Let y(o) be the third derivative of o**7/315 + o**6/45 - o**5/90 - 4*o**4/9 - 4*o**3/3 - o**2 - 7*o. Find f, given that y(f) = 0.
-3, -2, -1, 2
Let l(r) = 10*r - 57*r**2 - 1 + 52*r**2 + 9. Let y(c) = -5*c**2 + 10*c + 9. Let x(u) = 6*l(u) - 7*y(u). Factor x(f).
5*(f - 3)*(f + 1)
Let n(y) be the second derivative of 4*y**2 - y + 4/3*y**4 + 6*y**3 + 10. Determine a so that n(a) = 0.
-2, -1/4
Let x(d) = 2*d**2 - 3*d - 2. Suppose 0 = -9*c + 5 + 13. Let o be x(c). Determine y, given that 0*y + 0*y**2 - y**3 - 1/2*y**4 + o = 0.
-2, 0
Let o(k) = 15 + 27*k**2 + 10*k**2 - 15*k**3 - 37*k + 0*k**2. Let d(p) = 10*p**3 - 25*p**2 + 25*p - 10. Let h(j) = -8*d(j) - 5*o(j). Factor h(q).
-5*(q - 1)**3
Let v be -16 + 10 + (-273)/(-45). Let z(d) be the first derivative of 2/15*d**3 + 0*d - 1 - 1/10*d**4 - 2/25*d**5 + v*d**6 + 0*d**2. Solve z(p) = 0.
-1, 0, 1
Let h(d) be the first derivative of -24 + 1/19*d**2 - 6/19*d - 1/38*d**4 + 2/19*d**3. Factor h(t).
-2*(t - 3)*(t - 1)*(t + 1)/19
Let i(p) = -3*p**2 - 3*p. Let o = -14 + 20. Let v be o*-2*(-2)/(-4). Let l(x) = 5*x**2 + 6*x. Let b(r) = v*l(r) - 11*i(r). Factor b(m).
3*m*(m - 1)
Suppose 181*u - 15 = 176*u. Let q = 204 + -1426/7. Factor 0*v + 0 + 4/7*v**2 + q*v**u - 2/7*v**4.
-2*v**2*(v - 2)*(v + 1)/7
Let t(q) be the second derivative of -q**6/285 + 24*q**5/95 - 332*q**4/57 + 704*q**3/19 - 1936*q**2/19 + 140*q. Solve t(m) = 0 for m.
2, 22
Let d(o) be the second derivative of -o**6/6 - 3*o**5/2 + 80*o**3/3 + 86*o - 1. Solve d(t) = 0 for t.
-4, 0, 2
What is b in 56*b**4 - 38*b + 40 + 7*b**2 + 38*b**3 + 39*b**4 - 49*b**2 - 93*b**4 = 0?
-20, -1, 1
Let q(s) = 140*s**3 - 1225*s**2 + 3365*s - 2885. Let g(l) = l**4 + 140*l**3 - 1226*l**2 + 3366*l - 2886. Let m(w) = 5*g(w) - 6*q(w). Find o such that m(o) = 0.
2, 12
Factor 40 - 560*u**2 + 44*u + 1134*u**2 + u**3 - 560*u**2.
(u + 2)**2*(u + 10)
Let m = -892 + 894. Solve 1/6*r**3 + 0 - 1/6*r**m + 0*r = 0.
0, 1
Let q(x) = -21*x**4 + 78*x**3 + 72*x**2 + 9*x. Let u(s) = 5*s**4 - 19*s**3 - 18*s**2 - 2*s. Let n(c) = 2*q(c) + 9*u(c). Suppose n(p) = 0. Calculate p.
-1, 0, 6
Let r(i) be the first derivative of -i**8/1680 + i**7/150 - i**6/40 + 3*i**5/100 + 45*i**2/2 + 36. Let g(f) be the second derivative of r(f). Factor g(a).
-a**2*(a - 3)**2*(a - 1)/5
Suppose 2/9*g**5 + 0 + 8/9*g**2 + 8/9*g**4 + 2/9*g + 4/3*g**3 = 0. Calculate g.
-1, 0
Let c be (-59)/2 - -5 - 5. Let h = c + 30. Factor h + q**2 - 1/4*q**3 - 5/4*q.
-(q - 2)*(q - 1)**2/4
Let f(m) be the second derivative of 5*m**4/12 + 5*m**3/3 + 5*m**2/2 - 3*m - 6. Determine i, given that f(i) = 0.
-1
Let r(z) be the third derivative of 0*z**3 - 1/300*z**6 + 0 - 1/30*z**4 - z**2 + 0*z + 1/50*z**5. Determine y, given that r(y) = 0.
