 z(k) = -k**2 - 5*k. Let u be z(-5). Suppose -2*o + 8 = a, 4*a - o = -0 + 5. Find x such that x - 2*x**2 + u*x**a + x = 0.
0, 1
Let u be 4*(-4)/(-16) + 66. Factor 67*d + 12*d**2 - 3*d**3 - u*d.
-3*d**2*(d - 4)
Let d = 81 + -80. Let t(u) = u**3 + u**2 + u - 1. Let b(j) = 25*j**3 + 25*j**2 + 30*j - 30. Let n(i) = d*b(i) - 30*t(i). Solve n(p) = 0 for p.
-1, 0
Let b be (-4 - (0 + -3))*(5 + -3). Let v(f) = -f. Let d be v(b). What is y in 3/5*y**5 + 18/5*y**3 - 12/5*y**d - 12/5*y**4 + 3/5*y + 0 = 0?
0, 1
Suppose 4*a - 11 = 3*a. Let j = 14 - a. Let v(t) = 6*t**2 - 66. Let p(k) = -k**2 + 13. Let i(q) = j*v(q) + 14*p(q). Suppose i(d) = 0. Calculate d.
-2, 2
Let j be ((1 - 1) + 0)/(10 + -8). Suppose j = -4*l + 9*l - 10. Factor l*p**3 - 18/7*p**2 + 10/7*p - 4/7*p**4 - 2/7.
-2*(p - 1)**3*(2*p - 1)/7
Let d = 67/70 + -6/7. Let a(r) be the first derivative of -8 + d*r**2 + 1/15*r**3 + 0*r. Factor a(t).
t*(t + 1)/5
Suppose -32 = 25*n - 82. Determine y so that -3/4 + 1/2*y + 1/4*y**n = 0.
-3, 1
Determine x so that 36*x - 96*x**4 - 8*x**5 - 27691*x**3 + 104*x**2 + 27707*x**3 - 44*x**5 - 8 = 0.
-1, 2/13, 1
Let q(p) be the first derivative of -p**7/168 - p**6/36 - p**5/24 - 11*p**3/3 + 9. Let h(j) be the third derivative of q(j). Determine s, given that h(s) = 0.
-1, 0
Let o(m) = -m**4 - 7*m**3 - 18*m**2 - 2*m + 8. Let c(b) = -2*b**4 - 6*b**3 - 16*b**2 - 3*b + 12. Let z(g) = 2*c(g) - 3*o(g). Factor z(u).
-u**2*(u - 11)*(u + 2)
Let y = -28/157 - -4391/21980. Let i(d) be the third derivative of y*d**7 - 3/40*d**5 + 0 + 0*d**3 + 1/8*d**4 - 1/40*d**6 - 2*d**2 + 0*d. Solve i(h) = 0 for h.
-1, 0, 2/3, 1
Let t(y) be the first derivative of 2*y**5/25 + 21*y**4/10 + 38*y**3/5 + 11*y**2 + 36*y/5 + 63. What is s in t(s) = 0?
-18, -1
What is t in -32/3*t**2 + 128/9 + 38/9*t**3 - 2/9*t**4 - 8/9*t = 0?
-1, 2, 16
Let h be (-26)/(-819)*91 - 1/(-9). Let o(g) be the third derivative of -2/9*g**h + 0*g + 0 + 2*g**2 + 1/18*g**4 - 1/180*g**5. Solve o(x) = 0.
2
Let n(u) be the first derivative of 4*u**5/5 + 5*u**4 + 8*u**3/3 - 16*u**2 - 22. Factor n(b).
4*b*(b - 1)*(b + 2)*(b + 4)
Let y = -17 - -21. Solve -y*h**2 + 7 - 16 - 20*h - 7 + 4*h = 0 for h.
-2
Suppose 27*p - 2 = 25*p + q, 5*q - 12 = -p. Factor -1/5*n**3 + 0 - 1/5*n + 2/5*n**p.
-n*(n - 1)**2/5
Suppose 2 = -u - 0. Let z be u/(-9) - ((-57)/(-27) - 3). What is n in 4/9*n - 2/3*n**5 + z*n**2 + 0 - 10/9*n**4 + 2/9*n**3 = 0?
-1, -2/3, 0, 1
Let z(r) = -28*r**3 + 36*r + 32. Let t(l) = 2*l**3 - l**2 - l. Let j(w) = 12*t(w) + z(w). Solve j(x) = 0.
-4, -1, 2
Let z be 7 - (3 + 4/2). Let k(o) be the second derivative of 0 - 1/16*o**4 - 7*o + 3/8*o**z + 0*o**3. Factor k(u).
-3*(u - 1)*(u + 1)/4
Let x(p) be the second derivative of -4*p + 0 + 0*p**2 - 5/2*p**4 + 5/6*p**3. Let x(o) = 0. What is o?
