5
Let r = -2037321 + 114100613/56. Let c = -1306/7 + r. Suppose 3/2*l - c*l**4 - 3/8 - 9/2*l**3 + 3/4*l**2 = 0. Calculate l.
-1, 1/3
Factor -2/7*r**3 + 18/7*r**2 + 20/7*r + 0.
-2*r*(r - 10)*(r + 1)/7
Let q = 5/21 - 1/63. Let m = 1/3804 + 2533/11412. Factor 2/3*y**2 + q*y + 0 + 2/3*y**3 + m*y**4.
2*y*(y + 1)**3/9
Factor 2/11*r**2 - 8/11*r - 42/11.
2*(r - 7)*(r + 3)/11
Suppose 5*m - 105 + 93 = 2*c, -2*m - 24 = 4*c. Determine l, given that -7/4*l**3 - 5/4*l**4 + 0*l + m - 3/4*l**2 - 1/4*l**5 = 0.
-3, -1, 0
Let v be 10/4 - 4/8. Let o(w) be the first derivative of 2/21*w**3 - 1 + 2/7*w + 2/7*w**v. Factor o(r).
2*(r + 1)**2/7
Let o(g) = 5*g**5 - 14*g**4 - 4*g**3 + 4*g**2 + 4*g - 4. Let v(x) = 5*x**5 - 13*x**4 - 3*x**3 + 3*x**2 + 3*x - 3. Let q(c) = 3*o(c) - 4*v(c). Factor q(l).
-5*l**4*(l - 2)
Let j = -46 + 48. Factor -j*f**3 + 0*f**2 - 4*f + 0*f**3 + 6*f**2.
-2*f*(f - 2)*(f - 1)
Let j(a) = -6*a**3 - 6*a**2 + 90*a - 96. Let x(m) = -5*m**3 - 4*m**2 + 91*m - 94. Let g(y) = -2*j(y) + 3*x(y). Factor g(f).
-3*(f - 5)*(f - 1)*(f + 6)
Suppose 14 = -9*m + 7*m. Let r be m/(-3) - 30/(-45). Solve -1 + 7*s - 4 - 4*s**2 + r - s**2 = 0 for s.
2/5, 1
Let z(c) be the second derivative of -c**5/50 + c**4/10 + 2*c**3/3 - 45*c + 1. Factor z(o).
-2*o*(o - 5)*(o + 2)/5
Let r(z) be the second derivative of 3*z**5/160 + 15*z**4/8 + 59*z**3/16 + 170*z + 2. Find h, given that r(h) = 0.
-59, -1, 0
Factor 3*v**3 - 120*v**3 + 43904 - 4536*v**2 - 22*v**4 + 20*v**4 - 88*v**3 - 39200*v + 39*v**3.
-2*(v - 1)*(v + 28)**3
Find k, given that 98/3 + 101/3*k + k**2 = 0.
-98/3, -1
Let h be (-260)/(-455)*21/18. Factor h*o**2 + 8/3*o + 2.
2*(o + 1)*(o + 3)/3
Let d = 1/278 - 595/10842. Let g = 47/156 + d. Let 0 + 3/4*a + g*a**2 = 0. Calculate a.
-3, 0
Let o(x) be the first derivative of 2 + 0*x**3 + 5*x**3 - 15*x - 6*x**3 - 9*x**2 + 0*x**3. Let o(f) = 0. What is f?
-5, -1
Let w(l) be the second derivative of -l**7/1785 + l**6/204 - l**5/170 - 3*l**4/68 + 7*l**2/2 + 10*l. Let o(d) be the first derivative of w(d). Factor o(q).
-2*q*(q - 3)**2*(q + 1)/17
Let t = 13 - 6. Suppose -10 = -c - t. What is q in c*q**2 + 13*q**3 - 4*q**3 - 3*q**4 - 9*q**2 = 0?
0, 1, 2
Let d(u) be the third derivative of u**7/945 - 7*u**6/540 + u**5/18 - u**4/12 + 3*u**2 - 9*u. Find f, given that d(f) = 0.
0, 1, 3
Let z = 71/9 - 68/9. Factor b**3 + 0 - z*b**4 - 4/3*b + 0*b**2.
-b*(b - 2)**2*(b + 1)/3
Let a(h) be the second derivative of -h**4/114 - 17*h**3/57 + 18*h**2/19 + 136*h. Find w such that a(w) = 0.
-18, 1
Factor -95306*s**2 - 17 + 45*s - 8 + 95*s**3 + 95471*s**2.
5*(s + 1)**2*(19*s - 5)
Factor -16/5*b - 8/5*b**2 + 2/5*b**4 + 0 + 4/5*b**3.
2*b*(b - 2)*(b + 2)**2/5
Let n(s) be the first derivative of -s**4/18 - 4*s**3/3 + 7*s**2/3 + 76*s/9 + 201. Factor n(c).
