - 1)**3*(l + 2)
Factor -13 + 40*q + 9*q**2 + 5*q**2 - 17*q**2.
-(q - 13)*(3*q - 1)
Let t(n) be the first derivative of -n**6/15 + 2*n**5/5 - n**4/2 - 4*n**3/3 + 4*n**2 + 4*n - 7. Let w(x) be the first derivative of t(x). Factor w(m).
-2*(m - 2)**2*(m - 1)*(m + 1)
Let h(c) be the third derivative of 0*c - 9/56*c**4 + 2/7*c**3 + 0 + 1/28*c**5 - 4*c**2. Factor h(s).
3*(s - 1)*(5*s - 4)/7
Suppose -3/2*s**2 + 18 - 3/2*s = 0. Calculate s.
-4, 3
Let u = -15/31 + 61/62. Suppose -1 = -5*q + 3*v, -q = -3*v + 5*v - 8. Factor u*a**3 + 1/2*a**4 + 0 - 2*a - q*a**2.
a*(a - 2)*(a + 1)*(a + 2)/2
Let w = 6852/5735 + 6/1147. Let j(x) be the first derivative of 3/5*x**4 + 12 + 8/5*x - w*x**2 - 4/15*x**3 - 4/25*x**5. What is s in j(s) = 0?
-1, 1, 2
Let x(y) = -2*y + 16. Let a be x(7). Let c be 5/(a - 6/8). Suppose 4/7*z**c - 8/7*z**2 - 4/7*z**3 + 0 + 0*z = 0. What is z?
-1, 0, 2
Let i(s) = -8*s**2 + 10*s**3 - 8*s - 8*s**4 - s**3 + 3*s**3 + 7 - 4*s. Let f(q) = -q**4 - q**3 - q**2 + q - 1. Let c(d) = 3*f(d) - i(d). Factor c(h).
5*(h - 2)*(h - 1)**2*(h + 1)
Let s(p) be the first derivative of 0*p**2 + 1/60*p**5 - 1/9*p**4 + 2/9*p**3 + 5 - p. Let d(u) be the first derivative of s(u). Suppose d(x) = 0. Calculate x.
0, 2
Let o(i) = -3*i**5 + 2*i**4 - 15*i**3 + 12*i**2 - 8*i + 4. Let g(x) = -2*x**5 + x**4 - x**2 - x + 1. Let v(f) = 4*g(f) - o(f). Suppose v(j) = 0. What is j?
-2, 0, 2/5, 1
Let g(d) be the first derivative of 5*d**4/4 - 10*d**3/3 - 65*d**2/2 - 50*d + 387. Determine x, given that g(x) = 0.
-2, -1, 5
Let y = 619 - 616. Let c(u) be the first derivative of 15*u**y + 21/4*u**4 + 27/2*u**2 + 0*u - 7 + 3/5*u**5. Factor c(x).
3*x*(x + 1)*(x + 3)**2
Let b(n) = 5*n**2 + 12*n - 18. Let r(o) = -10 + 1 + 0*o + 19*o**2 - 16*o**2 + 6*o. Let u(p) = 4*b(p) - 7*r(p). Find q, given that u(q) = 0.
3
Let z be 50/15 + (1 - 7/3). Let t(i) be the first derivative of 1/24*i**3 - 1/40*i**5 - 1/16*i**z + 1/32*i**4 + 5 + 0*i. Find r such that t(r) = 0.
-1, 0, 1
Let n(s) = -s**3 - s + 3. Let p(h) = -5*h**3 - 3*h**2 - 7*h + 21. Let j(t) = -30*n(t) + 5*p(t). Factor j(f).
5*(f - 3)*(f - 1)*(f + 1)
Determine i, given that -4/3*i**5 + 8/3*i**3 - 8/3*i**2 + 4/3 - 4/3*i + 4/3*i**4 = 0.
-1, 1
Let n(m) be the second derivative of -27*m**5/5 - 21*m**4 - 25*m**3/2 - 3*m**2 + 128*m. Factor n(l).
-3*(l + 2)*(6*l + 1)**2
Let y(r) be the third derivative of -1/12*r**4 + 0*r**3 - 4*r**2 + 0 + 1/60*r**5 + 0*r. Factor y(i).
i*(i - 2)
Suppose -10*b - 3*b + 3*b + b**3 - 12 - 3*b**2 - 6*b = 0. Calculate b.
