et c(s) be the first derivative of s**5/15 - 19*s**4/36 - 5*s**3/18 - 34*s + 43. Let k(q) be the first derivative of c(q). Factor k(a).
a*(a - 5)*(4*a + 1)/3
Let n be 42/20 - (-50)/125. Let s(d) = -2*d**2 - 36*d - 32. Let v be s(-17). Factor -n*j**v - 5*j + 0.
-5*j*(j + 2)/2
Factor 21*k**2 + 32*k**3 - 32*k + 1446 - 4*k**4 + 19*k**2 + 0*k**4 - 1482.
-4*(k - 9)*(k - 1)*(k + 1)**2
Let f be (0 - -2 - -6) + -6. Solve -1/2 + i - 1/2*i**f = 0.
1
Let r = 1210 + -1210. Factor 0 - 3/4*v + 0*v**4 + r*v**2 - 3/4*v**5 + 3/2*v**3.
-3*v*(v - 1)**2*(v + 1)**2/4
Let 0 + 7*s**2 - 19*s - 6*s**2 + 24*s + 6 = 0. Calculate s.
-3, -2
Let c be (-4 + 12 + -7)/(1/3). Let g = 2 + 0. Find o such that 2 + o**3 - c*o**2 + 0*o**3 - 1 + 3*o - g = 0.
1
Let x(w) be the third derivative of w**9/241920 - w**7/20160 + w**5/10 - 11*w**2. Let m(q) be the third derivative of x(q). Find h such that m(h) = 0.
-1, 0, 1
Suppose -3 = 2*x - 5*x - 4*m, 2*x - m - 13 = 0. Factor u + 748*u**3 - 4 + x*u - 750*u**3.
-2*(u - 1)**2*(u + 2)
Let v(r) be the first derivative of r**4/24 - r**3/6 - r**2/3 + 59. Solve v(p) = 0 for p.
-1, 0, 4
Let f(j) be the first derivative of j**3/8 + 15*j**2/2 - 174. Factor f(p).
3*p*(p + 40)/8
Let q(u) = -2*u**2 + 181*u - 1746. Let n be q(11). Let m be 13/15 - 2/(-6). Suppose m*r**n + 0 + 2*r**2 - 4/5*r = 0. What is r?
-2, 0, 1/3
Let x(r) be the first derivative of r**5/50 - r**4/24 - r**3/5 - 13*r**2/2 + 8. Let o(g) be the second derivative of x(g). Factor o(u).
(6*u**2 - 5*u - 6)/5
Factor 44*g**2 + 66*g - 561*g - 85*g**2 + 46*g**2.
5*g*(g - 99)
Suppose -9 = -0*x + 3*x, -2*y + 3 = 3*x. Suppose 3*w - y = -6. Factor -2/9*r**3 + w + 4/9*r**2 - 2/9*r.
-2*r*(r - 1)**2/9
Let u be (65/(-26) + (-3)/2)*(-75)/60. Factor 0 - 2*m**3 + 10/9*m**4 - 2/9*m**u + 14/9*m**2 - 4/9*m.
-2*m*(m - 2)*(m - 1)**3/9
Let r(l) be the second derivative of l**6/40 + 33*l**5/80 + 13*l**4/8 + 2*l**3 + 118*l. Suppose r(t) = 0. Calculate t.
-8, -2, -1, 0
Let q(i) = -i + 2*i - 2*i. Let p(a) = a**3 - 3*a**2 + 2*a + 4. Suppose 0 = 6*m + 10 - 4. Let b(z) = m*p(z) - 2*q(z). Suppose b(w) = 0. What is w?
-1, 2
Let g(y) be the first derivative of -y**4/4 + 32*y**3/3 - 221*y**2/2 - 578*y - 101. Factor g(s).
-(s - 17)**2*(s + 2)
Let o(z) be the second derivative of 1/24*z**4 - 3/4*z**2 + 0 - 1/6*z**3 - 16*z. Factor o(y).
(y - 3)*(y + 1)/2
Let j(d) be the first derivative of 3 + 0*d - 4/3*d**3 + 1/2*d**4 + d**2. Factor j(u).
2*u*(u - 1)**2
Suppose -408 - 104 - 5*n**3 + 96*n**2 - 58*n + 186*n - 35*n**3 + 4*n**4 = 0. What is n?
-2, 4
Let g(s) be the second derivative of 0*s**3 + 1/36*s**4 + 0*s**2 + 0 - 1/60*s**5 - 8*s. Factor g(u).
-u**2*(u - 1)/3
Let g(u) = 4*u**2 + 1154*u - 164618. Let q(v) = 3*v**2 + 1153*v - 164638. Let a(y) = -5*g(y) + 6*q(y). What is s in a(s) = 0?