-2*(c - 2)*(c + 1)*(c + 19)/9
Let l(w) = -w**3 - w - 1. Let m(b) = 30*b**3 - 60*b**2 + 10*b + 2. Let k = -5 - -3. Let s(h) = k*l(h) - m(h). Factor s(o).
-4*o*(o - 2)*(7*o - 1)
Suppose -5*t + 16 = x - 2*x, -5*t - x + 24 = 0. Determine v, given that -197*v - 6*v**t - 24*v**3 + 237*v - 16*v**3 + 80 + v**4 - 75*v**2 = 0.
-4, -1, 1
Let j(b) be the third derivative of b**6/600 - 27*b**5/100 + 729*b**4/40 - 6561*b**3/10 + 147*b**2. Factor j(n).
(n - 27)**3/5
Let l be 1/((6/8)/((-48)/(-256))). What is o in 0*o - l*o**2 + 0 = 0?
0
Let k(n) be the first derivative of n**3/9 - 5*n**2/3 + 7*n - 67. Suppose k(y) = 0. What is y?
3, 7
Suppose 2 = -4*d + 10. Determine h, given that -10 + 25*h - 31*h**3 + 26*h**3 + 5*h**4 - 5*h**d - 10*h**2 = 0.
-2, 1
Let f(a) = 2*a**2 + 27*a - 39. Let r be f(-17). Suppose -79*i = -r*i + 2. Factor -4/3*u**i - 8/3*u + 4*u**3 + 0.
4*u*(u - 1)*(3*u + 2)/3
Let i(u) be the first derivative of 5*u**3/9 - 155*u**2/6 + 233. Let i(k) = 0. What is k?
0, 31
Let -477*t**2 + 8*t + 446*t**3 + 50*t**5 + 65*t**4 + 737*t**2 - 16 + 195*t**4 = 0. Calculate t.
-2, -1, -2/5, 1/5
Suppose -3*o + m + 116 - 34 = 0, 0 = -4*o - 5*m + 103. Let y be 12/o + (-5 - 282/(-54)). Factor 4/3*v + y*v**2 + 2/3.
2*(v + 1)**2/3
Let f be (-378)/(-441) - (-1012)/126. Let l(q) be the first derivative of 100/9*q**4 - 32/9*q - 32/3*q**2 - 9 - f*q**3 + 50/3*q**5. Let l(s) = 0. What is s?
-2/5, 2/3
Let f(q) be the first derivative of -2*q - 6 + 1/3*q**3 + 1/2*q**2. Solve f(u) = 0.
-2, 1
Let j(x) = x**3 + 3*x**2 - x - 1. Let a be j(-3). Let b(c) be the second derivative of -c**3 + 2/3*c**a + 1/6*c**4 + 0 + 2/15*c**5 + 3*c. Factor b(w).
2*(w - 1)*(w + 2)*(4*w - 1)/3
Let y(k) = k**2. Suppose -11*a = -15*a + 16. Let f(n) = n**2 - 12*n + 15. Let m(q) = a*y(q) - f(q). Find x such that m(x) = 0.
-5, 1
Let b(s) be the first derivative of -3*s**5/5 + 31*s**4/10 - 68*s**3/15 + 4*s**2/5 + 295. Factor b(z).
-z*(z - 2)**2*(15*z - 2)/5
Suppose -p + 4*c + 25 = 0, -6 = -2*p - 3*c - 0*c. Let g be 1 - p/(27/(-6)). Find u, given that -1/2*u**g + 3/2*u + 0*u**2 - 1 = 0.
-2, 1
Let t(x) be the second derivative of -x**6/45 - 2*x**5/15 - 2*x**4/9 - 41*x + 3. Factor t(j).
-2*j**2*(j + 2)**2/3
Factor -1/3*j**2 + 26/3*j - 25/3.
-(j - 25)*(j - 1)/3
Let z(h) be the first derivative of -3*h**4/28 + 40*h**3/7 + 13. Find f, given that z(f) = 0.
0, 40
Factor -102*i**4 + 25*i**2 + 0*i**3 + 97*i**4 - 5*i**3 + 0*i - 15*i.
-5*i*(i - 1)**2*(i + 3)
Suppose -50/9*r**4 + 0*r + 0 - 2/9*r**5 - 286/9*r**3 + 338/9*r**2 = 0. Calculate r.
-13, 0, 1
Let v(k) be the first derivative of k**6/270 - k**5/45 + k**4/36 + 23*k - 6. Let d(g) be the first derivative of v(g). Factor d(u).
u**2*(u - 3)*(u - 1)/9
What is z in -1562/19*z**2 + 452/19*z**3 + 8/19*z**5 + 142/19*z**4 + 1160/19*z - 200/19 = 0?
