3 + 1/5*x**5 + 0*x - x**2 + 3/4*x**4 - 1/6*x**6 - 225. Factor a(b).
-b*(b - 2)*(b - 1)*(b + 1)**2
Let m(d) be the third derivative of d**9/12096 + d**8/576 - d**7/126 + 139*d**5/30 - 167*d**2. Let p(y) be the third derivative of m(y). Factor p(w).
5*w*(w - 1)*(w + 8)
Let n(r) = -4*r**3 + 1190*r**2 + 604*r - 1796. Let t(j) = -2*j**2 - 1. Let b(x) = n(x) - 2*t(x). Find o, given that b(o) = 0.
-3/2, 1, 299
Factor 3/7*w**3 + 1269/7*w + 633/7 + 639/7*w**2.
3*(w + 1)**2*(w + 211)/7
Suppose -20 + 44 = 6*l. Let t(h) = -11*h**2 + 18*h - 24. Let m(u) = -57*u**2 + 90*u - 120. Let z(f) = l*m(f) - 21*t(f). Factor z(i).
3*(i - 4)*(i - 2)
Let t(i) be the third derivative of -i**5/270 + 5*i**4/54 - 8*i**3/9 - 2*i**2 - 152. Suppose t(k) = 0. What is k?
4, 6
Factor 7/4*s + 1/2*s**2 + 3/4.
(s + 3)*(2*s + 1)/4
Solve 2/7*s**3 - 150/7*s**2 + 16000/7 + 2400/7*s = 0 for s.
-5, 40
Suppose 3155 + 9089 = -1995*q + 6911*q - 2504. Factor -1/6*b**5 - 1/2 - 13/6*b - 7/6*b**4 - 11/3*b**2 - q*b**3.
-(b + 1)**4*(b + 3)/6
Let m(t) = -21*t**2 + 55*t - 4. Let u(k) = 47*k**2 - 112*k + 9. Let g(r) = 9*m(r) + 4*u(r). Suppose g(j) = 0. Calculate j.
0, 47
Let t be (-2022)/(-2359) - (-180)/(-14) - 14/(-1). Let l = -2332 + 9397/4. Let 15*a + 21/4*a**3 + 3 + l*a**t = 0. What is a?
-2, -1, -2/7
Factor -3/7*c**3 - 852/7*c - 1152/7 + 297/7*c**2.
-3*(c - 96)*(c - 4)*(c + 1)/7
Let v(x) be the first derivative of -3*x**4/8 + 4*x**3 - 12*x**2 + 1437. Factor v(w).
-3*w*(w - 4)**2/2
Suppose 0 = 4*d - 4*g, 15*g = -2*d + 16*g + 2. Factor -4*y**2 - 76*y**3 - 6*y**4 + 84*y**3 + d*y**4.
-4*y**2*(y - 1)**2
Let n(u) be the second derivative of -4*u**6/165 - 151*u**5/110 + 87*u**4/11 - 449*u**3/33 + 82*u**2/11 + 6239*u. Suppose n(l) = 0. Calculate l.
-41, 1/4, 1, 2
Let k(c) be the first derivative of 3*c**3 - 1 + 0*c**2 - 3/4*c**4 - 12*c. Factor k(p).
-3*(p - 2)**2*(p + 1)
Let i = 15397 - 15395. Let z(n) be the second derivative of 4/9*n**3 - 4/3*n**i + 1/18*n**4 + 0 - 1/30*n**5 + 41*n. Let z(d) = 0. What is d?
-2, 1, 2
Let f be 3/(-9) + 3/9. Let r(i) = i**2 + 8*i + 3. Let t be r(f). What is s in 32/7 - 80/7*s**2 + 800/7*s**t - 750/7*s**4 - 128/7*s = 0?
-2/5, 2/5, 2/3
Let t(b) be the first derivative of -b**4/30 - 190*b**3/9 - 158*b**2/5 + 1670. Factor t(s).
-2*s*(s + 1)*(s + 474)/15
Factor -1/4*w**4 - 3/2*w**2 - 7/4*w**3 + 8 + 8*w.
-(w - 2)*(w + 1)*(w + 4)**2/4
Let i(l) be the third derivative of -l**7/2520 + l**4/2 - 5*l**2 - l. Let w(a) be the second derivative of i(a). Suppose w(h) = 0. What is h?
0
Let q be 9 - (3540/(-472) - (-16)/1). Factor 0 + 1/4*c**4 - q*c**3 + 3*c - 11/4*c**2.
c*(c - 4)*(c - 1)*(c + 3)/4
Let b(m) be the third derivative of -m**5/210 - 257*m**4/28 - 110*m**3/3 - 2871*m**2. Let b(h) = 0. What is h?
