5*r**3/27 + 11*r**2 + 15. Factor l(b).
2*(b + 5)*(20*b + 1)/9
Let s(u) be the second derivative of u**4/12 + u**3/3 - 4*u**2 - 19*u - 1. Factor s(l).
(l - 2)*(l + 4)
Let t be 261/(-260) + (4 - (-75)/(-20)). Let u = 3/65 - t. Factor 2/5 - u*v - 2/5*v**4 + 0*v**2 + 4/5*v**3.
-2*(v - 1)**3*(v + 1)/5
Let i(p) be the third derivative of p**7/210 - p**6/120 - p**5/20 + 5*p**4/24 - p**3/3 + 3*p**2 - 12*p. Factor i(n).
(n - 1)**3*(n + 2)
Let j(s) be the third derivative of s**7/14 - s**6/12 - 4*s**2 - 4. Factor j(p).
5*p**3*(3*p - 2)
Let q(c) be the second derivative of c**4/42 + 80*c**3/21 + 1600*c**2/7 + 58*c. Find l such that q(l) = 0.
-40
Factor 62 + 21 + 13*l**2 + 54*l - 83 - 3*l**4 - 76*l**2 + 24*l**3.
-3*l*(l - 3)**2*(l - 2)
Let y(b) = -b**3 + 8*b**2 - 8*b + 10. Let v be y(7). Factor 19*i - 4*i**3 + 3*i**v + 3*i**2 - 19*i.
-i**2*(i - 3)
Let n be ((-5)/10)/((-3)/(-1212)). Let d = n + 1016/5. Let 0 - 3/5*z - 3/5*z**3 - d*z**2 = 0. What is z?
-1, 0
Let d be 20/350*(-10)/(-4). Factor -6/7*p - d*p**2 + 1.
-(p - 1)*(p + 7)/7
Let d(k) be the third derivative of k**7/1680 + k**6/120 + k**5/20 - k**4 - 40*k**2. Let j(y) be the second derivative of d(y). What is a in j(a) = 0?
-2
Suppose -65 = -38*s - 27*s. Let o(j) be the first derivative of 1/27*j**6 - s + 0*j + 4/45*j**5 + 0*j**4 - 4/27*j**3 - 1/9*j**2. Find g, given that o(g) = 0.
-1, 0, 1
Let n(v) be the first derivative of -4/3*v**3 + 0*v - 2*v**5 + 10 + 0*v**2 - 11/2*v**4. Factor n(t).
-2*t**2*(t + 2)*(5*t + 1)
Let u = 10 - 8. Let d be 3*(u - (-2)/(-2)). Suppose -5*h**d + 3*h**3 - h**3 = 0. What is h?
0
Let m(f) be the first derivative of 343*f**6/6 - 392*f**5/5 - 5649*f**4/4 - 4570*f**3/3 - 638*f**2 - 120*f - 34. Factor m(d).
(d - 5)*(d + 3)*(7*d + 2)**3
Factor 19/2*n**3 + 5/2*n + 29/2*n**2 - 5/2*n**4 + 0.
-n*(n - 5)*(n + 1)*(5*n + 1)/2
Let k(n) be the second derivative of 2/225*n**6 + 0 + 1/315*n**7 + 0*n**4 + 3*n + 0*n**2 + 0*n**3 + 1/150*n**5. Let k(m) = 0. What is m?
-1, 0
Let h = 6 - 3. Let t be (-46)/(-8) + 1/(12/3). Find v, given that -h + 0*v**2 - v**2 - 5*v**2 + 3*v**2 + t*v = 0.
1
Factor 3*q**3 - 25*q - 3*q**2 + 96 + 121*q + 33*q**2.
3*(q + 2)*(q + 4)**2
Suppose 6 + 24 = 3*p. Suppose 7*o - 2*o - p = 0. Factor -u**5 + 1 - 7*u + 0*u**5 + 4*u + o*u**3 + u**4 + 2*u - 2*u**2.
-(u - 1)**3*(u + 1)**2
Let b(p) = 2*p**3 + 3*p**3 - 6 + 7*p + 7 - 6*p**3 + 5*p**2. Let u(a) = -a**3 + 11*a**2 + 14*a + 2. Let i(k) = -11*b(k) + 6*u(k). Factor i(q).
(q + 1)**2*(5*q + 1)
Suppose -10*l**4 - 7*l**4 + 24*l**4 + 6*l**3 - 5*l**4 - 8*l**2 = 0. Calculate l.
-4, 0, 1
Solve -61/5*o + 1/5*o**3 + 31/5 + 29/5*o**2 = 0 for o.
-31, 1
Let d(c) be the first derivative of -50/3*c**6 + 17 - 4/3*c**3 + 0*c**2 + 9*c**4 + 0*c - 12*c**5. Factor d(p).
