o. Factor n(m).
-2*(m + 1)**3*(m + 2)
Let x(n) be the third derivative of n**8/120960 + 13*n**7/30240 + 73*n**5/60 - 2*n**2 + 7*n. Let p(f) be the third derivative of x(f). Factor p(q).
q*(q + 13)/6
Let k(z) be the third derivative of -1/60*z**5 + 0*z + 1/120*z**7 - 1/1344*z**8 + 1/6*z**4 - 1/40*z**6 - 196*z**2 + 0*z**3 + 0. What is w in k(w) = 0?
-1, 0, 2, 4
Let m(n) be the first derivative of -1/6*n**3 - n + 82 - 3/4*n**2. Factor m(o).
-(o + 1)*(o + 2)/2
Let r(x) be the second derivative of -x**8/10080 - x**7/945 - x**6/216 - x**5/90 + 7*x**4/3 + 72*x. Let y(h) be the third derivative of r(h). Factor y(t).
-2*(t + 1)**2*(t + 2)/3
Let n(w) be the second derivative of w**4/60 - 41*w**3/15 + 16*w**2 - 2*w + 1079. Let n(h) = 0. Calculate h.
2, 80
Let i(w) = 2*w - 15. Let v be i(8). Let s be (4 + -6)*(v + -2). Determine o so that -2*o - 4718*o**2 - 12*o**3 - 2*o**5 + 4726*o**s + 3 + 8*o**4 - 3 = 0.
0, 1
Let u(h) = h**4 + 2*h**2 + 2*h - 1. Let q(k) = 7*k**4 + 22*k**2 + 24*k - 5. Let w(b) = -q(b) + 8*u(b). Factor w(v).
(v - 3)*(v + 1)**3
Let o be (-190)/(-56) - 528/462. Let q(r) be the first derivative of 0*r + 1/7*r**3 - o*r**4 + 6 + 3/7*r**2. Factor q(u).
-3*u*(3*u - 1)*(7*u + 2)/7
Let v(m) = -m**2 - m - 3. Let t(z) = -2*z**3 + 14*z**2 - 4*z + 22. Let l be ((-7)/(-28)*-18)/((-6)/(-16)). Let s(h) = l*v(h) - 2*t(h). Factor s(j).
4*(j - 2)*(j - 1)**2
Let j be ((-4)/10)/(-2) - 10776/30. Let x = j - -363. Factor 4/9*p**3 + 0 + 0*p**x - 2/9*p - 2/9*p**5 + 0*p**2.
-2*p*(p - 1)**2*(p + 1)**2/9
Let p(i) be the third derivative of i**7/280 - 1333*i**6/160 + 29637*i**5/4 - 5507487*i**4/2 + 10941048*i**3 - 2786*i**2 + i - 2. Factor p(l).
3*(l - 444)**3*(l - 1)/4
Let a(r) = r**2 - 4*r - 3. Let x be a(7). Suppose 4*l - 88 = -x*l. Solve 4/3*s**l - 32/9*s**2 + 4 - 4/3*s**3 - 2/9*s**5 + 10/3*s = 0 for s.
-1, 2, 3
Suppose -2*t - 5 = 3*o - 3, 0 = -4*o + t + 12. Suppose -78*x + 188*x = -215*x. What is l in -7/6*l**o + 5/6*l**3 - 1/6*l**4 + 1/2*l + x = 0?
0, 1, 3
Let k(c) be the third derivative of 3*c**7/280 + 7*c**6/60 + 17*c**5/40 + 3*c**4/4 - c**3/6 - 50*c**2. Let f(d) be the first derivative of k(d). Factor f(g).
3*(g + 1)*(g + 3)*(3*g + 2)
Determine s so that 2/13*s**2 + 68/13*s + 480/13 = 0.
-24, -10
Let b(x) = 14*x**2 - 491*x + 80. Let s(z) = -15*z**2 + 245*z - 40. Let f(j) = 5*b(j) + 9*s(j). Find o, given that f(o) = 0.
-4, 2/13
Let k(m) be the first derivative of m**3/3 + m**2/2 - m + 66. Let u(d) = -6*d + 2. Let t(a) = 2*k(a) + u(a). Suppose t(s) = 0. Calculate s.
0, 2
Let a(c) = 69*c**2 - 4008*c - 4017. Let u(g) = 9*g**2 - 573*g - 574. Let x(d) = -2*a(d) + 15*u(d). What is i in x(i) = 0?
