 240. Let t be m(12). Let b(i) be the third derivative of 10*i**2 + 0*i + 1/120*i**5 + 0 + t*i**3 + 0*i**4. Determine j, given that b(j) = 0.
0
Let f(o) = -14*o**5 - 6*o**4 + 19*o**3 + o**2 - 5*o. Let a(p) = -21*p**5 - 8*p**4 + 28*p**3 + p**2 - 7*p. Let x(s) = 5*a(s) - 7*f(s). Find r such that x(r) = 0.
-1, 0, 2/7, 1
Factor h**2 - 13*h - 5*h + 3*h**2 - 96 + 110*h.
4*(h - 1)*(h + 24)
Let a(x) be the first derivative of x**8/9240 - x**6/660 + x**5/330 + x**3/3 + 13. Let w(g) be the third derivative of a(g). Determine j, given that w(j) = 0.
-2, 0, 1
Let k(a) = -36*a**2 + 63*a - 27. Let x(c) = -5*c**2 + 9*c - 4. Suppose -4 = -5*y + 3*u, 4 = -2*y + 2*u + 2*u. Let t(q) = y*k(q) - 15*x(q). Factor t(w).
3*(w - 2)*(w - 1)
Let y = 2/5331 - -18954/1777. Factor 2/3*x**2 - 16/3*x + y.
2*(x - 4)**2/3
Let s(n) be the first derivative of 6*n**5/25 + 47*n**4/10 + 72*n**3/5 + 52*n**2/5 + 421. Suppose s(x) = 0. What is x?
-13, -2, -2/3, 0
Let r(t) be the third derivative of 0 - 1/18*t**4 + 5/9*t**3 + 0*t + 1/450*t**5 + 37*t**2. Determine h so that r(h) = 0.
5
Let 9468*w**2 + w - 9467*w**2 - 3*w**4 + w - 4*w**3 = 0. What is w?
-1, 0, 2/3
Let a be -8*(75/10 - 0). Let m be (a/35)/6 - (-2)/1. Factor 2/7*l**2 + 18/7 + m*l.
2*(l + 3)**2/7
Suppose 0 = 3*j - 1 - 8. Let o(w) be the first derivative of j + 0*w**4 + 0*w - 1/4*w**3 + 0*w**2 + 3/20*w**5. Factor o(g).
3*g**2*(g - 1)*(g + 1)/4
Solve -5*z**5 - 23557*z + 16 + 23545*z - 16*z**2 + 4*z**5 + 13*z**3 = 0.
-4, -1, 1, 2
Factor 21/2*z**2 + 15/2*z - 3.
3*(z + 1)*(7*z - 2)/2
Let l be (-651)/(-9) + (-1)/3*1. Let s = 72 - l. Factor -2/5*o**4 - 2/5*o + s - 6/5*o**3 - 6/5*o**2.
-2*o*(o + 1)**3/5
Let i = 12505/9 - 1389. Let i + 8/9*h**2 + 4/3*h = 0. Calculate h.
-1, -1/2
Let d(j) = j**4 + j**3 + j**2 + 2*j + 2. Let w(m) = m**5 - 2*m**4 - 3*m**3 + 6*m**2 + 12*m + 12. Let r(n) = 6*d(n) - w(n). Determine i, given that r(i) = 0.
-1, 0, 9
Let m be 10/15 + (-39)/(-9). Let s be 0 - (0 - 2) - (m + -3). Factor j + s - 1/2*j**2.
-j*(j - 2)/2
Suppose 0 = 50*a + 11 - 161. Let i(f) be the first derivative of -12/7*f - 1/7*f**a - 11 + 6/7*f**2. Factor i(k).
-3*(k - 2)**2/7
Let z(k) be the third derivative of k**8/2352 - k**6/280 + k**5/210 + 87*k**2. Let z(o) = 0. What is o?
-2, 0, 1
Let b be (-12 - -10)/((-4)/2). Let f(w) = -4 + 3*w**2 + 3*w - w**2 - 9*w - b. Let z(v) = 2*v**2 - 6*v - 4. Let j(l) = -4*f(l) + 5*z(l). What is r in j(r) = 0?
0, 3
Let o be 2*-1 + 1/(120/1086). Let b = o + -25/4. Suppose -4*f - 8/5 - b*f**3 - 16/5*f**2 = 0. Calculate f.
-2, -1
Let d(o) be the first derivative of o**6/30 + o**5/25 - o**4/4 - o**3/15 + 4*o**2/5 - 4*o/5 - 61. Factor d(g).
(g - 1)**3*(g + 2)**2/5
Let d(i) be the second derivative of -i**6/10 + 27*i**5/20 - 23*i**4/4 + 3*i**3/2 + 54*i**2 - 141*i. Factor d(n).