-4*p**2*(p + 1)*(5*p - 1)**2
Let v be (-27)/(-15)*2 - 4/(-10). Let k be 2 - ((-6)/v)/((-3)/(-4)). Suppose 16/5*y**2 + 4/5*y + 4/5*y**5 - 8/5*y**3 - 8/5 - 8/5*y**k = 0. What is y?
-1, 1, 2
Let h(j) = j**2. Let k(w) = 3*w**3 + 23*w**2 + 45*w. Let i(g) = -3*g**3 - 23*g**2 - 44*g. Let t(p) = -3*i(p) - 4*k(p). Let n(f) = h(f) - t(f). Solve n(d) = 0.
-4, 0
Factor -38/3 - 1/3*k**4 - 115/3*k - 39*k**2 - 41/3*k**3.
-(k + 1)**3*(k + 38)/3
Let g(w) be the third derivative of -w**7/840 - w**6/120 - w**5/240 + w**4/16 - 3*w**2 + 2*w. Let g(k) = 0. Calculate k.
-3, -2, 0, 1
Determine n, given that 4/9 + 20/3*n**3 + 106/9*n**2 + 50/9*n = 0.
-1, -2/3, -1/10
Let z(j) be the third derivative of 0 - 25/9*j**3 - 1/90*j**5 + 9*j**2 - 5/18*j**4 + 0*j. Suppose z(g) = 0. What is g?
-5
Factor -22*w**5 - 4*w**4 - 224*w + 61*w**5 - 19*w**5 - 192*w**2 - 38*w**3 + 7*w**4 - 19*w**5.
w*(w - 7)*(w + 2)*(w + 4)**2
Let g(u) = u**4 - u**3 + u**2 + 2*u + 1. Let s(r) = 2*r**4 + 35*r**3 + 54*r**2 + 32*r + 5. Let v(d) = -3*g(d) - s(d). What is k in v(k) = 0?
-4, -1, -2/5
Find u such that -543/8*u**2 + 495/2*u + 33/4*u**3 - 675/2 - 3/8*u**4 = 0.
5, 6
Let l(p) = -p**2 - p - 6. Let j(i) = -2*i**2 + 21*i - 118. Let a(g) = -5*j(g) + 5*l(g). Factor a(w).
5*(w - 14)*(w - 8)
Let n(m) be the first derivative of -m**5/20 + 5*m**4/4 - 37*m**3/6 - 77*m**2/2 + 363*m/4 - 425. Factor n(c).
-(c - 11)**2*(c - 1)*(c + 3)/4
Let s = 70 + -50. Factor -141*u**2 + 3*u**4 + 150*u**2 - s*u**3 + 8*u**3.
3*u**2*(u - 3)*(u - 1)
Let i = -9607/110 + 877/10. Factor -14/11*d + 8/11 + i*d**2 + 2/11*d**3.
2*(d - 1)**2*(d + 4)/11
Find m, given that -3/4*m**5 + 9/4*m**2 - 9/4*m**4 - 3/4*m**3 + 3/2*m + 0 = 0.
-2, -1, 0, 1
Let r(d) = -14*d**3 + 27*d**2 - 30*d + 62. Let s(v) = 5*v**3 - 9*v**2 + 10*v - 21. Let x(y) = 4*r(y) + 11*s(y). Let w be x(8). Factor w + 1/2*c**2 - 3/2*c.
(c - 2)*(c - 1)/2
Find s such that 3*s**3 - 3/2*s**5 - 3/2*s + 0*s**4 + 0*s**2 + 0 = 0.
-1, 0, 1
Let w(s) be the second derivative of -s**5/110 + 10*s**4/11 + s**3/33 - 60*s**2/11 + 4*s + 48. Factor w(t).
-2*(t - 60)*(t - 1)*(t + 1)/11
Let i(w) be the second derivative of -1/57*w**3 - 12*w - 1/399*w**7 + 0*w**2 + 0*w**4 + 1/95*w**5 + 0 + 0*w**6. Factor i(h).
-2*h*(h - 1)**2*(h + 1)**2/19
Let r be 69/6*-2*(-20)/10. Let z = r - 89/2. Find v, given that v**2 + z*v - 1/2*v**3 + 0 = 0.
-1, 0, 3
Let s(f) be the third derivative of 7*f**6/24 + 11*f**5/12 + 5*f**4/24 - 5*f**3/2 + 7*f**2 - 1. Let s(h) = 0. What is h?
-1, 3/7
Let n(q) be the first derivative of -5*q**4/4 - 52*q**3/15 - 29*q**2/10 - 2*q/5 + 407. Factor n(p).
-(p + 1)**2*(25*p + 2)/5
Suppose -42 = -90*s + 87*s. Factor -12*c - s*c**2 - 8 + 5*c**2 + 7*c**2 + 4*c.
-2*(c + 2)**2
Let g = 20512/7513 + -2/683. Let p = 71/22 - g. Let 0*r + 0 - p*r**2 + 3/4*r**3 = 0. Calculate r.
