7. Let r(c) = 106*c + 222. Let o(k) = -2*p(k) - 5*r(k). Factor o(l).
2*(l - 54)*(l + 2)
Let k(s) = -8*s**3 + 68*s**2 - 169*s - 242. Let a(p) = -7*p**3 + 67*p**2 - 171*p - 243. Let i(f) = 3*a(f) - 2*k(f). Factor i(q).
-5*(q - 7)**2*(q + 1)
Suppose -19*v - p - 8 = -21*v, p - 4 = -4*v. Factor -891 + v*k**3 + 585*k + 2*k**3 - k**3 - 153*k**2 + 1440*k - 984.
3*(k - 25)**2*(k - 1)
Determine s, given that 3*s**3 - 11*s**2 - 21*s**2 - 51*s**2 - 13*s**2 = 0.
0, 32
Suppose 45*f + 27*f = -73009 + 73297. Determine d, given that -104/3*d**3 + 188*d**2 + 1456/3*d + 784/3 + 4/3*d**f = 0.
-1, 14
Let l = -870 + 873. Let s(h) be the third derivative of 0*h - 1/4*h**4 + 0 + 0*h**l - 1/40*h**6 + 3/20*h**5 + 8*h**2. Determine a, given that s(a) = 0.
0, 1, 2
Let i(z) be the first derivative of 3*z**4/4 + 28*z**3 + 663*z**2/2 + 1014*z - 531. Let i(r) = 0. What is r?
-13, -2
Suppose 5*s - 4*n = 10, 6*s = 11*s - 2*n - 10. Let o(q) be the first derivative of 24/7*q**s - 16/7*q - 4/7*q**3 + 5 - 5/7*q**4. Factor o(r).
-4*(r - 1)*(r + 2)*(5*r - 2)/7
Let g = 3369025/1185391 + -1/62389. Suppose 336/19*i - g*i**2 + 392/19 + 2/19*i**3 = 0. What is i?
-1, 14
Let s(o) = 80*o**3 + 1484*o**2 + 2075*o + 759. Let k(h) = 2*h**2 - 5*h - 3. Let w(a) = -2*k(a) + s(a). Suppose w(y) = 0. What is y?
-17, -3/4
Let o(b) be the third derivative of -b**8/5040 + b**7/1260 + b**6/90 + 3*b**5/20 - b**4/4 - b**2 + 29*b. Let h(m) be the third derivative of o(m). Factor h(k).
-4*(k - 2)*(k + 1)
Let a(h) be the third derivative of -h**6/150 - 8*h**5/75 + 61*h**4/30 - 104*h**3/15 - 7*h**2 - 25*h. Suppose a(j) = 0. What is j?
-13, 1, 4
Let b be ((-3)/102)/(788/(-53584)). Factor 1296 - 36*z + 1/4*z**b.
(z - 72)**2/4
Let c(m) be the first derivative of -m**4/16 - m**3/3 + 29*m**2/8 - 6*m + 964. Factor c(b).
-(b - 3)*(b - 1)*(b + 8)/4
Let j(y) be the first derivative of 14*y**5/75 - 22*y**4/15 - 46*y**3/3 - 206*y**2/15 + 176*y/15 - 1001. Solve j(r) = 0 for r.
-4, -1, 2/7, 11
Let d = 1349950 + -1349948. What is x in 16 - 46/3*x - 2/3*x**d = 0?
-24, 1
Let i be 24/(-216) + (-1)/(-99)*29. Let g(l) be the first derivative of 10 - 1/11*l**4 + 0*l**3 + 2/11*l - 2/55*l**5 + i*l**2. Factor g(m).
-2*(m - 1)*(m + 1)**3/11
Let j(o) be the third derivative of o**5/150 - 833*o**4/60 + 832*o**3/15 - 7270*o**2. Factor j(y).
2*(y - 832)*(y - 1)/5
Let l = -20288/3 - -6862. Let j = l - 99. Factor -p**2 - p**3 + 0 - j*p - 1/3*p**4.
-p*(p + 1)**3/3
Let v(c) be the third derivative of -c**5/90 - 61*c**4/18 + 41*c**3/3 - 35*c**2 - 41. Find z such that v(z) = 0.
-123, 1
Suppose 9787*l + 20 = 9792*l. Let q(i) be the third derivative of 0*i + 1/30*i**5 - 8*i**2 + 4/3*i**3 - 1/3*i**l + 0. Factor q(b).
2*(b - 2)**2
Let y(u) be the second derivative of -u**4/120 + 13*u**3/60 + 99*u**2/10 - 2376*u. Find z such that y(z) = 0.