0, 1, 2
Let c be 447/15 - (0 - -1)/(-5). Solve c*w**4 - 25*w**5 + 5*w**4 + 20 - 55*w**2 + 36*w**3 - 40*w + 29*w**3 = 0 for w.
-1, 2/5, 1, 2
Factor 3568 - 353*y + 5*y**2 + 3665 - 37*y + 372.
5*(y - 39)**2
Let k(o) be the first derivative of -o**4/12 - 17*o**3/9 - 31*o**2/6 - 5*o - 841. Let k(g) = 0. What is g?
-15, -1
Let q(x) be the second derivative of 0*x**2 + 3/160*x**5 - 1/8*x**3 - 1/32*x**4 - 2 - 13*x. Factor q(m).
3*m*(m - 2)*(m + 1)/8
Factor -2/9*k**2 + 208/9 - 44/9*k.
-2*(k - 4)*(k + 26)/9
Let x(s) be the third derivative of s**6/120 - s**5/20 + 5*s**4/24 - 2*s**3/3 - 2*s**2 + 72*s. Let w be x(2). Factor 0*t + 2/11 - 2/11*t**w.
-2*(t - 1)*(t + 1)/11
Let s(c) = 2*c**2 + 17*c - 11 - c**2 - 4*c. Let m be s(-14). Factor -1 - 4*o**2 + 3*o**4 + 2*o**3 + 2 - o**m + o**3 - 2*o**5.
-(o - 1)**3*(o + 1)*(2*o + 1)
Let r(t) be the second derivative of -t**7/1260 - t**6/135 + t**5/36 + 7*t**3/2 + 37*t. Let i(j) be the second derivative of r(j). Let i(a) = 0. Calculate a.
-5, 0, 1
Suppose -24 = -4*a - 4*l, 4*a - 19 - 5 = l. Let o be 0 + a/8 - 0. Factor 0*m**2 + 0 + 3/2*m**3 + 0*m**4 - o*m**5 - 3/4*m.
-3*m*(m - 1)**2*(m + 1)**2/4
Let y(i) = 11*i**2 + 62*i - 1089. Let w(h) = -25*h**2 - 123*h + 2178. Let l(t) = 4*w(t) + 9*y(t). Solve l(o) = 0.
33
Let z(g) be the third derivative of -g**10/302400 + g**8/20160 - g**6/1440 - 7*g**5/60 + 11*g**2. Let x(w) be the third derivative of z(w). Factor x(d).
-(d - 1)**2*(d + 1)**2/2
Let z(v) = 3*v**2 - 20*v - 5. Let u(j) = 3*j**2 - 16*j - 4. Let p(n) = 5*u(n) - 4*z(n). Suppose p(i) = 0. Calculate i.
0
Let l(q) be the second derivative of q**6/15 + 4*q**5/5 + 23*q**4/6 + 28*q**3/3 + 12*q**2 + 6*q + 8. Determine r so that l(r) = 0.
-3, -2, -1
Let t(u) be the first derivative of -u**3/6 - 153*u**2/2 - 23409*u/2 - 558. Suppose t(j) = 0. What is j?
-153
Let z(p) = -1. Let y(t) = -t + 7. Let q(n) = y(n) + 4*z(n). Let g be q(1). Factor 11*m**2 - 8*m + 4*m**3 - 12*m**4 + 4*m**5 - 4*m**2 + 5*m**g.
4*m*(m - 2)*(m - 1)**2*(m + 1)
Let a(g) be the third derivative of g**8/2016 - g**7/224 + g**6/144 - 13*g**5/30 + 12*g**2. Let d(h) be the third derivative of a(h). Factor d(k).
5*(k - 2)*(4*k - 1)/2
Let t(l) = 2*l**5 + 4*l**3 + 3*l**2 + 3*l + 3. Let n(m) = -m**5 - m**2 - m - 1. Let c(a) = -3*n(a) - t(a). Factor c(y).
y**3*(y - 2)*(y + 2)
Suppose -4*m = 4*d + 168, d + 18 = 3*m - 12. Let t = 41 + d. Solve 0 + 2/13*w**t - 4/13*w + 58/13*w**3 - 56/13*w**4 = 0 for w.
-1/4, 0, 2/7, 1
Let s(d) be the first derivative of d**9/3024 - d**8/1008 + d**7/2520 + d**6/1080 + 8*d**3/3 - 17. Let q(r) be the third derivative of s(r). Factor q(k).
k**2*(k - 1)**2*(3*k + 1)/3
Let s = -2108 + 2110. Solve -2/3*h**s + 0*h - 2/3*h**3 + 0 = 0.
-1, 0
Let b be 71 + -57 - (-47)/(-4). Factor 27/2*n + 1/8*n**3 - 27 - b*n**2.