-3*(n - 4)*(n - 3)**2*(n + 1)
What is t in 3 + 33/4*t**2 + 3/4*t**5 - 9*t - 9/4*t**4 - 3/4*t**3 = 0?
-2, 1, 2
Suppose a - 5*m - 629 = 0, 4*m + 1942 = a + 2*a. Factor -5*f - 654*f**2 + 5*f**3 + a*f**2.
5*f*(f - 1)*(f + 1)
Suppose -5*b + 3*u = 2*u + 2, -4*u + 8 = 3*b. Let m be b + (2 - (5 + -5)). Solve -2/7*f**3 + 0*f + 0 - 4/7*f**m = 0.
-2, 0
Let v = -31 - -34. What is c in 2*c**4 - 3*c - 2*c**v + 2*c**5 + 3*c + 15*c**2 - 17*c**2 = 0?
-1, 0, 1
Let z(q) be the first derivative of -1/5*q**5 + 0*q - 4 + 0*q**3 + 3/4*q**4 - 2*q**2. Suppose z(p) = 0. Calculate p.
-1, 0, 2
Let l(k) be the third derivative of -k**8/10080 + k**7/2520 - k**5/360 + k**4/144 + 3*k**3/2 + 7*k**2. Let y(w) be the first derivative of l(w). Factor y(a).
-(a - 1)**3*(a + 1)/6
Solve -60*g**3 + g**4 + 32*g**3 - 7*g**2 + 27*g**3 + 5*g**2 = 0.
-1, 0, 2
Let v(m) be the third derivative of m**6/24 + 65*m**5/6 + 21125*m**4/24 + 552*m**2. What is g in v(g) = 0?
-65, 0
Let s(x) = 2*x**2 + 26*x - 134. Let i be s(-17). Factor 7/4*k - 2 + 1/4*k**i.
(k - 1)*(k + 8)/4
Let c(m) = m**4 + 3*m**2 - 1. Let k(h) = 8*h**4 - 24*h**3 - 708*h**2 - 2592*h - 4. Let d(p) = 4*c(p) - k(p). Factor d(j).
-4*j*(j - 18)*(j + 6)**2
Let l(h) = 60*h**2 + 65*h + 29. Let s(u) = 300*u**2 + 324*u + 152. Let b(y) = -16*l(y) + 3*s(y). Determine t, given that b(t) = 0.
-1, -2/15
Let f = 2/795 - -3496/795. Factor 16/3*t**2 + f*t + 6/5 + 32/15*t**3.
2*(t + 1)*(4*t + 3)**2/15
Suppose 6*p = 8*p. Let t be 4/4*(1 + p). Let i(n) = -n**3 + n. Let q(w) = 2*w**4 + 6*w**3 + 6*w**2 - 2. Let h(m) = t*i(m) - q(m). Find d, given that h(d) = 0.
-2, -1, 1/2
Let a(c) = c - 1. Let h be a(3). Suppose h*q - 2*q = 8*q. Let -1/2*p + 1/2*p**4 - 3/2*p**3 + 3/2*p**2 + q = 0. What is p?
0, 1
Let j(k) = 2*k**3 - 167*k**2 + 73*k + 830. Let p be j(83). Factor 13/2*n + 1/2*n**2 + p.
n*(n + 13)/2
Let t(q) = -q**2 + 72*q - 894. Let w be t(16). Factor -2/23*v**3 + 2/23*v - 6/23 + 6/23*v**w.
-2*(v - 3)*(v - 1)*(v + 1)/23
Suppose 3*w - 38 + 26 = 0. Factor -8*f**4 + 14*f**w + 6*f - 4*f**2 - 2 - 4*f**3 + 0*f**2 - 2*f**5.
-2*(f - 1)**4*(f + 1)
Suppose -3*i = n - 5, 792*i - 795*i + 7 = 2*n. Find v such that 0 - 2/7*v**3 - 12/7*v - 10/7*v**n = 0.
-3, -2, 0
Let d be 21/(-6) - -1 - 221/(-78). Let b(z) be the first derivative of -d*z**2 + 4/9*z + 2/27*z**3 + 1. Factor b(x).
2*(x - 2)*(x - 1)/9
Let h(c) be the first derivative of -c**4/20 - 22*c**3/15 - 41*c**2/10 - 4*c - 33. Factor h(t).
-(t + 1)**2*(t + 20)/5
Factor -2/3*p**2 - 14/3*p + 0.
-2*p*(p + 7)/3
Let a be (-18 - -16) + 3 + 1. Determine k, given that -10*k**4 + 22*k**5 + 25*k + 3*k**5 - 20*k**a - 90*k**3 - 2*k + 30 + 42*k = 0.
-1, -3/5, 1, 2
Let v(c) be the third derivative of c**5/120 - 23*c**4/12 + 529*c**3/3 - 102*c**2. Determine k, given that v(k) = 0.