-770, -1
Factor 117 + 40*r + 1/3*r**2.
(r + 3)*(r + 117)/3
Suppose -1311*r - 4*i + 68 = -1309*r, r + i - 17 = 0. Find f, given that r*f + 2/15 - 2/15*f**2 = 0.
-1, 1
Let u(x) be the second derivative of -x**6/105 + 31*x**4/42 - 10*x**3/7 - 74*x. Factor u(a).
-2*a*(a - 5)*(a - 1)*(a + 6)/7
Let r(t) be the first derivative of 2*t**3/27 - 23*t**2/3 - 284*t/9 + 1196. What is f in r(f) = 0?
-2, 71
Let c(g) be the third derivative of -g**6/160 - g**5/5 - 9*g**4/8 + 18*g**3 - 2387*g**2. Factor c(p).
-3*(p - 2)*(p + 6)*(p + 12)/4
Suppose 0*h + 27 = -3*v - 3*h, v + 29 = 3*h. Let l be (-1 + 0)*(v + -3). Find p such that 1 - 9*p - 5*p**2 + p - 5 + l*p**2 = 0.
-1/3, 1
Let k(r) be the third derivative of r**6/72 - 7*r**5/24 - 25*r**3/3 - 2*r**2 + 6*r. Let f(t) be the first derivative of k(t). Let f(w) = 0. Calculate w.
0, 7
Let v be (-4)/(-18) + 816715/4275. Let y = -191 + v. Solve y*q**5 + 0*q + 2/15*q**4 + 0*q**2 + 0 - 2/15*q**3 = 0.
-1, 0, 1/2
Let u = 4384 - 4382. Let h(o) be the first derivative of -2/3*o**3 - 13 - 3*o**u - 9/2*o. Find m, given that h(m) = 0.
-3/2
Let m(w) be the first derivative of w**8/2352 + 4*w**7/735 - 3*w**6/280 - 97*w**2/2 + 2*w + 123. Let g(x) be the second derivative of m(x). Factor g(k).
k**3*(k - 1)*(k + 9)/7
Let d(q) be the first derivative of q**3/4 + 387*q**2/8 + 381*q/2 - 3051. What is v in d(v) = 0?
-127, -2
Let j(y) be the first derivative of -8/7*y**3 - 1/14*y**4 - 87 + 24/7*y + 1/7*y**2. Factor j(t).
-2*(t - 1)*(t + 1)*(t + 12)/7
Factor 2/7*u**2 + 48/7*u + 88/7.
2*(u + 2)*(u + 22)/7
Factor -621/7 - 96/7*p - 3/7*p**2.
-3*(p + 9)*(p + 23)/7
Suppose 3*n - 553 = -v + 696, 2*v = 4*n - 1682. Let g = n + -414. Let 2/13*i**g + 4/13*i + 10/13*i**2 + 0 + 8/13*i**3 = 0. Calculate i.
-2, -1, 0
Let c(s) be the second derivative of s**4/48 + s**3/8 - 7*s**2/2 + 11*s + 82. Find a such that c(a) = 0.
-7, 4
Let w(n) = -60*n + 5*n**2 - 3*n**2 + 61*n + 25. Let q be w(12). Factor -4*z**2 + 2*z + 325 - q.
-2*z*(2*z - 1)
Solve 617/2*r + 1/4*r**2 + 380689/4 = 0.
-617
Let o be -1*(-18)/(-3)*5/(-10). Let d be (42 + 4 + 2)*8/o. Factor 10*w + d*w**2 - 2*w**3 + 0*w**3 - 120*w**2.
-2*w*(w - 5)*(w + 1)
Let a(d) = -5*d**3 - 104*d**2 - 268*d + 383. Let l(i) = 85*i**3 + 1770*i**2 + 4555*i - 6510. Let y(u) = -50*a(u) - 3*l(u). Factor y(h).
-5*(h - 1)*(h + 4)*(h + 19)
Let q(j) = 51*j + 59*j - 6*j**2 - 111*j. Let g(b) = 4*b**2 + b. Let w(x) = 7*g(x) + 5*q(x). Determine i, given that w(i) = 0.
0, 1
Let u(i) be the first derivative of i**7/315 - 8*i**6/225 + 7*i**5/150 - 55*i + 107. Let o(w) be the first derivative of u(w). Solve o(v) = 0 for v.
0, 1, 7
Let r = -524 + 528. Suppose -5*h = -10, -5*n = 26*h - 28*h + r. Factor -2/3*u**5 + n*u**4 + 2/3*u**3 + 0*u + 0 + 0*u**2.