-192, -1
Let z(u) be the second derivative of 1/30*u**6 + 2/5*u**5 - 3/4*u**4 - 12*u + 0*u**3 - 6 + 0*u**2. Factor z(v).
v**2*(v - 1)*(v + 9)
Suppose -8*w + 54 = -6*w. Suppose -4*y + 11 = -2*v - w, 0 = -y + v + 10. Factor -9*o**2 - 12*o**4 + y*o**4 + 3*o + o**3 + 8*o**3.
-3*o*(o - 1)**3
Let l = 159250/9 - 17694. What is q in 70/9*q + l + 32/9*q**3 + 98/9*q**2 = 0?
-2, -1, -1/16
Let n(j) be the second derivative of 0 + 0*j**3 + 1/60*j**4 + 70*j - 2/5*j**2. Solve n(d) = 0.
-2, 2
Let v = -1272 + 6361/5. Let b(z) be the first derivative of 2/5*z - 16/25*z**5 + 7/30*z**6 + 14/15*z**3 + v*z**4 - 11/10*z**2 + 7. Factor b(k).
(k - 1)**3*(k + 1)*(7*k - 2)/5
Let p = 9 - 4. Solve 12*l**5 - 67*l**4 + 132*l**4 + 15*l**3 + 8*l**p = 0 for l.
-3, -1/4, 0
Let y(s) be the second derivative of 1/3*s**3 + 1/6*s**4 - 86*s + 0*s**2 + 0. Suppose y(z) = 0. Calculate z.
-1, 0
Let a be (-2 - -1)*(0/61)/(3 + 0). Let i(v) be the third derivative of a + 11/30*v**6 - 4/3*v**5 + 0*v + 4/3*v**3 + 7/6*v**4 - 20*v**2. What is y in i(y) = 0?
-2/11, 1
Let o = -209219 + 1882973/9. Determine q, given that -4/9*q + 10/3 - o*q**2 = 0.
-5, 3
Let q = 60343/2 - 30171. Factor 0 - q*i**2 - 1/2*i**4 + i**3 + 0*i.
-i**2*(i - 1)**2/2
Let h be 30/56 + 222/(-888). Let u = -1858/7 + 266. Factor -2/7*l**3 - u*l**2 + h*l + 4/7.
-2*(l - 1)*(l + 1)*(l + 2)/7
Factor 93 + 39*h + 187*h + 2*h + 15 + 23*h**2 - 2*h**3.
-(h - 18)*(h + 6)*(2*h + 1)
Let s = -24240 - -24243. Let k(m) be the third derivative of 1/210*m**5 + 0*m**4 + 0*m**s - 35*m**2 + 1/735*m**7 + 0*m + 0 - 1/210*m**6. Factor k(t).
2*t**2*(t - 1)**2/7
Let v = 285 - 283. Find k such that 11*k**4 + 3042*k**v + 68149 + 50449 - 32915 - 156*k**3 - 8*k**4 - 26364*k = 0.
13
Let i(f) be the first derivative of -f**3 + 174*f**2 + 1440*f + 343. Factor i(h).
-3*(h - 120)*(h + 4)
Let y be 45/18*(-16)/(-20). Factor -13 + 22*o**2 - 3*o**y + 4*o + 3*o**3 + 2 - 1.
(o + 1)*(o + 6)*(3*o - 2)
Suppose 376 - 425 = -3*p - 5*y, 5*p - 23 = -y. Determine t, given that 0 + 0*t - 13/5*t**p + 1/5*t**5 + t**4 + 7/5*t**2 = 0.
-7, 0, 1
Suppose -8*v - 6 = -10*v. Suppose -v*p - 32 = -5*l + p, l + 2*p = -2. Factor 2*s**3 - 7*s**2 - l*s**3 + 13*s**2.
-2*s**2*(s - 3)
Let l(h) be the second derivative of -h**4/36 - 155*h**3/9 + 104*h**2 + 5351*h. Factor l(t).
-(t - 2)*(t + 312)/3
Let s = 359 - 357. Let o(n) be the first derivative of -6*n**4 + 16*n - 4 - 24*n**s + 4/5*n**5 + 52/3*n**3. Factor o(l).
4*(l - 2)**2*(l - 1)**2
Let b be ((-2)/10)/((-1557)/(-865)) + 3*(-76)/(-108). Determine z, given that 42*z - b + 43/2*z**2 = 0.
-2, 2/43
Let w(h) = 31*h**3 + 342*h**2 + 3*h - 88. Let o be w(-11). Factor o + 0*d**3 - 32/9*d**2 - 2/9*d**5 + 8/9*d**4 + 32/9*d.
-2*d*(d - 2)**3*(d + 2)/9
Suppose 0 = -198*s + 192*s - 414. Let t be 12/(-10) + s/(-45). Let 2/3 - t*c**2 - 1/3*c = 0. What is c?