287
Factor 3*n**5 - 40*n**2 + 2*n**5 + 10*n**2 - 152*n**3 + 117*n**3.
5*n**2*(n - 3)*(n + 1)*(n + 2)
Let c(i) = 10*i**2 - 30*i + 48. Let z(s) = -9*s**2 + 33*s - 48. Let r(u) = 6*c(u) + 7*z(u). Let r(l) = 0. Calculate l.
1, 16
Factor -200 - 7*q**2 - 7*q**2 + 892*q - 202*q + 49*q**2.
5*(q + 20)*(7*q - 2)
Let w(f) be the third derivative of -7/120*f**6 + 2/3*f**3 + 0*f + 1/60*f**5 - 6*f**2 + 1/3*f**4 - 3 - 1/336*f**8 - 1/42*f**7. Factor w(c).
-(c - 1)*(c + 1)**2*(c + 2)**2
Let s(l) be the third derivative of -l**5/12 - 85*l**4/12 + 175*l**3/6 + 176*l**2. Suppose s(n) = 0. What is n?
-35, 1
Suppose -4*o - 5*f - 9 = -21, 0 = -2*f. Let y(h) be the third derivative of 1/80*h**5 - 5/96*h**4 + 1/12*h**o + 0*h + 0 - h**2. Let y(r) = 0. What is r?
2/3, 1
Let b(g) be the third derivative of -g**7/420 + 13*g**6/240 + g**5/40 - 41*g**4/48 + 13*g**3/6 + 2*g**2 + 444*g. Determine h so that b(h) = 0.
-2, 1, 13
Suppose 4 = -2*s, 2*j - 6*j - s = 2. Let n(m) be the first derivative of j*m + 1/18*m**6 + 1/5*m**5 - 9 + 0*m**2 + 1/9*m**3 + 1/4*m**4. Factor n(z).
z**2*(z + 1)**3/3
Let i(d) be the first derivative of 2*d**3/3 + 7*d**2 + 12*d + 55. Find b such that i(b) = 0.
-6, -1
Factor -9*x**2 + 9 + 1/2*x - 1/2*x**3.
-(x - 1)*(x + 1)*(x + 18)/2
Let y(u) be the third derivative of -u**5/180 - 5*u**4/72 + 11*u**3/3 + 232*u**2. Factor y(i).
-(i - 6)*(i + 11)/3
Let f be (3/2)/(2/12). Let g = -4 + f. Suppose -4*m**2 + m**2 + g - 2 = 0. What is m?
-1, 1
Suppose 0 = -3811*v + 3682*v + 258. Let -1/3*x**v - 1/3*x**4 + x - x**3 + 2/3 = 0. What is x?
-2, -1, 1
Let a be -3*(3 + 1*-4). Let n = 5 - a. Factor -13*l**3 - 4*l + 14*l**2 + 4*l**4 + l**3 + 0*l**3 - n*l**2.
4*l*(l - 1)**3
Let u be 6 + (-145)/(-25)*-1. Let m(i) be the first derivative of 0*i + 0*i**3 - u*i**2 - 2 + 1/10*i**4. What is v in m(v) = 0?
-1, 0, 1
Determine z so that 63*z**3 + 5*z**4 + 506*z**2 - 160 - 18*z**3 - 486*z**2 - 180*z = 0.
-8, -2, -1, 2
Let n = 152/5 + -30. Let a be (-42)/35*1*4/(-6). Factor -n*h**5 + 0 + a*h**4 + 0*h**3 + 0*h**2 + 0*h.
-2*h**4*(h - 2)/5
Let v(t) be the second derivative of 5*t**4/12 + 5*t**3/2 - 91*t + 2. Factor v(h).
5*h*(h + 3)
Let o(m) = -m**3 - 15*m**2 - 15*m - 11. Let v = 24 - 38. Let l be o(v). Factor 6*g**l + 93*g - 39*g**2 - 11 - 7 - 21*g - 9.
3*(g - 3)**2*(2*g - 1)
Let c(k) be the second derivative of 0*k**3 + 0*k**2 + 0*k**4 + 17*k - 3/20*k**5 + 0 + 2/5*k**6. Let c(i) = 0. Calculate i.
0, 1/4
Let m(b) = -10*b**3 - 64*b**2 + 32*b + 4. Let s(h) = -30*h**3 - 191*h**2 + 98*h + 14. Let i(v) = -14*m(v) + 4*s(v). Factor i(q).
4*q*(q + 7)*(5*q - 2)
Let k(c) be the second derivative of 1/26*c**4 + 1/130*c**5 - 39*c + 0 - 4/13*c**2 + 0*c**3. Factor k(i).
