 j(v).
-2*v*(v - 6)*(v - 1)
Let m(p) be the second derivative of -p**4/30 - 5*p**3/6 - 33*p**2/10 + 4106*p. Find u, given that m(u) = 0.
-11, -3/2
Suppose 24*q**3 + 138*q**2 + 4*q**3 + 77163*q**4 - 77161*q**4 + 288*q + 216 = 0. Calculate q.
-6, -3, -2
Let g(u) = 2*u**2 + 6*u - 2. Let i be g(-4). Suppose 2 = -i*s + 14. Factor 74 - 74 + 8*m + 42*m**3 - 98*m**4 + 48*m**s.
-2*m*(m - 1)*(7*m + 2)**2
Let j(c) = 14*c**2 + 31*c - 9. Let x(s) = s**2 - s + 2. Let g(z) = -j(z) - 4*x(z). Let m(y) = 9*y**2 + 13*y. Let i(n) = -2*g(n) - 5*m(n). Factor i(o).
-(o + 1)*(9*o + 2)
Let b(v) be the second derivative of -7/9*v**3 + v + 1/30*v**5 + 26 - 1/9*v**4 - 4/3*v**2. Factor b(w).
2*(w - 4)*(w + 1)**2/3
Let n = 13974/11 + -41834/33. Let h = -2 - -6. Factor h*k**3 + 2/3*k**5 + 2/3*k + 8/3*k**4 + 0 + n*k**2.
2*k*(k + 1)**4/3
Determine x, given that -5*x**4 + 578/7*x - 221/7*x**2 + 0 - 1/7*x**5 - 321/7*x**3 = 0.
-17, -2, 0, 1
Let b be (6 - 5)/((-2)/(-318)). Let d = 430 - 271. Let -d + b + 0*n**3 + 4*n - n**3 = 0. What is n?
-2, 0, 2
Let z be ((-120)/(-144) + -1)*-60. Factor z*o**2 - 175*o**3 - 2695/6*o**4 + 20/3*o + 0.
-5*o*(7*o + 2)**2*(11*o - 2)/6
Let s(f) be the third derivative of 0 + 2/9*f**4 + 16/45*f**5 + 0*f**3 - 32/315*f**7 + 1/30*f**6 + 0*f - 1/36*f**8 - 149*f**2. Find j, given that s(j) = 0.
-2, -1, -2/7, 0, 1
Let t be (48/1216)/(3/8). Let v be -6*(7 + (-135)/19). Factor -v*i - t*i**2 + 14/19.
-2*(i - 1)*(i + 7)/19
Let q = 147 - 144. Determine s so that -22*s + s**5 + s**5 - 2*s**4 - 33*s**3 + 96*s**q + 6 + 28*s**2 - 41*s**3 - 34*s**3 = 0.
-3, 1
Let f(z) be the second derivative of -1/12*z**3 + 1/2*z**2 - 3*z + 1/40*z**5 + 9 - 1/8*z**4 + 1/60*z**6. Factor f(o).
(o - 1)**2*(o + 1)*(o + 2)/2
Let o(x) be the first derivative of -x**4/6 - 20*x**3/9 + 91*x**2/3 - 160*x/3 - 2102. Find u, given that o(u) = 0.
-16, 1, 5
Let k = -13052 + 65269/5. Let p be (4/(-10))/(4/(-20)). Solve k*z + 3/5*z**3 + 27/5 - 3*z**p = 0 for z.
-1, 3
Suppose 6*k + 2*k - 27 = -11. Let a(u) be the first derivative of -5*u**4 - 4 - 2/3*u**6 + 8/3*u**3 + 16/5*u**5 + 0*u**k + 0*u. Suppose a(p) = 0. Calculate p.
0, 1, 2
Let c(o) be the third derivative of -1/120*o**6 - o**2 + 4*o - 13/12*o**4 - 8/3*o**3 + 0 - 11/60*o**5. Factor c(t).
-(t + 1)*(t + 2)*(t + 8)
Let r(m) be the third derivative of m**5/30 + 39*m**4/4 + 230*m**3/3 + 13686*m**2. Factor r(q).
2*(q + 2)*(q + 115)
Let u(k) = 6041*k - 6036. Let p be u(1). Solve 0*d**4 + 0 - 1/3*d + 8/9*d**2 + 1/9*d**p - 2/3*d**3 = 0 for d.
-3, 0, 1
Let q(d) be the second derivative of -d**4/42 - 5*d**3/21 + 24*d**2/7 + 3359*d + 1. What is b in q(b) = 0?
-8, 3
Let s be -3 - 55/(-20) - 297/(-324). Let r(p) be the second derivative of -s*p**3 - 12*p**2 + 33*p + 1/3*p**4 + 0. Factor r(v).
