20*x**6 + 3*x**4. Factor f(o).
3*(o - 4)**2*(o + 1)**2
Let u = 388 + -397. Let d = u - -11. Find v, given that -2/9*v**d + 2/3*v + 2/9 - 2/3*v**3 = 0.
-1, -1/3, 1
Let f(r) be the second derivative of -r**7/70 + 23*r**6/50 - 513*r**5/100 + 513*r**4/20 - 54*r**3 - 4615*r. Determine c so that f(c) = 0.
0, 3, 5, 12
Let p be (14/((-14)/(-9)) + 12)*1. Suppose -p*z**2 - 144/5*z - 64/5 - 49/10*z**3 = 0. What is z?
-2, -8/7
Let q(j) be the third derivative of -4*j**7/63 - 127*j**6/180 - 139*j**5/90 - 17*j**4/36 + 5*j**3/3 - 6665*j**2. Find y such that q(y) = 0.
-5, -1, -3/5, 1/4
Let n(l) be the third derivative of 5*l**8/336 + 325*l**7/42 + 1107*l**6 + 2187*l**5 - 4*l**2 + 69*l. Find q, given that n(q) = 0.
-162, -1, 0
Let i(x) be the first derivative of -16/3*x - 4/15*x**5 - 282 - 2*x**2 - 1/2*x**4 + 38/9*x**3. Solve i(j) = 0 for j.
-4, -1/2, 1, 2
Let c(y) = -y**4 + 35*y**3 + 317*y**2 + 673*y + 4. Let t(z) = 4*z**4 - 106*z**3 - 952*z**2 - 2018*z - 14. Let w(j) = -7*c(j) - 2*t(j). Factor w(u).
-u*(u + 3)*(u + 15)**2
Let l(j) = -22*j**2 + 783*j. Let q(r) = -4*r**2 - 5*r. Let u(p) = 2*l(p) - 10*q(p). Factor u(d).
-4*d*(d - 404)
Let w(s) be the second derivative of s**9/3024 - s**7/72 - s**6/24 + s**4/12 - 95*s**2 - 208*s. Let b(y) be the third derivative of w(y). Factor b(n).
5*n*(n - 3)*(n + 1)*(n + 2)
Let x(k) be the third derivative of k**6/40 + k**5/20 - 25*k**4/8 - 25*k**3/2 - 941*k**2 + 4. Factor x(t).
3*(t - 5)*(t + 1)*(t + 5)
Let f(u) = 39*u**2 + 2664*u + 12129. Let k(j) = -11*j**2 - 760*j - 3465. Let l(n) = -5*f(n) - 18*k(n). Factor l(w).
3*(w + 5)*(w + 115)
Let d(f) be the second derivative of -1/42*f**7 + 0 + f**2 + 1/10*f**5 + 84*f - 1/3*f**4 + 1/15*f**6 - 1/6*f**3. Suppose d(i) = 0. What is i?
-1, 1, 2
Let v = -52 + 54. Suppose -4 = -3*g + v. Factor 2*z + 6 + g*z**2 - 2*z**3 + 8*z + 0*z.
-2*(z - 3)*(z + 1)**2
Let q(r) = 632*r + 49299. Let t be q(-78). Let -3/2*v**2 + 9/4*v - 1 + 1/4*v**t = 0. What is v?
1, 4
Suppose 1/4*l**2 + 198025/4 - 445/2*l = 0. Calculate l.
445
Let p(k) be the second derivative of -49 + 6*k**2 + 27/20*k**5 + 21/4*k**4 + 8*k**3 - 2*k. Factor p(f).
3*(f + 1)*(3*f + 2)**2
Let i(t) be the second derivative of -3/140*t**5 + 3/7*t**3 + 46*t + 5/28*t**4 + 0*t**2 + 0. Factor i(h).
-3*h*(h - 6)*(h + 1)/7
Let i(j) be the first derivative of -26*j**3 - 75*j**2/2 + 3*j - 1437. Factor i(b).
-3*(b + 1)*(26*b - 1)
Suppose 8*y - 3*y - 4*x - 332 = 0, 329 = 5*y - 3*x. Suppose -y*m + 67*m = 12. Factor 5*i**m + 28*i**3 - 161*i - 13*i**3 + 141*i.
5*i*(i - 1)*(i + 2)**2
Suppose -r - 5*n - 3 = 0, -146 = -5*r + 3*n - 133. Factor -2/9*l**r + 10/9*l + 28/9.
-2*(l - 7)*(l + 2)/9
Let w(d) be the first derivative of -28*d - 17*d**3 - 34*d**2 - 172 + 1/5*d**5 - 5/2*d**4. Find p such that w(p) = 0.