0, 1/6
Let t be (15/(-30))/((-1)/20). Let f(n) be the first derivative of 15/8*n**4 - t - 5/12*n**6 + 1/2*n**5 - 5/6*n**3 - 5/2*n**2 + 0*n. What is z in f(z) = 0?
-1, 0, 1, 2
Let d = -14669 + 73357/5. What is x in 18/5*x**3 + d*x**2 + 48/5 - 6/5*x**4 - 72/5*x = 0?
-2, 1, 2
Let b(o) = -o**2 + 11*o - 16. Suppose 0 = -4*h + 14 + 22. Let k be b(h). Solve 1/5 + 1/5*t**k + 2/5*t = 0.
-1
Solve -28*c**2 + 374 - 422 - 13*c - 4*c**3 - 51*c = 0 for c.
-3, -2
Factor 3*o - 16 - 5*o**2 + 7*o - 4*o**2 + o**2 + 7*o**2.
-(o - 8)*(o - 2)
What is s in 3380 + 1112*s**2 + 156*s + s**3 - 1196*s**2 + 3*s**3 = 0?
-5, 13
Let y(b) = b**3 - 4*b**2 + 2*b - 3. Let p be y(2). Let t = p + 19. Suppose -23*l**2 + 9*l + 3*l + t + 26*l**2 = 0. What is l?
-2
Let z(c) be the third derivative of c**7/350 - c**6/100 - 3*c**5/20 + 110*c**2. Factor z(k).
3*k**2*(k - 5)*(k + 3)/5
Let h(v) be the second derivative of 3/4*v**5 - 2*v**6 + 5/6*v**7 + 0 + 0*v**2 + 0*v**3 - 2*v + 5/6*v**4. Solve h(g) = 0.
-2/7, 0, 1
Let p(c) = -29*c**2 + 104*c - 32. Let m(d) = -19*d**2 + 69*d - 22. Let z(b) = 8*m(b) - 5*p(b). Factor z(g).
-(g - 4)*(7*g - 4)
Let o = 2468 - 2455. Let c(w) be the first derivative of -8*w - 2*w**2 + 8/3*w**3 + w**4 - o. Factor c(t).
4*(t - 1)*(t + 1)*(t + 2)
Let j(f) be the third derivative of -1/4*f**5 + 5/6*f**4 + 0 + 1/42*f**7 - 19*f**2 + 10/3*f**3 + 0*f - 1/12*f**6. Factor j(n).
5*(n - 2)**2*(n + 1)**2
Suppose 0 = -252*a + 250*a - 30. Let j = a + 20. Let 0 - 3*u**2 - 3/4*u**j - 3/4*u - 3*u**4 - 9/2*u**3 = 0. What is u?
-1, 0
Let v = -28 - -28. Let r(w) be the third derivative of v + 1/16*w**4 + 1/6*w**3 + 0*w**7 - 1/60*w**6 + 0*w + 1/672*w**8 - 1/60*w**5 - 4*w**2. Factor r(y).
(y - 2)*(y - 1)*(y + 1)**3/2
Let q be (-2)/(-14) - 93/651. Let j = 481/9 + -53. Solve 10/9*f**3 - j*f + q - 2/3*f**2 = 0 for f.
-2/5, 0, 1
Let j(n) be the second derivative of 2*n**7/147 - 2*n**6/35 - 2*n**5/35 + 2*n**4/7 + 2*n**3/21 - 6*n**2/7 - 43*n. Let j(l) = 0. Calculate l.
-1, 1, 3
Let m(f) be the third derivative of f**8/336 - f**7/21 + 31*f**6/120 - 13*f**5/30 - 7*f**4/6 + 20*f**3/3 + 144*f**2. Find k such that m(k) = 0.
-1, 2, 5
Let r = -490397/221 - -2219. Let u = r + 215/663. Suppose 0 - u*l + 1/3*l**2 = 0. Calculate l.
0, 1
Let z(r) be the third derivative of -3*r**8/1120 - r**7/180 + r**6/180 - 5*r**4/8 + 21*r**2. Let u(t) be the second derivative of z(t). Solve u(n) = 0 for n.
-1, 0, 2/9
Let p(s) = s**2 + s**2 - 3*s**2 + 2*s**2 + 2 - 9*s. Let t be p(9). Find v, given that 17*v**t - 4*v**3 - 4*v**4 - 9*v**2 + 0*v**3 = 0.
-2, 0, 1
Let f(r) be the second derivative of 2*r**7/21 + 14*r**6/5 + 174*r**5/5 + 710*r**4/3 + 950*r**3 + 2250*r**2 + 35*r - 1. Suppose f(t) = 0. Calculate t.
-5, -3
Determine c, given that 252/5*c**2 - 27/5*c**4 + 54*c - 81/5 + 12/5*c**5 - 138/5*c**3 = 0.