-9, 22
Let x(z) be the first derivative of -z**6/72 + z**5/8 - 5*z**4/12 + 25*z**3/3 + 47. Let c(y) be the third derivative of x(y). Factor c(v).
-5*(v - 2)*(v - 1)
Let s(y) be the second derivative of 2*y**4/21 + 1427*y**3/21 - 51*y**2 - 608*y. Factor s(k).
2*(k + 357)*(4*k - 1)/7
Suppose -121*d + 44*d = 86*d. Let a(v) be the third derivative of -10*v**2 - 2/21*v**4 + 1/21*v**5 + d*v**3 + 0*v + 0 - 1/210*v**6. Factor a(i).
-4*i*(i - 4)*(i - 1)/7
Let y = -90668/45 - -18148/9. Let n(f) be the first derivative of -y*f**5 - 41 + 5*f**2 - 2*f**4 + 4*f + 4/3*f**3 - 1/3*f**6. Factor n(w).
-2*(w - 1)*(w + 1)**3*(w + 2)
Let d(z) = 4*z**2 - 28*z + 26. Let l be d(6). Suppose -2*u + 3*j = -22, 5*u + 2*j = -2*j + 32. Factor 15*a + 2 + 187*a**2 + u - 10*a**3 - 202*a**l.
-5*(a - 1)*(a + 2)*(2*a + 1)
Suppose -s + 4 = 0, 0 = 5*u - 4*u + s - 354. Factor 0 - 21*j**4 - 3*j**5 - 24*j - 54*j**3 + 0 + 290*j**2 - u*j**2.
-3*j*(j + 1)*(j + 2)**3
Let t(h) be the first derivative of -h**6/10 - 11*h**5/20 - h**4 - 2*h**3/3 - 63*h + 62. Let j(f) be the first derivative of t(f). Suppose j(y) = 0. What is y?
-2, -1, -2/3, 0
Let x(z) be the second derivative of -z**6/15 + z**5/5 + 5*z**4/6 - 55*z. Let t(i) = -i**3 - i**2 - i. Let f(p) = -4*t(p) - x(p). Find d, given that f(d) = 0.
-2, 0, 1
Let z(b) = -b**2 + 330*b - 3813. Let f be z(12). Let p(q) be the first derivative of -24 - 1/3*q**f - 1/12*q**4 - 1/3*q - 1/2*q**2. What is r in p(r) = 0?
-1
Let a(k) be the first derivative of 2/27*k**3 + 2/3*k - 99 + 4/9*k**2. Solve a(o) = 0 for o.
-3, -1
Let c(y) be the first derivative of y**5/30 - y**4/3 - 5*y**3/9 + 2*y**2/3 + 3*y/2 - 600. Find g, given that c(g) = 0.
-1, 1, 9
Let t(b) be the second derivative of -b**6/6 + 19*b**5/2 + 425*b**4/4 + 980*b**3/3 + 440*b**2 - 2047*b - 1. Solve t(p) = 0.
-4, -1, 44
Let o(v) = v**3 - 42*v**2 + 81*v - 18. Let y be o(40). Suppose -y*l = -92 + 48. Solve -1/3 + 8/3*r**l - 7/3*r = 0 for r.
-1/8, 1
Suppose -17*v - 187 = -204. Let g(b) be the first derivative of 4/7*b - 6/7*b**2 - 16/21*b**3 + v. Factor g(c).
-4*(c + 1)*(4*c - 1)/7
Let 1/2*n**3 - 877/2*n + 145*n**2 + 293 = 0. Calculate n.
-293, 1, 2
Suppose -32 - 39 = -678*d - 71. Let r = 6 - 3. Factor 0*h + 4/7*h**5 + 0 + 0*h**4 - 4/7*h**r + d*h**2.
4*h**3*(h - 1)*(h + 1)/7
Find i, given that 176/7*i - 4/7*i**2 - 640/7 = 0.
4, 40
Let m(y) be the second derivative of 55*y - 3/2*y**3 - 4*y**2 + 0 - 1/12*y**4. Factor m(h).
-(h + 1)*(h + 8)
Let p = 975/28 - 935/28. Factor 0 - p*d - 2/7*d**2.
-2*d*(d + 5)/7
Let m(s) = 217*s - 21045. Let c be m(97). Let i(n) be the third derivative of 0 - 4/15*n**5 + 1/2*n**c + 16*n**2 + 2/3*n**3 + 0*n. What is f in i(f) = 0?
-1/4, 1
Suppose 0 = -0*i + 4*i + 8. Let a be (-4)/i*((-15)/(-10) - -1). Suppose 16*s - 3*s + a*s**2 + 12*s - 5*s**4 - 25*s**3 = 0. What is s?