4*(v - 3)*(v + 2)
Suppose 19*j - 37 = 1. Let -22 - 2*d**j - 9 - d**3 - 10 + d + 43 = 0. Calculate d.
-2, -1, 1
Let g(s) be the third derivative of s**7/420 - s**6/30 + s**5/20 + s**4/6 - 7*s**3/12 + 354*s**2 + s. Suppose g(w) = 0. Calculate w.
-1, 1, 7
Let r(p) = 2*p**2 + 4*p - 1. Let q(j) = 16*j**2 + 76*j + 79. Let m(d) = -2*q(d) + 18*r(d). Let m(h) = 0. Calculate h.
-2, 22
Let 2*z**2 - 213*z - 77 + 114*z - 279*z - 303 = 0. Calculate z.
-1, 190
Factor 8762043 + 3/4*m**2 - 5127*m.
3*(m - 3418)**2/4
Let r be ((-22)/40)/((-902)/6765). Factor -9/4 + 3/8*w**4 + r*w - 9/8*w**3 - 9/8*w**2.
3*(w - 3)*(w - 1)**2*(w + 2)/8
Suppose -68*v**4 + 18494 - 1950*v**3 + 63814 - v**5 - 62453*v - 18088*v**2 + 252*v**3 = 0. What is v?
-19, -12, 1
Let k(u) = -3160*u**2 + 1390*u + 25. Let s(o) be the first derivative of -81*o**3 + 107*o**2/2 + 2*o + 239. Let p(v) = -3*k(v) + 40*s(v). Factor p(m).
-5*(2*m - 1)*(24*m + 1)
Let s(v) be the first derivative of -5/2*v**4 + 0*v**2 + 19 + 0*v - v**5 - 5/3*v**3. Factor s(m).
-5*m**2*(m + 1)**2
Let m(h) = -17*h**3 - 34*h**2 - 21*h + 4. Let n(i) = 37*i**3 + 69*i**2 + 41*i - 9. Let j(u) = -9*m(u) - 4*n(u). Factor j(z).
5*z*(z + 1)*(z + 5)
Let b(d) = d**3 + 6*d**2 - 3*d - 20. Let o be b(-6). Let f(g) = g**2 + 247*g - 266. Let s(w) = 62*w - 66. Let v(q) = o*f(q) + 9*s(q). Solve v(x) = 0 for x.
1, 31
Suppose -5*u + 18 - 70 = -3*r, -5*r - 2*u + 97 = 0. Factor -5*g**4 + r*g - 9*g - 2*g**4 - 1 + 5*g**3 - 24*g**2 + 17*g**3.
-(g - 1)**3*(7*g - 1)
Let h(b) be the second derivative of -b**4/66 + 125*b**3/33 + 126*b**2/11 - b - 1055. Factor h(t).
-2*(t - 126)*(t + 1)/11
Suppose -216/7*m + 4/7*m**2 + 2916/7 = 0. Calculate m.
27
Let a(y) be the second derivative of 221*y**4/60 - y**3/30 - 2*y + 21. Factor a(q).
q*(221*q - 1)/5
Let n(a) = -4*a + 29. Let s be n(6). Let f be 0*(s + 33/(-6)). Solve 0*w**3 + 0*w**2 + 2/3*w**4 + f + 2/3*w**5 + 0*w = 0 for w.
-1, 0
Factor 6*w**2 - 192/7 + 152/7*w - 2/7*w**3.
-2*(w - 24)*(w - 1)*(w + 4)/7
Let d be (-9 - (-153)/18)/((-1)/4). Let z(m) be the first derivative of -8/21*m**3 - 25 + 1/14*m**4 - 5/7*m**d + 0*m. Factor z(l).
2*l*(l - 5)*(l + 1)/7
Let o(l) be the third derivative of l**8/336 + 8*l**7/105 - 3*l**6/20 - 4*l**5/15 + 17*l**4/24 - 455*l**2. Let o(q) = 0. What is q?
-17, -1, 0, 1
Let i = -107 - -111. Factor 2*x**4 + 20*x**3 + x**4 + x**i + 2*x**4 - x**4.
5*x**3*(x + 4)
Let n(p) = -6*p + 11. Let h be n(-5). Find w such that -w**2 + 102 - 140*w + 5*w**2 + h - 14 + 7 = 0.
1, 34
Let w(i) be the first derivative of i**6/72 + 5*i**5/24 + 5*i**4/6 - 5*i**3/3 + 3. Let y(c) be the third derivative of w(c). Factor y(b).
5*(b + 1)*(b + 4)
Suppose 128*h = 123*h + 50. Suppose 70*n**3 + 132*n + 356*n**4 - 723*n**4 - 188*n**2 + 363*n**4 - h*n**3 = 0. Calculate n.