-2, -1, 6
Let w(n) be the second derivative of -n**6/15 + n**5/2 - 3*n**4/2 + 7*n**3/3 - 2*n**2 - 2*n + 2. Let w(k) = 0. Calculate k.
1, 2
Suppose 2*v - 2*c - c = -12, -4*c = 3*v - 16. Let m be 20*(507/165 + v + -3). Solve 2/11*d**4 - 4/11*d**2 - 8/11*d - 8/11*d**5 + m*d**3 + 2/11 = 0.
-1, 1/4, 1
Let o(z) be the third derivative of -z**7/42 + z**5/3 + 2*z**2 + 13. Determine f so that o(f) = 0.
-2, 0, 2
Let u = -633 + 637. Let j(z) be the second derivative of 0 - 3/7*z**2 + 9*z - 1/42*z**u - 4/21*z**3. What is c in j(c) = 0?
-3, -1
Let n be 294/70 - (-2)/(-10). Let u = 302/7 + -43. Factor 0 + u*t - 1/7*t**3 + 1/7*t**2 - 1/7*t**n.
-t*(t - 1)*(t + 1)**2/7
Let p(m) = -m**3 - 2*m**2 + m + 1. Let l(v) = 15*v**4 - 75*v**3 - 132*v**2 - 30*v + 6. Let d(j) = l(j) - 6*p(j). Let d(u) = 0. Calculate u.
-1, -2/5, 0, 6
Find m such that 1/2*m**4 - 5/2*m**3 + 0*m**2 + 0 + 0*m = 0.
0, 5
Let f be (-7)/46*((-112)/(-32) - (-57)/(-14)). Determine b so that 2/23*b**2 + f*b - 12/23 = 0.
-3, 2
Let x be ((-4)/6)/((-11)/297). Determine u so that -x*u**3 - 6 + 9*u + 12*u**2 - 5*u**4 - 4*u**4 - 6*u**4 + 9*u**5 + 9*u**4 = 0.
-1, 2/3, 1
Let k(b) = 16*b**3 + b**2. Let y be k(1). Suppose 6*c - 2*c - 5*s = y, c - 6 = 3*s. Solve -1 - 7 + 6*m**c + 6*m**2 - 4*m**3 = 0 for m.
-2, 1
Let j(y) be the third derivative of -y**7/210 + y**6/12 + y**5/20 - 7*y**4/6 - 10*y**3/3 + 16*y**2 - y. What is g in j(g) = 0?
-1, 2, 10
Let n be 5 + 78/(-12) + (-27)/(-12). Let p(k) be the first derivative of -12*k + 0*k**2 + 3*k**3 + 3 + n*k**4. Suppose p(m) = 0. What is m?
-2, 1
Let z = 23 + -16. Suppose -3*u - 2*d + 16 = 0, z*d - 5*d = 10. Determine l so that -10/3*l - 4/3 - 2*l**u + 2/3*l**4 + 2/3*l**3 = 0.
-1, 2
Let a(m) = -m**2 + 16*m + 61. Let n be a(19). Let 28*t**n + 14*t**5 + 60*t + 8*t**2 - 36 - 56*t**3 - 10*t**5 - 8*t**5 = 0. Calculate t.
-1, 1, 3
Let f(k) be the third derivative of k**6/600 + 3*k**5/50 + 11*k**4/40 + 8*k**3/15 + 46*k**2. Find p, given that f(p) = 0.
-16, -1
Let q(w) be the third derivative of w**8/560 + w**7/1050 - 32*w**2. Solve q(m) = 0 for m.
-1/3, 0
Let c = -841/2 + 4213/10. Factor -8/5*u + c + 4/5*u**2.
4*(u - 1)**2/5
Let a = 3687135/71266 - -192/2741. Let d = a - 103/2. Factor d*g + 6/13*g**2 + 0 + 2/13*g**3.
2*g*(g + 1)*(g + 2)/13
Factor -19 + 32 + 9*h + 6*h**2 - 10.
3*(h + 1)*(2*h + 1)
Let t(r) = -55*r**2 + 135*r - 530. Let b(d) = 3*d**2 - 7*d + 28. Let q(x) = -75*b(x) - 4*t(x). Determine i so that q(i) = 0.