0, 2/3
Let o(a) be the first derivative of -a**4 - 8*a**3 + 14*a**2 - 619. Factor o(h).
-4*h*(h - 1)*(h + 7)
Let g(r) = 2*r**4 - 3*r**3 - 38*r**2 - 27*r + 6. Let f(c) = -25*c**4 + 35*c**3 + 455*c**2 + 325*c - 70. Let m(x) = 3*f(x) + 35*g(x). Factor m(d).
-5*d*(d - 3)*(d + 1)*(d + 2)
Let l(z) be the first derivative of z**3 - 270*z**2 + 24300*z + 10. Factor l(p).
3*(p - 90)**2
Suppose -4*a + 75 = -29. Let q = 31 - a. Factor -3 - q*j + 4*j - 2 + 3 - j**4 + 3*j**2 + j**3.
-(j - 2)*(j - 1)*(j + 1)**2
Factor 2*p**3 - 80 + p**2 + 9*p**2 - 4*p**2 - 2*p + 8*p**2 + 6*p.
2*(p - 2)*(p + 4)*(p + 5)
Factor -2*p**3 - 4/3*p - 16/9 + 46/9*p**2.
-2*(p - 2)*(p - 1)*(9*p + 4)/9
Let d be 5/1 + (-14953)/76. Let v = d - -192. Factor 0 - 1/4*c**2 - v*c**3 + 0*c.
-c**2*(c + 1)/4
Let 69 + 65 - 119 - 7*o + o**2 - o = 0. Calculate o.
3, 5
Let k be (-1)/(-2) - 6/(-4). What is m in -2*m**2 + 1 - k*m - 5 + 3*m**2 + m**2 = 0?
-1, 2
Let o(z) be the first derivative of 11*z**3/3 + 49*z**2/6 - 10*z/3 + 94. Factor o(c).
(3*c + 5)*(11*c - 2)/3
Let u = 3/1763 + 3511/8815. Solve u*h**5 - 2/5*h**3 - 2/5*h**4 + 2/5*h**2 + 0*h + 0 = 0 for h.
-1, 0, 1
Suppose -40 = 219*w - 229*w. Factor 3*u**3 + 21/5*u**2 + 3/5*u**w + 0 + 9/5*u.
3*u*(u + 1)**2*(u + 3)/5
Let q(n) be the first derivative of n**3 - 9*n**2 + 24*n + 38. Suppose q(i) = 0. What is i?
2, 4
Suppose 0*v + 400 = -5*v. Let m = 163/2 + v. Let m + a + 1/6*a**2 = 0. Calculate a.
-3
Let g = -936/31 - -1965/62. Find i, given that 9 + g*i**2 - 21/2*i = 0.
1, 6
Solve 0 + 3/2*a**3 + 3*a**2 + 0*a - 3/2*a**5 - 3*a**4 = 0.
-2, -1, 0, 1
Let s(k) be the third derivative of k**8/20160 - k**7/1680 + 3*k**5/5 - 23*k**2. Let q(w) be the third derivative of s(w). Solve q(r) = 0 for r.
0, 3
Let l(j) be the third derivative of -j**5/30 - 2*j**4/3 - 16*j**3/3 + 5*j**2. Determine m so that l(m) = 0.
-4
Determine q, given that -68/3*q**3 - 2/3*q**4 - 680*q - 698/3*q**2 - 600 = 0.
-15, -2
Let p be (1 + 1)/((-12)/84). Let h = p - -16. What is r in 2*r**h + 4*r**2 - 7*r**2 + 2 + 2*r - r = 0?
-1, 2
Let c be (-32)/(-40)*20/72. Let p(q) be the first derivative of c*q**3 + 2*q**2 + 6*q - 2. Factor p(i).
2*(i + 3)**2/3
Factor 33/7 - 100/7*l - 36/7*l**3 + 102/7*l**2 + 1/7*l**4.
(l - 33)*(l - 1)**3/7
Let 3*r**4 - 3*r**4 + 12*r**3 + 6*r - 3*r**4 - 5*r**2 - 10*r**2 = 0. What is r?
0, 1, 2
Let s be (-1)/(-3)*(-15801)/92. Let z = -57 - s. Find b such that 0*b + 0 - 1/2*b**4 - 1/4*b**5 + 0*b**2 - z*b**3 = 0.
-1, 0
Let q(o) be the third derivative of -o**7/126 - o**6/12 - o**5/36 + 5*o**4/3 - 40*o**3/9 - 63*o**2. Solve q(k) = 0.
-4, 1
Suppose 0 = -3*y + 12*v - 9*v, 4*y = -4*v + 32. Let m(k) be the first derivative of 0*k - 3 - 1/6*k**y - 2/9*k**3 + 0*k**2. Factor m(z).
-2*z**2*(z +