46
Let v(w) = -2*w**2 + 87*w - 40. Let h be v(43). Factor 0*m**2 + 6*m + 0 - 3/2*m**h.
-3*m*(m - 2)*(m + 2)/2
Let k(f) be the third derivative of 0*f**6 + 0 + 1/30*f**3 + 0*f + 1/1050*f**7 - 1/150*f**5 + 0*f**4 + f**2. Find n, given that k(n) = 0.
-1, 1
Let m be (-1)/((-30)/275) - 9. Factor 1/6*w**4 + 2/3*w + m + 2/3*w**3 + w**2.
(w + 1)**4/6
Let a = -14562946 - -30116173843/2068. Let h = a + -1/188. Determine j so that 0 - 40/11*j**4 + h*j + 10/11*j**3 - 18/11*j**5 + 40/11*j**2 = 0.
-2, -1, -2/9, 0, 1
Suppose -g + 27*g - 8*g - 36 = 0. What is c in 0 + 12/11*c**3 - 6/11*c + 6/11*c**g = 0?
-1, 0, 1/2
Let p be (-2)/(6/(-3)) + -4. Let z be ((-3)/12)/(p/24). Solve 5*f**z + 20*f**2 - 4*f**2 + 4 - 22*f - 3*f**2 = 0.
2/9, 1
Let r be 815/(-90)*-3 - -5. Let t = r - 32. Factor -1/6 + 1/6*q**2 + 1/6*q**3 - t*q.
(q - 1)*(q + 1)**2/6
Suppose -2*x = -4*s - 2 + 16, 5*s = 5*x + 15. Let n(b) be the second derivative of -2/21*b**3 + 0*b**2 + 0 - 2*b + 1/42*b**s. Factor n(q).
2*q*(q - 2)/7
Suppose 0 = 5*k + 11*k - 80. Let b(f) be the first derivative of k + 12*f**2 + 4*f**3 + 1/2*f**4 + 16*f. Solve b(s) = 0 for s.
-2
Suppose -a + 3*a - 5*l + 38 = 0, 4*l = -2*a - 2. Let j be (6/a)/((-1)/3) - -1. Let 0*w**2 + 1/3*w - 1/3*w**j + 0 = 0. What is w?
-1, 0, 1
Factor -d**2 + 4520 - 9019 + 3*d + 4517.
-(d - 6)*(d + 3)
Let i be (35/7 - 4)*5. Let j(l) be the second derivative of 2/3*l**4 - 1/15*l**6 - 4*l - 1/15*l**i + 8/9*l**3 + 0 + 0*l**2. Suppose j(x) = 0. Calculate x.
-2, -2/3, 0, 2
Suppose 2*i = 6*i + 16. Let w(f) = f + 8. Let q be w(i). Factor 2*p + 16*p**3 + 6*p**2 + 6*p**3 - q*p**3 - 18*p**2.
2*p*(3*p - 1)**2
Find a, given that -41*a**4 - 2304*a - 3*a**5 - 488 - 735*a**3 + 3*a**4 - 46*a**4 - 2094*a**2 - 459 + 83 = 0.
-12, -2, -1
Let j(c) = -2*c**2 - 17*c - 17. Suppose -4*a + 2 = -2*x, 2*x + 5*a = -0*x - 29. Let q be j(x). Factor -19*y**3 - 1 - 13/2*y - 16*y**2 - 5/2*y**5 - 11*y**q.
-(y + 1)**4*(5*y + 2)/2
Let r(c) be the second derivative of 1/60*c**4 + 11*c + 1/30*c**3 - 1/100*c**5 + 0 - 1/10*c**2. Let r(a) = 0. What is a?
-1, 1
Let k be 3 + (1 - (-8)/(-4)). Let f be 14/4 + k/4. Let -11*l**3 + l**2 + l**4 + 9*l**3 + f*l**3 = 0. What is l?
-1, 0
Let f(r) = -167*r + 4681. Let g be f(28). Factor 0 - 8/7*d**2 - 8/7*d**4 + 2/7*d**g + 2/7*d + 12/7*d**3.
2*d*(d - 1)**4/7
Let n(p) = p**3 + 4*p**2 - 7*p - 6. Let h be n(-5). Let l be 23/h + 3/12. Let -4*k**2 - 2 + 8*k - 8*k**3 + l*k**4 + 4*k**2 - 4*k**2 = 0. Calculate k.
-1, 1/3, 1
Let j(g) = 6*g**2 + 30*g + 24. Let x(c) = -2*c**2 - 10*c - 8. Let w = 87 - 95. Let f(r) = w*x(r) - 3*j(r). Solve f(v) = 0 for v.
-4, -1
Let x(a) be the third derivative of a**5/210 - a**4/28 + 2*a**3/21 + 39*a**2 - 3*a. Factor x(v).
2*(v - 2)*(v - 1)