-5, -1, 0, 1
Let a be ((-3)/2)/(84/24 + -4). Factor -3*s**3 - 14*s**2 - 5*s + 10*s**2 + 3*s + s**a.
-2*s*(s + 1)**2
Let c(p) = 3*p**3 + 83*p**2 + 480*p + 655. Let j(a) = -2*a**3 - 55*a**2 - 321*a - 437. Let v(q) = 5*c(q) + 7*j(q). Factor v(x).
(x + 3)**2*(x + 24)
Let h be (-138 - -139)*2/(-34) + (-546)/(-1190). Solve 16/5 - 4/5*d - h*d**2 = 0.
-4, 2
Let f = 1241/66 - 3283/198. Find q, given that 0 + f*q**2 - 4/9*q**3 - 16/9*q = 0.
0, 1, 4
Let w(k) = -10*k**2 - 120*k - 450. Let f = 324 + -321. Let n(u) = -7*u**2 - 60*u - 225. Let i(q) = f*w(q) - 5*n(q). Factor i(b).
5*(b - 15)*(b + 3)
Let q(v) be the third derivative of -v**7/175 + 31*v**6/300 + 74*v**5/75 + 7*v**4/5 + 3*v**2 + 1972. Find j such that q(j) = 0.
-3, -2/3, 0, 14
Let g(j) = 101*j + 3032. Let v be g(-30). Let y(f) be the second derivative of 2 + 2/15*f**4 + 1/3*f**3 + 2/5*f**2 + v*f + 1/50*f**5. Factor y(r).
2*(r + 1)**2*(r + 2)/5
Factor -3/2*p**2 - 2154*p - 773286.
-3*(p + 718)**2/2
Factor 2*v**4 - 73/4*v**3 + 0 - 36*v + 50*v**2.
v*(v - 4)**2*(8*v - 9)/4
Let k(t) be the second derivative of 1/130*t**5 + 131*t + 0*t**2 - 7/78*t**4 + 0 - 6/13*t**3. What is o in k(o) = 0?
-2, 0, 9
Let s(f) be the second derivative of 0 + 19/7*f**3 + 0*f**2 + 75/28*f**4 + 36*f - 1/70*f**6 + 27/35*f**5. Factor s(a).
-3*a*(a - 38)*(a + 1)**2/7
Let w(q) be the first derivative of 0*q - 4 + 0*q**2 + 2/7*q**3 - 1/14*q**4. Solve w(k) = 0.
0, 3
Let l(k) be the third derivative of -69*k**2 + 0 + k + 10/3*k**3 - 2/3*k**4 - 1/15*k**5. Factor l(n).
-4*(n - 1)*(n + 5)
Find h, given that -138/13*h**4 + 0 + 2310/13*h**3 + 0*h + 2450/13*h**2 + 2/13*h**5 = 0.
-1, 0, 35
Factor 355*m - 15*m**2 + 0*m**2 - 6*m**2 + 4940 - 6*m**2 + 32*m**2.
5*(m + 19)*(m + 52)
Let a = -6825 - -6827. Let y(o) be the third derivative of -9/100*o**5 - 22*o**a + 0 - 1/5*o**3 - 11/40*o**4 + 0*o. Find w such that y(w) = 0.
-1, -2/9
Let i(t) be the second derivative of 44/3*t**2 - 1/9*t**4 + 107*t + 2*t**3 + 0. Suppose i(b) = 0. What is b?
-2, 11
Let a(z) be the third derivative of z**6/60 + 16*z**5/15 + 221*z**4/12 - 578*z**3/3 + 3*z**2 - 8*z. Find k, given that a(k) = 0.
-17, 2
What is t in -24*t**2 - 3/2*t**3 + 0 - 45/2*t = 0?
-15, -1, 0
Let f(c) be the third derivative of -1/525*c**7 - 1/15*c**4 + 1/100*c**6 + 0*c**3 + 0 + 0*c**5 + 2*c**2 - 103*c. Factor f(w).
-2*w*(w - 2)**2*(w + 1)/5
Let o(h) be the third derivative of -7/8*h**4 + 0*h + 1 - 13*h**2 - 11/20*h**5 - 1/40*h**6 + 147/2*h**3. Factor o(l).
-3*(l - 3)*(l + 7)**2
Let n be 5/(-2)*9/90*-8. Factor 6*b - 2*b**4 + 3*b**n + 0*b**5 - b**4 - 20*b**3 + 11*b**3 + 3*b**5.
3*b*(b - 2)*(b - 1)*(b + 1)**2
What is y in -26/9 