2*(i - 1)*(i + 2)**2/13
Let s be -3 - 19*(-13)/78. Let g(b) be the second derivative of s*b**4 - b**3 - 6*b + 2*b**2 + 0. Factor g(c).
2*(c - 2)*(c - 1)
Let c(u) = u**2 - 98*u + 5. Let m(w) = 2*w**2 - 146*w + 8. Let d(y) = -8*c(y) + 5*m(y). Factor d(n).
2*n*(n + 27)
Let j(t) = -2*t - 1. Let h be j(0). Let s be (-24)/(-3) + -2 + h. Factor -s*x**2 - 13*x + 2 + 3*x**2 + 13*x.
-2*(x - 1)*(x + 1)
Let g(z) = -19*z**4 - 480*z**3 - 9102*z**2 + 20159*z. Let s(n) = 3*n**4 + 80*n**3 + 1517*n**2 - 3360*n. Let i(h) = 6*g(h) + 39*s(h). Factor i(r).
3*r*(r - 2)*(r + 41)**2
Factor 210 - 1357*k + 671*k + 629*k + 3*k**2.
3*(k - 14)*(k - 5)
Let b(t) be the first derivative of t**6/6 - 2*t**5/5 - t**4/2 + 4*t**3/3 + t**2/2 - 2*t + 153. Factor b(f).
(f - 2)*(f - 1)**2*(f + 1)**2
Determine o, given that -1/4*o**3 - 1/4*o**4 + 0 + 2*o**2 + 3*o = 0.
-2, 0, 3
Let n be 38/12 + (-67)/134. Factor n*p + 4/3*p**2 - 4.
4*(p - 1)*(p + 3)/3
Suppose 246*q**5 + 252*q**5 - 20*q**2 - 745*q**5 - 24*q + 248*q**5 + 2*q**3 + 5*q**4 = 0. Calculate q.
-3, -2, 0, 2
Suppose 3*w + 85 = 94. Let t(l) be the first derivative of -1/7*l**4 + 1/7*l**2 + 2/21*l**3 + w + 0*l. Factor t(i).
-2*i*(i - 1)*(2*i + 1)/7
Let o(d) = d**4 - d**3 + d**2 + d + 1. Let v(l) = -4*l**4 + 36*l**3 + 32*l**2 - 36*l - 37. Let m(a) = 15*o(a) + 5*v(a). Factor m(t).
-5*(t - 34)*(t - 1)*(t + 1)**2
Let k(i) be the second derivative of -i**6/90 + i**4/6 - 3*i**3 + 5*i. Let n(o) be the second derivative of k(o). Factor n(q).
-4*(q - 1)*(q + 1)
Let q(z) be the third derivative of -z**5/210 - 5*z**4/14 - 29*z**3/21 - 23*z**2 - 2. Determine y so that q(y) = 0.
-29, -1
Let q(m) = -m**2 + 9*m - 11. Let l be q(6). Factor 11*u - 9 - 5*u - l*u**2 + 4*u**2 + 2*u**2.
-(u - 3)**2
Let g(i) = 4*i**3 - 20*i**2 + 32*i - 16. Let x(p) = -2*p**3 + 10*p**2 - 16*p + 8. Suppose 5*z - 16 = 4. Let d(h) = z*g(h) + 9*x(h). Let d(l) = 0. Calculate l.
1, 2
Let l = 41 + -42. Let f be (0 - (24 - l))*102/(-510). Factor 2/3*q**3 + 1/3*q**f - q + q**4 - 2/3*q**2 - 1/3.
(q - 1)*(q + 1)**4/3
Let i = -229679/180 - -1276. Let z(v) be the third derivative of 0*v + 1/9*v**4 + 0 + i*v**5 - 2*v**2 + 8/9*v**3. Determine c so that z(c) = 0.
-4
Factor 157 + 5*i**2 - 312 + 150.
5*(i - 1)*(i + 1)
Let y(o) = 6*o**3 + 32*o**2 - 52*o + 24. Let i(l) = -4*l**3 - 16*l**2 + 26*l - 12. Let w(d) = 5*i(d) + 3*y(d). Determine s so that w(s) = 0.
1, 6
Let p(x) be the first derivative of -2*x**6/15 - 36*x**5/25 - 14*x**4/5 + 8*x**3/15 + 6*x**2 + 28*x/5 + 156. Suppose p(v) = 0. What is v?
-7, -1, 1
Let r be -5*19/6650 - (-3)/10. Factor r*s**2 + 0*s - 2/7.
2*(s - 1)*(s + 1)/7
Let m be (-4)/14 + 217/(-98) - -4. Let t(h) be the first derivative of 0*h + 1 - 3/4*h**4 + m*h**2 + 0*h**3. Factor t(a).
-3*a*(a - 1)*(a + 1)
Let h(t) be the third derivative of t**5/240 - 9*t