-2, -1, 14
Let i(k) be the third derivative of k**7/2100 - 8*k**6/135 - 3*k**5/25 + 98*k**3/3 + 85*k**2. Let l(f) be the first derivative of i(f). What is s in l(s) = 0?
-2/3, 0, 54
Factor -41/4*x + 20 + 1/8*x**2.
(x - 80)*(x - 2)/8
Let u = -12029/2 - -6015. Let t(d) be the third derivative of 0*d - 10*d**2 - u*d**4 + 0 + 4/3*d**3 + 1/15*d**5. Let t(r) = 0. Calculate r.
1, 2
Let v(q) be the first derivative of q**3/5 - 963*q**2/10 + 192*q + 2280. Suppose v(f) = 0. What is f?
1, 320
Suppose -101*d + 42 = -98*d + 2*x, 0 = -5*d + 3*x - 44. Determine b so that -6/5*b + 1 + 1/5*b**d = 0.
1, 5
Let s(h) be the third derivative of -h**6/300 + 251*h**5/150 - 15367*h**4/60 - 16129*h**3/5 - 158*h**2. Factor s(y).
-2*(y - 127)**2*(y + 3)/5
Let q(z) = -5*z**3 + 25*z**2 - 1706*z + 8532. Let m be q(5). Factor -4 + 5/4*i**m + 1/2*i.
(i + 2)*(5*i - 8)/4
Let u be 19/57*(85/(-400) - (-2)/5). Let i(s) be the third derivative of -9*s**2 + 0*s - 1/280*s**7 + 1/80*s**6 - u*s**4 + 0 + 0*s**3 + 1/80*s**5. Factor i(a).
-3*a*(a - 2)*(a - 1)*(a + 1)/4
Let h(z) be the first derivative of 0*z - 181 - 2*z**2 - 2/9*z**3. Factor h(j).
-2*j*(j + 6)/3
Let u(m) be the first derivative of 32/21*m**3 - 46 - 2*m**2 + 0*m - 1/7*m**4. Factor u(h).
-4*h*(h - 7)*(h - 1)/7
Suppose 16*s - 63 = 4*s + 9. Let g(h) be the first derivative of 4 + 3/2*h**2 + h**3 - s*h. Factor g(i).
3*(i - 1)*(i + 2)
Let f(b) be the first derivative of -4/3*b**3 + 0*b - 3/8*b**4 + 107 - 4/3*b**2 - 1/30*b**5. Factor f(j).
-j*(j + 1)*(j + 4)**2/6
Let w(k) = -k**3 - 9*k**2 + 15*k - 25. Let m be w(-12). Let 426 - 235 - m - 2*b**2 - 38*b = 0. What is b?
-18, -1
Let p(g) be the first derivative of g**4/21 - 8*g**2/7 - 70*g - 158. Let w(x) be the first derivative of p(x). Factor w(u).
4*(u - 2)*(u + 2)/7
Let s be 8/(-14) - (-7 + (-595)/98). Let p(d) = 21*d**2 + 13*d + 12. Let w be p(-1). Find h, given that -s*h**2 + 5/2*h**3 + w*h - 10 = 0.
1, 2
Let m = 331727/5 + -66343. Factor 0 + 2/5*a**3 - m*a - 2/5*a**2.
2*a*(a - 3)*(a + 2)/5
Suppose -m + 19 = -4*u, 6*u + 8 = 4*u. Suppose 5*j + v = 14, 5 - 27 = -m*j - 4*v. Factor -3/7 - 3/7*s**j + 6/7*s.
-3*(s - 1)**2/7
Suppose 1/4*q**4 + 9*q + 36 - 3/4*q**3 - 7*q**2 = 0. What is q?
-4, -2, 3, 6
Let p(u) = 7*u**3 - 82*u**2 + 6*u - 6. Let m(s) = -5*s**3 + 85*s**2 - 5*s + 5. Let o(h) = 6*m(h) + 5*p(h). Suppose o(n) = 0. What is n?
-20, 0
Let t be (-1)/2 + (-28)/(-8) + -2. Solve -k**2 - t + 4 - 11 - 9*k = 0.
-8, -1
Factor 0 + 3/4*v**2 - 93*v.
3*v*(v - 124)/4
Find c such that 937/3*c**2 + 177*c**3 + 89/3*c**4 - 2/3*c**5 + 647/3*c + 50 = 0.
-3, -1, -1/2, 50
Suppose -5*s = -3*s + 3*r - 33, r = -4*s + 91. Suppose 23 - 17 - 4*a**3 + 26 + s*a + 48*a**2 - 60*a**2 = 0. What is a?