-3, -1, 1/4, 3
Suppose 7*l = 5*l. Let z be (-46)/(-102) + 4 + 700/(-170). Factor l - z*m**3 + m + 2/3*m**2.
-m*(m - 3)*(m + 1)/3
Let f(x) be the first derivative of -x**4 - 1604*x**3/3 - 79998*x**2 + 161604*x + 416. Determine c so that f(c) = 0.
-201, 1
Factor 1 + 2*b**5 + 47*b**4 + 58*b + 68*b**3 - 30*b**2 - 62*b**2 - 69*b**4 - 15.
2*(b - 7)*(b - 1)**4
Let u(z) be the first derivative of -z**5/60 + z**4/6 - z**3/2 + 2*z**2/3 + 7*z + 16. Let m(o) be the first derivative of u(o). Let m(d) = 0. Calculate d.
1, 4
Let h be ((-10)/14 - -1)*(-564)/(-282). Find l, given that -h + 8/7*l - 4/7*l**2 = 0.
1
Let r = -7 - 0. Let u be (-1)/4 - (-1)/(-6 - r). Factor -u*z + 1/4 - 1/4*z**3 + 3/4*z**2.
-(z - 1)**3/4
Solve 24/7*y + 5/7*y**2 + 27/7 = 0 for y.
-3, -9/5
Let c = -1614 + 814. Let y be 1/(-4) + (-520)/c. Solve 0*f + y*f**2 - 2/5 = 0 for f.
-1, 1
Suppose 5*j - 10*j = 4090. Let o = 9016/11 + j. Factor 8/11*n - 4/11*n**4 + o*n**3 + 0 - 24/11*n**2.
-2*n*(n - 2)**2*(2*n - 1)/11
Let i be (-4125)/(-110)*8/66. Solve i + 2/11*b**2 - 20/11*b = 0.
5
Let z = 96 + -862/9. Let i(s) be the first derivative of 2/27*s**6 + 4/9*s**4 - 14/45*s**5 + 2/9*s - 4/27*s**3 - 4 - z*s**2. Suppose i(p) = 0. Calculate p.
-1/2, 1
Suppose 3*a - d = -3*d - 3, -4*a - 4 = 3*d. Let n(u) = -u**2. Let k(x) = 5*x**2 - x. Let r(f) = a*k(f) - 4*n(f). Find c such that r(c) = 0.
0, 1
Let v(o) = o**4 - o**3 + o**2 - 1. Let j(a) = -31 + 4*a**3 - 52*a**2 - 12*a + 35 - 3*a**3 + 59*a**4. Let m(r) = j(r) + 4*v(r). Solve m(f) = 0.
-2/3, -2/7, 0, 1
Factor 28/13*a**3 + 0*a**2 + 0*a + 0 + 30/13*a**4 + 2/13*a**5.
2*a**3*(a + 1)*(a + 14)/13
Determine p, given that -800 - 2/9*p**2 + 80/3*p = 0.
60
Let p(r) = r**2 + 0 + 5*r**3 + 4 - 6 - r. Let b be p(1). Determine a, given that a**4 - 1/4*a**5 - 5/4*a**b + 0*a + 1/2*a**2 + 0 = 0.
0, 1, 2
Solve 0 + 24/5*c**2 - 9/5*c**4 + 12/5*c + 3/5*c**3 = 0 for c.
-1, -2/3, 0, 2
Let h(m) be the first derivative of 2/33*m**3 - 2/11*m**2 + 0*m - 2. Factor h(i).
2*i*(i - 2)/11
Let b(r) be the first derivative of r**5/20 - 3*r**4/16 - r**3/4 + 11*r**2/8 - 3*r/2 - 69. Factor b(i).
(i - 3)*(i - 1)**2*(i + 2)/4
Let d(b) = 4*b**4 - 11*b**3 - 49*b**2 - 37*b - 3. Let k(p) = 4*p**4 - 10*p**3 - 50*p**2 - 38*p - 2. Let f(i) = 2*d(i) - 3*k(i). Factor f(s).
-4*s*(s - 5)*(s + 1)*(s + 2)
Let k = -855 + 855. Factor -1/5*l**2 + k - 1/5*l**3 + 0*l.
-l**2*(l + 1)/5
Let n(m) be the second derivative of -m**6/75 - 7*m**5/50 - 17*m**4/30 - 17*m**3/15 - 6*m**2/5 - 39*m. Find r such that n(r) = 0.
-3, -2, -1
Solve -9/2 + 51/8*h - 15/8*h**2 = 0 for h.
1, 12/5
Let d = 8 - 6. Suppose 0*j = -5*j - 15, d*i = 4*j + 132. Solve -28*b**3 + i*b**2 + 42*b**2 - 24*b - 10*b**2 = 0.
0, 2/