 1)
Let p(i) be the second derivative of -25*i - 1/66*i**4 - 1/110*i**5 + 0 + 4/11*i**2 + 4/33*i**3. Factor p(g).
-2*(g - 2)*(g + 1)*(g + 2)/11
Factor -1/5*l + 1/10*l**5 + 0 - 1/2*l**2 + 1/10*l**4 - 3/10*l**3.
l*(l - 2)*(l + 1)**3/10
Let f(p) be the third derivative of -p**6/120 + p**5/3 - 17*p**4/8 + 833*p**2. Determine i, given that f(i) = 0.
0, 3, 17
Let g(o) be the first derivative of -1/5*o**3 + 9 - 12/5*o + 3/2*o**2. Factor g(r).
-3*(r - 4)*(r - 1)/5
Factor -4/19 - 10/19*c**2 - 14/19*c.
-2*(c + 1)*(5*c + 2)/19
Suppose o - 2*o + 5 = 0. Let t(b) = -6*b**2 - 54*b - 96. Let r(y) = 11*y**2 + 107*y + 191. Let a(u) = o*t(u) + 2*r(u). Factor a(z).
-2*(2*z + 7)**2
Let g(o) = -4*o + 27. Let y be g(6). Let f(p) be the first derivative of -4*p**2 - 1 - 8*p - 2/3*p**y. Factor f(n).
-2*(n + 2)**2
Let o(v) be the first derivative of 3*v**4/2 - 2*v**3/3 - 2*v**2 + 300. Suppose o(y) = 0. What is y?
-2/3, 0, 1
Suppose 10*q**2 - 3*q**2 + 152*q + 43*q - 12*q**2 - 190 = 0. What is q?
1, 38
Let o(m) = m**2. Let c(s) = -2 + 6*s + 24*s**2 + 0 + 6. Let v(g) = g**2 + 9*g + 16. Let w be v(-7). Let k(f) = w*c(f) - 44*o(f). Factor k(x).
4*(x + 1)*(x + 2)
Let r(b) be the second derivative of -b**4/102 + b**3/17 - 2*b**2/17 - 132*b. Suppose r(u) = 0. Calculate u.
1, 2
Let r(n) be the third derivative of n**5/210 + 5*n**4/14 + 75*n**3/7 + 7*n**2 - 1. Factor r(v).
2*(v + 15)**2/7
Let z be (8/18)/((-1)/(-9)). Suppose 5*j - w = -0*j - 4, w - z = -2*j. Suppose -2/5*a**3 + j + 2/5*a**5 + 2/5*a**2 - 2/5*a**4 + 0*a = 0. What is a?
-1, 0, 1
Let -2/9*p + 0 - 2/3*p**2 - 2/3*p**3 - 2/9*p**4 = 0. Calculate p.
-1, 0
Let f be -9*(9/(-90) - 14/60). Factor -2/3*i**2 - 2/3*i**f + 1/3*i + 1/3*i**4 + 1/3 + 1/3*i**5.
(i - 1)**2*(i + 1)**3/3
Find q such that -8 - 32/7*q**2 - 12/7*q**3 + 100/7*q = 0.
-14/3, 1
Let k(f) be the third derivative of 3*f**2 + 0*f**4 + 0*f**3 + 0*f**5 - 1/120*f**6 + 0 + 0*f + 5/1344*f**8 + 1/105*f**7. Let k(c) = 0. What is c?
-2, 0, 2/5
Let b(l) be the first derivative of -l**4/2 - 4*l**3/3 + l**2 + 4*l + 209. Let b(c) = 0. What is c?
-2, -1, 1
Let i(c) be the first derivative of -7*c**4/24 - 13*c**3/9 - 13*c**2/12 + c - 84. Factor i(j).
-(j + 1)*(j + 3)*(7*j - 2)/6
Suppose -28 = -4*x + 108. Let j = x - 65/2. Factor -3*z - j*z**2 + 0.
-3*z*(z + 2)/2
Determine z, given that 46*z**4 + 228*z - 449*z**3 + 1322*z**3 - 2*z**5 + 240*z**2 - 1389*z**2 + 180 - 157*z**4 - 19*z**5 = 0.
-10, -2/7, 1, 3
Let n = 10059 - 10056. Solve -58/3*t - 34*t**n - 134/3*t**2 - 6*t**4 - 8/3 = 0.
-4, -1, -1/3
Let p = 188 - 209. Let k(n) = 2*n + 44. Let f be k(p). Solve 4/15*h**3 - 2/15*h - 2/15*h**5 + 4/15*h**4 + 4/15 - 8/15*h**f = 0 for h.
-1, 1, 2
Let o(f) be the first derivative of -f**4/14 + 64*f**3/7 - 2304*f**2/7 - 115. Let o(q) = 0. What is q?