-10, 1/4, 1
Let m(z) = -z - 1. Let w be m(-1). Let r = 689/60 + -133/12. Factor w + 2/5*p**2 - 1/5*p + 1/5*p**5 - r*p**4 + 0*p**3.
p*(p - 1)**3*(p + 1)/5
Let o = -1 + 1. Let s be (-148)/(-168) + 9/(-42). Solve o - s*u**2 + 2/3*u = 0.
0, 1
Let i be 33 - (-5)/(5/(-3)). Factor l**2 - 10*l - 11*l + i*l + l.
l*(l + 10)
Determine y, given that -64/3*y - 52/3*y**2 - 16/3 + 20/3*y**5 + 68/3*y**4 + 44/3*y**3 = 0.
-2, -1, -2/5, 1
Let s(j) be the third derivative of 0*j**4 + 0*j**5 - 2/105*j**7 + 0*j**3 + 1/30*j**6 + 0 + 17*j**2 + 0*j. Determine o so that s(o) = 0.
0, 1
Let n(p) = -p**2 - p. Let i(m) = m**4 + 8*m**3 + 18*m**2 + 14*m. Let v(y) = -i(y) + 2*n(y). Factor v(t).
-t*(t + 2)**2*(t + 4)
What is n in 0 - 10/3*n**2 + 35*n**3 + 0*n - 95/3*n**4 = 0?
0, 2/19, 1
Let c(b) be the second derivative of b**4/18 - b**3 - 24*b. Let c(f) = 0. What is f?
0, 9
Let m(q) = q**2 - 2*q - 7. Let d be m(5). Determine c so that -4*c**3 + 8 + c - 7*c + 7*c - d*c**2 + 3*c = 0.
-2, -1, 1
Let j(l) be the third derivative of 0*l + 1/210*l**5 - 18*l**2 + 0 - 1/21*l**4 + 1/7*l**3. Factor j(s).
2*(s - 3)*(s - 1)/7
Let k(f) be the first derivative of -9*f**4 - 116*f**3/3 - 48*f**2 - 16*f + 89. Let k(h) = 0. Calculate h.
-2, -1, -2/9
Let n be (-14)/7 + 5 + -1. Factor -6*o + 22*o**n - 5*o**2 + 3 - 7*o**2 - 7*o**2.
3*(o - 1)**2
Suppose -3*h + 4*g = -242 - 210, -5*h + 4*g = -740. Suppose 17*y - 113*y + 0 + h + 3*y**3 - 44*y**2 - 7*y**3 = 0. Calculate y.
-6, 1
Let u(l) be the third derivative of -1/140*l**6 + 0 + 1/784*l**8 + 3*l**2 + 1/56*l**4 + 0*l - 1/35*l**5 + 1/7*l**3 + 1/245*l**7. Determine a so that u(a) = 0.
-2, -1, 1
Let r(q) be the second derivative of -q**5/50 - q**4/15 - 58*q. Solve r(k) = 0.
-2, 0
Let v(q) = -41*q**4 - 56*q**3 + 14*q**2 + 44*q + 21. Let f(i) = -83*i**4 - 113*i**3 + 27*i**2 + 87*i + 43. Let b(k) = -6*f(k) + 13*v(k). What is j in b(j) = 0?
-1, -3/7, 1
Let x(a) be the second derivative of 9/2*a**3 + 0 - 3/4*a**5 + 1/10*a**6 - 29*a + 3/4*a**4 + 0*a**2. Factor x(w).
3*w*(w - 3)**2*(w + 1)
Let k = -61 - -65. Suppose -n = 3*o - 8*o - 10, -2 = -k*n + o. Solve -4/7*i**2 + 8/7*i**3 + n + 0*i - 4/7*i**4 = 0 for i.
0, 1
Factor -9/7*a**2 - 492/7 - 744/7*a.
-3*(a + 82)*(3*a + 2)/7
Let n be 784/1408 + 3/(-8). Factor 0 - n*b**2 + 4/11*b.
-2*b*(b - 2)/11
Let i(u) be the second derivative of -u**5/30 + 5*u**4/6 - 3*u**3 + 13*u**2/3 + u - 76. Factor i(z).
-2*(z - 13)*(z - 1)**2/3
Let 880/9*v + 86/9*v**2 + 2/9*v**3 - 968/9 = 0. What is v?
-22, 1
Let z(d) be the second derivative of d**6/65 - 19*d**5/130 + d**4/13 + 32*d**3/13 - 32*d**2/13 - 4*d + 35. Solve z(k) = 0 for k.
-2, 1/3, 4
Let o(x) = x**3 - 3*x**2 - x + 3. Let g be o(2). Let s be -3 + (-43)/(-10) + g/6. Supp