(n - 6)**3/8
Let y(k) = -k**5 + k**4 + k**2 + k + 1. Let d(t) = -t**5 + 66*t**4 - 330*t**3 + 516*t**2 + 171*t - 754. Let z(w) = -d(w) - 4*y(w). Find q, given that z(q) = 0.
-1, 2, 3, 5
Let p be (42/(-4))/(9 + (-17457)/1936). Let d = 5558/9 - p. Factor 2*b**2 + d*b + 2/9*b**4 + 10/9*b**3 + 4/9.
2*(b + 1)**3*(b + 2)/9
Let h(d) be the first derivative of 81*d**3/4 - 255*d**2/8 + 3*d - 590. Suppose h(s) = 0. What is s?
4/81, 1
Let y be 6/(-117)*3 - 168/(-78). Let g(w) be the second derivative of -1/5*w**y + 0*w**3 - 4*w + 1/30*w**4 + 0. Find t, given that g(t) = 0.
-1, 1
Factor 3*l**2 + 2*l**3 - 6*l**3 + 9*l**2 + 12*l**2.
-4*l**2*(l - 6)
Let h = -401 + 1605/4. Let d(j) be the first derivative of -3 + 0*j**3 - 3/32*j**4 - 1/40*j**5 + h*j**2 + 0*j. Let d(k) = 0. Calculate k.
-2, 0, 1
Suppose -98/17*w + 2/17*w**5 - 48/17 - 4/17*w**2 + 52/17*w**4 + 96/17*w**3 = 0. What is w?
-24, -1, 1
Suppose -14*r = -21*r + 35. Let v(d) be the second derivative of -1/40*d**r + 6*d + 1/8*d**4 + 0*d**2 + 0 - 1/6*d**3. Factor v(k).
-k*(k - 2)*(k - 1)/2
Let a(c) = c**3 + 4*c**2 - 4*c + 7. Let u be a(-4). Suppose -k - 19 + u = 0. Factor -2/3*b**2 + 0 + 0*b**3 + 0*b + 2/3*b**k.
2*b**2*(b - 1)*(b + 1)/3
Suppose 0 = b - 92 + 85. Factor -14*s**3 + 22*s**3 + b*s**3 + 18*s + 51*s**2.
3*s*(s + 3)*(5*s + 2)
Let x be (29862/9072)/(1/20). Let 115/6*d - 25*d**4 - 175/3*d**2 - 5/3 + x*d**3 = 0. What is d?
2/15, 1/2, 1
Suppose -3 = -4*v - 23. Let j be (-1)/(v/27) + (-3)/5. Factor -36/5*p + j - 3/5*p**3 + 18/5*p**2.
-3*(p - 2)**3/5
Suppose 0 = 4*y - 2*y - 6. Let f = 39 + -37. Find c, given that 3*c**2 + c**3 + 2*c - 4*c - f*c**y = 0.
0, 1, 2
Let p(o) be the second derivative of o**5/12 + o**4/18 - 10*o**3/9 - 4*o**2/3 - 2*o + 26. Factor p(m).
(m - 2)*(m + 2)*(5*m + 2)/3
Let v = 421 + -417. Let a(n) be the third derivative of 0*n + 3*n**2 - 1/270*n**5 + 0 - 1/108*n**v + 0*n**3. Factor a(k).
-2*k*(k + 1)/9
Determine n so that 27/7*n + 0 - 180/7*n**2 + 354/7*n**3 + 27/7*n**5 - 180/7*n**4 = 0.
0, 1/3, 3
Let v be (-21)/56 - (-9)/12. Let s(c) be the third derivative of 0 + c**2 + v*c**4 + 1/2*c**3 + 1/40*c**6 + 0*c + 3/20*c**5. Factor s(q).
3*(q + 1)**3
Let t be -1 + ((-49)/(-147))/((-3)/(-13)). Let r(d) be the first derivative of t*d + d**2 + 11 + 14/27*d**3. Factor r(s).
2*(s + 1)*(7*s + 2)/9
Let j(c) be the first derivative of -5*c**6/6 + 5*c**5 + 5*c**4/4 - 85*c**3/3 - 30*c**2 - 189. Let j(z) = 0. Calculate z.
-1, 0, 3, 4
Factor 2/9*h**4 - 17576/9*h + 57122/9 - 104/9*h**3 + 676/3*h**2.
2*(h - 13)**4/9
Let t = 6103 - 6101. Let -2*v + 1/2*v**3 - 1/2*v**2 + t = 0. Calculate v.
-2, 1, 2
Let d be ((-1)/2)/(66/36 - 2). What is x in 42*x - 98*x**d - 4 + 42*x**2 + 12 + 6*x = 0?
-2/7, 1
Let j(r) be the first derivative of 3*r**5/25 - 9*r**4/20 + 341