0, 48
Let n be 7/1*28/98. Solve -300*l**n - 415*l**4 - 155*l**4 - 24*l + 96*l**2 - 570*l**3 + 45*l**4 = 0 for l.
-2/5, -2/7, 0
Let -5/4*d**3 + 0 + 5/4*d**4 - 15/4*d - 25/4*d**2 = 0. What is d?
-1, 0, 3
Let x(r) be the first derivative of -5*r**4/4 + 130*r**3/3 - 120*r**2 - 44. Determine z, given that x(z) = 0.
0, 2, 24
Let b(k) = 4*k - 5. Let y be b(-1). Let w be (-2)/y + 325/117. Let -24/7*t**2 - 2*t**w + 8/7*t + 0 = 0. Calculate t.
-2, 0, 2/7
Suppose 15*s - 11*s - 52 = 0. Factor -s*h**3 - 4*h**3 + 21*h**3.
4*h**3
Suppose -19 = -7*i - 5. What is c in 9*c + 9 + 12*c**3 + 26*c**2 + 0*c + i*c**4 + 15*c - 1 = 0?
-2, -1
Let j(c) be the second derivative of c**5/8 + 185*c**4/12 + 725*c**3/12 + 90*c**2 - 291*c. Solve j(w) = 0.
-72, -1
Find z such that 3/4*z**3 - 15/2*z**2 + 54 + 9*z = 0.
-2, 6
Let s(j) be the third derivative of 0*j**5 + 0*j + 3*j**2 + 0 - 5/6*j**3 + 1/360*j**6 - 1/24*j**4. Let y(q) be the first derivative of s(q). Factor y(l).
(l - 1)*(l + 1)
Suppose -567 + 489 = -2*v. Suppose 21*c + 72 = v*c. Factor 0*m**2 + 0*m + 2/11*m**c + 0 - 2/11*m**3.
2*m**3*(m - 1)/11
Suppose -3*o - 36 = -3*d + 2*o, -3*d - 3*o = 12. Suppose -4/11*b**d + 6/11 + 8/11*b**3 - 8/11*b - 2/11*b**4 = 0. What is b?
-1, 1, 3
Let v(k) = k**4 + 3*k**3 + k**2 - k - 1. Let x(j) = 10*j**4 - 11*j**3 + 49*j**2 - 29*j - 5. Let m(n) = 10*v(n) - 2*x(n). Factor m(d).
-2*d*(d - 2)**2*(5*d - 6)
Determine n so that -n**2 - 13 - 13 - 2*n + 26 - 11*n = 0.
-13, 0
Suppose 62*x - 27 + 2 - 161 = 0. Find b such that -2/3*b**x + 1/2*b**2 + 2/3*b + 1/6*b**4 - 2/3 = 0.
-1, 1, 2
Let r(j) be the second derivative of -j**5/80 - j**4/32 + 3*j**3/4 + 14*j**2 + 14*j. Let s(k) be the first derivative of r(k). Factor s(g).
-3*(g - 2)*(g + 3)/4
Let x(v) be the third derivative of -v**8/3024 - v**7/1890 + v**6/540 + v**2 + 44*v. Find n, given that x(n) = 0.
-2, 0, 1
Let s be 1 + (4 - 3) + (0 - 0). Factor 0 - s*r + 12/5*r**2 - 2/5*r**3.
-2*r*(r - 5)*(r - 1)/5
Let x(g) be the second derivative of -g**6/90 - g**5/20 - g**4/12 - g**3/18 + 287*g. Factor x(z).
-z*(z + 1)**3/3
Factor -55*j**3 + 3 - 1885*j**2 - 3 + 1675*j**2.
-5*j**2*(11*j + 42)
Let v(t) be the third derivative of 27*t**8/112 - 27*t**7/35 - 63*t**6/8 - 203*t**5/10 - 53*t**4/2 - 20*t**3 - 4*t**2 + 3. Factor v(q).
3*(q - 5)*(q + 1)*(3*q + 2)**3
Let l(g) be the third derivative of -1/1320*g**6 + 0 - 1/3696*g**8 + 0*g**4 + 0*g + 0*g**3 + 0*g**5 + 1/1155*g**7 + 14*g**2. Factor l(c).
-c**3*(c - 1)**2/11
Let c(l) be the third derivative of -l**5/30 + 3*l**4/4 - 14*l**3/3 + 2*l**2 + 1. Factor c(a).
-2*(a - 7)*(a - 2)
Let o be ((-2)/42)/((-240)/3360). Solve 0*j**2 + 4/3*j**3 + o*j**4 - 2/3 - 4/3*j = 0 for j.
-1, 1
Let s = -10028/11 + 912. Let z(u) be the first derivative of -s*u**2 - 32/33*u**3 - 6 + 10/11*u**5 - 5/22*u**4 + 0*u. Find t such that z(t) = 0.