-2*u**3*(u - 1)*(u + 1)/3
Factor -3/2*z**4 + 183*z**2 + 6*z**3 - 378*z - 11907/2.
-3*(z - 9)**2*(z + 7)**2/2
Let s(z) = -2*z**2 - 36*z - 36. Let f(b) = b**2 + 22*b + 16. Let v(q) = -9*f(q) - 4*s(q). Factor v(h).
-h*(h + 54)
Suppose -i - 4*i = -5*z - 105, 3*i = -z + 63. Let -56*k**2 + i*k**4 - 5*k**4 - 207 + 144*k - 36*k**3 + 175 = 0. What is k?
-2, 1/4, 2
Let i(m) = -2*m + 10. Let t(n) = n**2 + 4*n - 17. Let d be t(-7). Let a be i(d). Let -a*k**2 - 3*k**2 - 4 - 7*k**2 - 12*k - 4*k**3 = 0. What is k?
-1
Let g(o) be the first derivative of o**6/1440 + 7*o**5/160 + 19*o**4/48 + o**3/3 - 131. Let q(y) be the third derivative of g(y). Factor q(l).
(l + 2)*(l + 19)/4
Let z(w) be the second derivative of w**6/660 - 2*w**5/165 + w**4/33 - 19*w**2/2 + 15*w. Let v(g) be the first derivative of z(g). Let v(f) = 0. What is f?
0, 2
Let n(m) = -2*m**2 - 11*m + 3. Suppose -f = 6*f + 35. Let h(d) = d**2 + 6*d - 1. Let o(b) = f*h(b) - 3*n(b). Find q, given that o(q) = 0.
-4, 1
Let s be 1/2 + 323/34. Suppose -22 = -i - 5*b, 0*i - b = 3*i - s. Suppose -233*u**2 - 5000 + 19*u**3 + 83*u**i - 444*u - 1056*u - 24*u**3 = 0. What is u?
-10
Let u(a) be the third derivative of -3*a**2 + 0*a**4 + 1/180*a**5 - 1/2016*a**8 + 7 + 0*a + 0*a**7 + 1/240*a**6 + 0*a**3. Determine n so that u(n) = 0.
-1, 0, 2
Let m(d) be the second derivative of d**7/42 + 34*d**6/45 - 103*d**5/30 + 5*d**4 - 56*d**3/3 - 4*d - 8. Let h(f) be the second derivative of m(f). Factor h(p).
4*(p - 1)*(p + 15)*(5*p - 2)
Suppose 0 = -3*d - 234 + 240. Factor 410*b**d - 450*b**2 + 4*b**3 + 2*b + 30*b + 4*b**4.
4*b*(b - 2)*(b - 1)*(b + 4)
Let n(h) be the second derivative of -3*h**6/50 + 183*h**5/20 + 411*h**4/20 + 103*h**3/10 + 1050*h. Let n(j) = 0. Calculate j.
-1, -1/3, 0, 103
Let h(n) = n + 13. Let d be h(-17). Let i(m) = -3*m**2 - 3*m + 9. Let p(r) = r**3 + 3*r**2 + 3*r - 11. Let u(s) = d*i(s) - 3*p(s). Factor u(z).
-3*(z - 1)**2*(z + 1)
Factor -13/5*f**3 + 8/5*f + 0 - 22/5*f**2.
-f*(f + 2)*(13*f - 4)/5
Let r(i) be the second derivative of i**7/14 - 29*i**6/30 - 3*i**5/4 + 49*i**4/12 + 2*i**3 - 10*i**2 - 624*i. Determine b, given that r(b) = 0.
-1, 2/3, 1, 10
Suppose -h + 4 = 0, 2*s - h + 11 = 13. Factor -267*q + 255*q - q**3 + 2*q**4 - 14*q**2 + q**s.
2*q*(q - 3)*(q + 1)*(q + 2)
Let w(h) be the third derivative of -h**6/240 + 11*h**5/120 + 5*h**4/3 - 75*h**3 - 2*h**2 - 3789*h - 1. Factor w(d).
-(d - 10)**2*(d + 9)/2
Let z(d) = d**3 - 79*d**2 + 124*d + 2310. Let i be z(77). Factor i + 2/13*k**4 - 2*k**2 + 0*k - 24/13*k**3.
2*k**2*(k - 13)*(k + 1)/13
Let v(o) = 8*o**2 + 6*o - 38. Let r(q) = -15*q**2 - 17*q + 76. Let z(g) = -6*r(g) - 11*v(g). Factor z(c).
2*(c - 1)*(c + 19)
Let z = 1463/1948 - 1/974. Let h(g) be the second derivative of 0 + 5/2*g**3 - 24*g + 5/12*g**4 - 1/6*g**6 - z*g*