-2, 1
Let g(n) be the second derivative of n**7/280 + n**6/60 + n**5/40 + 8*n**3/3 + 39*n. Let d(w) be the second derivative of g(w). Let d(o) = 0. What is o?
-1, 0
Let n(u) be the first derivative of -u**5/10 + 19*u**4/8 + 560*u**3/3 + 2303*u**2 + 5055. Factor n(g).
-g*(g - 47)*(g + 14)**2/2
Let l(z) be the first derivative of -2*z**5/45 - 409*z**4/18 - 1630*z**3/27 - 407*z**2/9 - 4696. Factor l(d).
-2*d*(d + 1)**2*(d + 407)/9
Let s(k) be the third derivative of k**5/300 + 35*k**4/24 - 2*k**2 - 546*k. Suppose s(c) = 0. What is c?
-175, 0
Suppose 3*o + s + 5 - 17 = 4*s, -10*s = 10. Factor -1/4*q**o - 1/4*q**2 + 0*q + 0.
-q**2*(q + 1)/4
Let y be (-8)/10*(21 - 6). Let z be y*3/(-6) + (-12)/(-6). Find u such that 11*u**4 + 6*u**4 - 4*u**3 - z*u**2 + 2*u + 2*u**5 + 4 - 13*u**4 = 0.
-2, -1, 1
Let s(t) be the third derivative of t**8/672 + 23*t**7/420 - 9*t**6/80 - 67*t**5/120 + 59*t**4/24 - 4*t**3 + 660*t**2 - t + 1. Find r, given that s(r) = 0.
-24, -2, 1
Let p(j) = 5*j**2 + 13*j - 3. Let r be p(-4). Factor 16*y - 11*y + 4*y + 22*y**2 - r*y**2.
-3*y*(y - 3)
Suppose 239*g + 670 - 1313 + 6*g**2 + 1018*g - 233 + 492*g = 0. What is g?
-292, 1/2
Let x = -127 - -129. Factor -2*z**x - 29 + z**3 + z**4 - 2*z**3 + 29.
z**2*(z - 2)*(z + 1)
Suppose 37*u + 247*u + 66*u - 5250 = 0. Let k(o) be the third derivative of -u*o**2 - 1/2*o**3 + 1/160*o**6 + 0 + 0*o + 1/80*o**5 - 1/8*o**4. Factor k(a).
3*(a - 2)*(a + 1)*(a + 2)/4
Suppose 5*j + 12 - 2 = 0. Let c(v) = -11*v**2 + 22*v - 8. Let u(s) = -s**2 + s - 2. Let k(g) = j*u(g) + c(g). Factor k(b).
-(b - 2)*(9*b - 2)
Let a = -556/17 - -21718/663. Let j(t) be the second derivative of 0*t**3 + 0 - 4/65*t**5 - a*t**4 + 0*t**2 - 1/273*t**7 - 5*t - 1/39*t**6. Factor j(s).
-2*s**2*(s + 1)*(s + 2)**2/13
Let d(r) be the first derivative of -r**5/210 - r**4/42 + r**3/7 - 8*r**2 - r + 56. Let l(q) be the second derivative of d(q). What is z in l(z) = 0?
-3, 1
Solve 1326/5 + 63/5*y - 3/5*y**2 = 0 for y.
-13, 34
Suppose 378/5*i**3 - 6/5*i**4 + 3726/5*i - 2418/5*i**2 - 336 = 0. Calculate i.
1, 5, 56
Let z be 50/20 - 1/2. Let -5*f**z - 16*f + 25*f**3 + 66*f**4 - 9*f - 61*f**4 = 0. What is f?
-5, -1, 0, 1
Let w = 15/44 - 1/11. Let s be (11 + (-187)/(-33))/2*33/110. Suppose w*j**2 + 0 - s*j = 0. What is j?
0, 10
Let g(h) = -6*h - 5. Suppose 14*n + 3 = 11*n. Let q(u) = -u**2 + 2*u + 1. Let x(m) = n*q(m) - g(m). Suppose x(o) = 0. What is o?
-2
Let r(m) be the second derivative of -m**7/21 + 2*m**6/7 + 41*m**5/70 - 6*m**4 + 236*m**3/21 - 48*m**2/7 - 1028*m. Suppose r(f) = 0. Calculate f.
-3, 2/7, 1, 2, 4
Let l(q) be the second derivative of 2*q**4/3 - 297*q**3 - 223*q**2 - 2*q + 347. Determine j so that l(j) = 0.
-1/4, 223
Let v(f) = -f**3 - 32*f**2 + 31*f - 56. Let t = 368 + -401. Let r be v(t). Factor r*x**2 - 105/4