-4, 1
Let l(m) = 5*m**2 - m. Let i(x) = 26*x**2 - 6*x. Let j = -18 + 22. Let t(r) = j*i(r) - 22*l(r). Factor t(d).
-2*d*(3*d + 1)
Let k = -2901 - -2903. Determine j, given that 4/7 + 2/7*j**3 - 2/7*j - 4/7*j**k = 0.
-1, 1, 2
Let f(g) be the second derivative of 0 + 3*g - 2/9*g**2 - 1/27*g**3 + 1/54*g**4. Factor f(m).
2*(m - 2)*(m + 1)/9
Let x(c) = -c**3 + 12*c**2 - 19*c - 2. Let m be x(10). Let -m*z**2 - 3 + 10*z + 13*z**2 - 10*z**2 - 2 = 0. What is z?
1
Let k = -21/43 - -511/430. Let d(l) be the second derivative of -4*l - 3/14*l**7 - k*l**6 + 0 + 0*l**3 - 4/5*l**5 + 0*l**2 - 1/3*l**4. What is x in d(x) = 0?
-1, -2/3, 0
Let b(j) = 8*j**3 + 19*j**2 - 26*j - 7. Let w(a) = -9*a**3 - 17*a**2 + 24*a + 6. Let g(n) = 2*b(n) + 3*w(n). Factor g(i).
-(i - 1)*(i + 2)*(11*i + 2)
Let i(s) = 4*s**3 - 6*s**2 - 12*s + 5. Let b(v) = -36*v**3 + 56*v**2 + 108*v - 44. Let a(c) = 3*b(c) + 28*i(c). Factor a(m).
4*(m - 1)**2*(m + 2)
Let i(b) be the first derivative of 2*b**5/25 - 253*b**4/40 + 37*b**3/2 - 367*b**2/20 + 61*b/10 + 13. Let i(m) = 0. What is m?
1/4, 1, 61
Let u(y) be the third derivative of y**8/144 + y**7/315 - 49*y**6/360 - 14*y**5/45 - y**4/6 - 149*y**2 - 1. Find q, given that u(q) = 0.
-2, -1, -2/7, 0, 3
Let v(x) = -2*x - 2. Let y be v(-21). Let k = y + -37. Factor 16/7*c**2 - 8/7*c + 0 - 10/7*c**k + 2/7*c**4.
2*c*(c - 2)**2*(c - 1)/7
Let s = 791/2 + -394. Let r = 287/4 + -71. Factor -s*j**3 + 0*j**4 + 0*j**2 + r*j**5 + 0 + 3/4*j.
3*j*(j - 1)**2*(j + 1)**2/4
Let g(b) = 3*b**2 - 10*b - 10. Let n(f) = -103 + 3*f**2 + 9*f - 6*f**2 + 112. Let s(y) = 5*g(y) + 6*n(y). What is o in s(o) = 0?
-2/3, 2
Let b(z) be the first derivative of -3/2*z**2 - 1/210*z**5 + 0*z - 2 + 0*z**3 + 1/28*z**4. Let y(k) be the second derivative of b(k). Factor y(w).
-2*w*(w - 3)/7
Let y be 9 + -3 - (-1 + -3). Suppose 4*j + 12 = y*j. Factor 0*t + 3/5 - 3/5*t**j.
-3*(t - 1)*(t + 1)/5
Let l = -2954 + 2955. What is z in l - 12*z**2 - 9/2*z - 13/2*z**3 = 0?
-1, 2/13
Let a(d) be the first derivative of d**5/4 + 2*d**4 + 19*d**3/4 + 19*d**2/4 + 2*d + 223. Factor a(k).
(k + 1)**2*(k + 4)*(5*k + 2)/4
Factor -5*w**2 - 19*w + 37*w + 5 - 18*w.
-5*(w - 1)*(w + 1)
Suppose 5*q - j - 2 = 12, 0 = -4*q - 5*j - 12. Let l(c) be the third derivative of c**q + 1/24*c**4 + 0 + 0*c**3 - 1/120*c**5 + 0*c. Factor l(d).
-d*(d - 2)/2
Let v(g) be the first derivative of -g**5/10 + 5*g**4/4 - 14*g**3/3 + 3*g**2/2 + 45*g/2 + 35. Factor