-4, -1, 2
Let u(b) be the first derivative of -16*b**2 + 2/5*b**5 + 40/3*b**3 + 121 + 0*b - 4*b**4. Suppose u(z) = 0. What is z?
0, 2, 4
Let x be 19 + (-3 - -8) + (-6)/2. Let i be (80/(-28))/((-6)/x). Factor -4*g**4 - i*g**3 - g**4 - 147*g + 147*g.
-5*g**3*(g + 2)
Let r(c) = 10*c**2 + 40*c - 48. Let o be r(-5). Solve -112 - 4/7*h**o + 16*h = 0 for h.
14
Factor 1 - 1 - 22847*n**3 - 80*n**2 + 22851*n**3 + 336*n.
4*n*(n - 14)*(n - 6)
Let o(m) be the second derivative of m**6/6 - 3*m**5/2 - 5*m**4/12 + 25*m**3 + 4638*m. Suppose o(f) = 0. Calculate f.
-2, 0, 3, 5
Let c(t) be the third derivative of -2/15*t**5 + 27*t**2 + 1/60*t**6 - t - 2/3*t**3 + 5/12*t**4 + 0. Factor c(a).
2*(a - 2)*(a - 1)**2
Suppose 0 = 6*q - 21 + 9. Factor -5555*m**q + 12*m + 25 + 5551*m**2 + 47.
-4*(m - 6)*(m + 3)
Factor 0 + 2/5*y**3 + 24/5*y + 14/5*y**2.
2*y*(y + 3)*(y + 4)/5
Factor -792/13 + 8*v**2 + 686/13*v + 2/13*v**3.
2*(v - 1)*(v + 9)*(v + 44)/13
Let m(d) be the second derivative of d**4/42 + 2*d**3/3 - 351*d**2/7 - 901*d + 1. Factor m(c).
2*(c - 13)*(c + 27)/7
Let q be (15/6)/(((-12)/64)/((-12)/80)). Find r such that r**3 + 1 - 1/2*r**5 - q*r**2 - 1/2*r + r**4 = 0.
-1, 1, 2
Suppose -1367*m + 2778 = 44. Solve -2/3*q**2 - 4/3 + m*q = 0 for q.
1, 2
Let z(w) = 1 - 97*w**2 - 2*w + w**3 - 2 + 104*w**2. Let l be z(-7). Suppose -3*u**5 - 9*u**3 + l*u**3 - 2*u + 4*u**5 - 3*u**5 = 0. What is u?
-1, 0, 1
Let j be (-3)/5*(-36 - 2356/(-93)). What is a in j*a**4 - 4/3*a - 16/15*a**3 - 2/15 - 58/15*a**2 = 0?
-1/3, -1/4, 1
Let z(a) be the second derivative of -a**4/12 + 83*a**3/6 + 27*a. Factor z(h).
-h*(h - 83)
Let k(d) be the first derivative of 21/2*d**2 - 22*d - 129 + 1/3*d**3. What is w in k(w) = 0?
-22, 1
Let d(m) be the first derivative of -144/7*m + 10/7*m**4 + 6 - 52/21*m**3 - 4/35*m**5 - 120/7*m**2. Suppose d(k) = 0. What is k?
-1, 6
Let k(v) be the second derivative of v**7/7560 + v**6/240 - 13*v**4/12 + 7*v**2/2 + 278*v. Let h(a) be the third derivative of k(a). Factor h(i).
i*(i + 9)/3
Let s = -26329/105 + 1254/5. Let g(m) be the second derivative of -4/7*m**2 - s*m**4 + 0 - 9*m - 2/7*m**3. Factor g(t).
-4*(t + 1)*(t + 2)/7
Let b(f) be the second derivative of -f**4/96 + 59*f**3/16 + 161*f**2/2 - 215*f - 13. Factor b(y).
-(y - 184)*(y + 7)/8
Let c(i) be the third derivative of -i**5/20 - 39*i**4/2 - 3042*i**3 - 1705*i**2. Factor c(a).
-3*(a + 78)**2
Let c(o) be the third derivative of o**5/12 - 45*o**4/2 + 530*o**3/3 + 143*o**2. Let c(q) = 0. What is q?
2, 106
Let a(y) be the first derivative of 165*y**3/2 - 3*y**2/4 - y - 1900. Factor a(s).
(15*s - 1)*(33*s + 2)/2
Let q(d) be the second derivative of -d**6/50 + 6*d**5/25 + 151*d**4/10 - 312*d**3/5 + 189*d**2/2 + 6158*d. Find x such that q(x) = 0.
-15, 1, 21
Let g be 852 + (2 + 4 - 5). Factor 423 +