-2/5, 0, 1
Let k(i) = -2*i**3 + 34*i**2 + 62*i + 35. Let d(t) = -5*t**3 + 72*t**2 + 125*t + 69. Let j(s) = 3*d(s) - 7*k(s). Let j(c) = 0. Calculate c.
-19, -2, -1
Let c(l) be the first derivative of 3*l**4/4 - 106*l**3 - 3*l**2/2 + 318*l + 838. Solve c(v) = 0 for v.
-1, 1, 106
Suppose 157 - 175 = -9*x. Let u(n) be the first derivative of -9 + 1/18*n**4 - 4/27*n**3 - 1/9*n**x + 4/9*n. Factor u(g).
2*(g - 2)*(g - 1)*(g + 1)/9
Let u(x) = 0*x - 3*x + 1 - 5 + 4*x. Let n be u(6). Factor 4*m**4 + 2 - m - m**3 - 3*m**2 - 3*m**4 + n*m.
(m - 2)*(m - 1)*(m + 1)**2
Let r(v) be the third derivative of -v**6/480 + 27*v**5/80 - 729*v**4/32 + 6561*v**3/8 + 48*v**2. Factor r(k).
-(k - 27)**3/4
Let c be (-4)/116 + (-2080)/(-6496). Suppose 0 - c*l + 1/7*l**2 = 0. What is l?
0, 2
Suppose -2*d + 1639 = 9*d. Let d*i - 3*i**3 + 8*i**3 - 164*i - 10*i**2 = 0. Calculate i.
-1, 0, 3
Let a(d) = -d - 7. Let i be a(-12). Suppose i*s = 4*r + 31, s - 5*r - 29 = -6. Factor -4 - 6*l**2 + l**2 + l**s + 6*l + 2*l.
(l - 2)**2*(l - 1)
Let x = 2/1207 - -1127/48280. Let o(i) be the third derivative of -1/72*i**4 + 0*i**3 + 0*i - 1/180*i**6 - x*i**5 + 2*i**2 + 0. Suppose o(r) = 0. What is r?
-2, -1/4, 0
Let f = -20 + 12. Let c be ((-318)/(-42) + f)/(2/(-14)). Determine h so that -6/7*h**4 + 6/7*h**c + 0 + 0*h + 2/7*h**5 - 2/7*h**2 = 0.
0, 1
Let f(j) be the third derivative of j**5/54 + 13*j**4/108 - 395*j**2. Factor f(q).
2*q*(5*q + 13)/9
Let q be 0 + (0/(-2))/(-4). Let i(x) be the second derivative of q - 1/7*x**7 - 1/4*x**3 + 9/40*x**5 - 1/4*x**4 + x + 0*x**2 + 1/5*x**6. Factor i(w).
-3*w*(w - 1)**2*(2*w + 1)**2/2
Let x(g) be the first derivative of -4*g**5/25 - 4*g**4/5 + 4*g**3/15 + 8*g**2/5 + 40. Determine v, given that x(v) = 0.
-4, -1, 0, 1
Let d(k) = -k**2 - 13*k - 6. Let a(l) = -2*l**2 - 25*l - 14. Let z(m) = -4*a(m) + 7*d(m). What is x in z(x) = 0?
-7, -2
Let h(r) = 87*r**2 - 177*r + 48. Let w(n) = -22*n**2 + 45*n - 12. Let m(l) = -5*h(l) - 21*w(l). Determine a so that m(a) = 0.
2/9, 2
Determine r so that -1/11*r**2 + 0*r**3 + 0*r + 0 + 1/11*r**4 = 0.
-1, 0, 1
Let a(k) be the first derivative of -18/5*k**5 + 0*k - 75/4*k**2 - 69/4*k**4 + 3 - 1/4*k**6 - 30*k**3. Factor a(v).
-3*v*(v + 1)**2*(v + 5)**2/2
Let l(b) = b**2 - 5. Let k be l(-3). Suppose 3*y + 3 = -3*z, k = -4*y - 2*z + 6. Factor 1 - 4*a**y - 16*a - 17 + 0.
-4*(a + 2)**2
Let r be ((-2)/(-6))/((-11)/(-132)). Factor 8 - 4*b + b**2 - 2 + 2*b**r - 4*b**3 + 8*b - 9*b**2.
2*(b - 3)*(b - 1)*(b + 1)**2
Let h be ((-16)/(-12))/(86/(-3)). Let x = h - -92/129. Let 2/3*y - x*y**3 - 2/3 + 2/3*y**2 = 0. What is y?
-1, 1
Let z(v) = -53*v**4 - 1046*v**3 - 805*v**2 - 154*v - 3. Let b(f