0, 1, 3, 11
Let o(y) be the first derivative of -y**7/84 - y**6/20 + y**5/40 + y**4/8 + 21*y + 40. Let c(l) be the first derivative of o(l). Solve c(d) = 0.
-3, -1, 0, 1
Let d be (((-40)/45)/(-4) - 4/18)*1. Let v(z) be the third derivative of 1/240*z**5 + 0*z**3 + 0*z**4 - 25*z**2 + 0*z + 1/320*z**6 + d. Factor v(k).
k**2*(3*k + 2)/8
Determine l so that 1119744/7 - 3360960/7*l - 1124930/7*l**3 - 2/21*l**5 + 1730/7*l**4 + 10093250/21*l**2 = 0.
1, 1296
Let v(k) be the first derivative of k**6/84 + 4*k**5/105 - k**4/21 - 2*k**2 - 129. Let r(i) be the second derivative of v(i). Find w, given that r(w) = 0.
-2, 0, 2/5
Let j(x) = 2*x**3 - 9*x**2 - 4*x - 1. Let v be j(5). Suppose 88*c - 27 = 79*c. Factor 1/6*w**v + 8/3 - 4*w + 1/6*w**2 + w**c.
(w - 1)**2*(w + 4)**2/6
Let t(f) be the second derivative of 5/14*f**2 + 1/12*f**4 - 2 - 16*f - 11/42*f**3 - 1/140*f**5. Factor t(d).
-(d - 5)*(d - 1)**2/7
Let q = 195220 + -390439/2. Factor 0 + q*p**2 + 1/3*p**3 + 1/6*p.
p*(p + 1)*(2*p + 1)/6
Let d(o) = 2*o**2 - 6840*o - 20536. Let n be d(-3). Factor 0 + 1/4*k**3 + 121/4*k - 11/2*k**n.
k*(k - 11)**2/4
Let v = -10/827 + 857/2481. Let p(c) be the third derivative of -19*c**2 - 1/6*c**4 + 0*c + 0 - 1/30*c**5 - v*c**3. Factor p(h).
-2*(h + 1)**2
Let x(f) be the first derivative of -2*f**3/15 + 36*f**2/5 - 448*f/5 + 503. Determine y so that x(y) = 0.
8, 28
Suppose o - 25 = 6*o + 3*v, 25 = -5*o - 2*v. Let y(j) = j**2 + 18*j + 32. Let p(l) = 2*l**2 + 46*l + 80. Let z(d) = o*p(d) + 12*y(d). Factor z(f).
2*(f - 8)*(f + 1)
Let p = -1115 - -1109. Let d be (-52)/22 + (p - -4)*-2. Factor -62/11*m + 32/11*m**2 + d*m**3 + 12/11.
2*(m - 1)*(m + 3)*(9*m - 2)/11
Let t = -16308 + 16310. Factor -6/11 + 2/11*n**t - 4/11*n.
2*(n - 3)*(n + 1)/11
Let w = -21 + 26. Let z be (16 - 15) + (-41)/(-8) - w. Find m such that -z*m - 3/4 - 3/8*m**2 = 0.
-2, -1
Let b(o) be the second derivative of 75*o**6 - 615*o**5/2 + 925*o**4/3 - 416*o**3/3 + 32*o**2 - 236*o + 2. Find w such that b(w) = 0.
1/5, 4/15, 2
Let t(s) be the third derivative of s**9/5544 + 3*s**8/3080 - s**6/165 + 89*s**3/6 + 4*s**2 - 4. Let k(u) be the first derivative of t(u). Factor k(o).
6*o**2*(o - 1)*(o + 2)**2/11
Suppose -a = -13*q + 15*q - 9, 3*q = -3*a + 15. Let w = 5/422 - -4112/211. Find j, given that -9/2*j**q - w*j**3 + 6*j**5 - 9/2*j + 51/2*j**2 - 3 = 0.
-2, -1/4, 1
Factor -44 + 1/2*w**2 - 791/6*w.
(w - 264)*(3*w + 1)/6
Let s be 16/6*36/16. Let z(c) = 5*c**4 - 11*c**3 - 15*c**2 + 11*c + 16. Let y = 86 + -85. Let i(o) = o**3 - o - 1. Let m(d) = s*i(d) + y*z(d). Factor m(g).
5*(g - 2)*(g - 1)*(g + 1)**2
Let x = 7167 + -7165. Let m(d) be the first derivative of 1/6*d**x - 1/3*d - 3 + 1/12*d**3. Find p, given that m(p) = 0.
-2, 2/3
Let d(r) = r**2 + 2