*(q - 1)**3*(q + 1)
Suppose -192 + 168 = -6*x. Let o be x/12 + 1*1/(-3). Factor 0 + 2/3*y**2 + o*y - 2/3*y**3.
-2*y**2*(y - 1)/3
Let -7*i**2 - 100*i - 654 + 5*i**2 - 596 = 0. What is i?
-25
Let w(y) = 6*y**3 + 38*y**2 - 152*y + 232. Let p(q) = q**3 + q**2 + q + 1. Let r(t) = 28*p(t) - 4*w(t). Find f such that r(f) = 0.
3, 25
Let s(z) be the second derivative of z**5/20 + z**4/12 - 4*z**3/3 - 6*z**2 + 41*z + 6. Factor s(w).
(w - 3)*(w + 2)**2
Let b = -536/13 + 4876/117. Factor b - 2/9*k**5 + 16/9*k**2 + 4/9*k**3 + 14/9*k - 4/9*k**4.
-2*(k - 2)*(k + 1)**4/9
Let h(j) be the second derivative of 0 + 0*j**3 + 0*j**2 + 1/48*j**4 - 11*j. Determine r so that h(r) = 0.
0
Let m(d) = d**3 - 6*d**2 + 4*d + 7. Let l be m(5). Let z(t) = 2*t + 102. Let n be z(-49). Factor -1/5*y**n + 2/5 - y + 1/5*y**3 + 3/5*y**l.
-(y - 1)**3*(y + 2)/5
Let u(x) = x**2 + 13*x + 14. Let l = -19 - -7. Let t be u(l). Factor -t*n**2 + 12*n - 3*n**2 + 14*n**2.
3*n*(3*n + 4)
Let u be 1/5 - (17 + (-4784)/280). Suppose 2/7*b + 2/7*b**2 - u*b**3 + 0 - 2/7*b**4 = 0. What is b?
-1, 0, 1
Let i(s) be the first derivative of s**8/336 + s**7/42 - s**6/72 - s**5/6 - 2*s**3/3 - 7. Let r(c) be the third derivative of i(c). Solve r(l) = 0 for l.
-4, -1, 0, 1
Suppose s + 3*z - 7 = 0, 4*s - 14 = 6*z - 4*z. Suppose -4*r**2 + 3*r + s + r + 6 - 2 = 0. What is r?
-1, 2
Let h(v) be the third derivative of v**7/945 + v**6/60 + v**5/10 + 31*v**4/108 + 4*v**3/9 - 4*v**2 - 3*v. Factor h(l).
2*(l + 1)**2*(l + 3)*(l + 4)/9
Let q(m) be the third derivative of -m**6/120 - 3*m**5/40 - m**4/4 + 5*m**3/2 - 7*m**2. Let l(w) be the first derivative of q(w). Find d such that l(d) = 0.
-2, -1
Let y(b) = 3*b**4 + 80*b**3 - 147*b**2 + 64*b. Let w(x) = x**4 + 20*x**3 - 37*x**2 + 16*x. Let g(a) = 22*w(a) - 6*y(a). Let g(s) = 0. Calculate s.
0, 1, 8
Find a, given that 10*a - 9*a**3 + 0*a**3 + 5*a**2 - 11*a**3 - 15*a**4 = 0.
-1, 0, 2/3
Let s be -4*(-1)/4 + 0 + 4. Let c(z) = 6*z**3 - 23*z**2 - 6*z + 18. Let y(w) = 15*w**3 - 57*w**2 - 15*w + 45. Let d(g) = s*y(g) - 12*c(g). Factor d(f).
3*(f - 3)*(f - 1)*(f + 1)
Let j(m) be the third derivative of 0 + 1/72*m**4 - 1/252*m**7 - 7/360*m**5 - 11*m**2 + 1/2016*m**8 + 1/80*m**6 + 0*m + 0*m**3. Suppose j(o) = 0. What is o?
0, 1, 2
Let c = 17201/40 + -430. Let b(u) be the third derivative of 0 - 1/4*u**4 + c*u**6 + 0*u**3 + 8*u**2 + 0*u + 1/20*u**5. Factor b(k).
3*k*(k - 1)*(k + 2)
Let q(g) be the second derivative of 4*g + 5/3*g**3 + 5/12*g**4 + 5/2*g**2 + 0. Solve q(j) = 0 for j.
-1
Let c be 6/(-16) - 327/24. Let v = 16 + c. Solve -8 - h**5 - 5*h**5 + 14*h**v + 8*h**5 - 5*h**4 - h**4 - 2*h**3 = 0.
-1, 1, 2
Let t(u) be the third derivative of u**6/300 - 2*u**5/15 + 19*u**4/60 - 111*u**2. Determine m, given that t(m) = 0.
0, 1, 19
Let m(r) be the second derivative of -r**5/60 - r**4/8 - r**3/3 + 6*r**2 - 8*r. Let d(g) be the first derivative of m(g). Let d(z) = 0. Calculate z.
-2, -1
Suppose -d = -3*b + 12, -5*b + 1419*d + 20 = 1414*d. Factor -5/9*f**3 + 1/9*f**b + 0 - 4/9*f + 8/9*f**2.
f*(f - 2)**2*(f - 1)/9
Let f(k) = k**3 - 2*k**2 + 4*k - 6. Let u be f(3). Let r = u + -13. Factor 16*y + 2 - y**2 + 5*y**r + 14.
4*(y + 2)**2
Let j(n) be the second derivative of -n**4/12 + 40*n**3/3 - 800*n**2 + 3*n - 20. Factor j(f).
-(f - 40)**2
Let j(x) be the first derivative of -x**7/1155 + x**6/165 - x**5/110 + x**2/2 - 22. Let d(f) be the second derivative of j(f). Factor d(p).
-2*p**2*(p - 3)*(p - 1)/11
Let k(u) = 2*u**2 - 2*u + 3. Let h be k(0). Let m(p) be the third derivative of 0 - 5*p**2 + 8/3*p**h + 1/60*p**5 + 1/3*p**4 + 0*p. Solve m(v) = 0.
-4
Let w(n) = -n**2 - n + 1. Let v(p) = -p**3 + 11*p**2 + 12*p - 20. Let g(q) = 3*v(q) + 24*w(q). Find i, given that g(i) = 0.
-2, 2, 3
Let n(s) be the first derivative of s**8/2800 - s**7/600 + s**6/360 - s**5/600 + 14*s**3/3 - 13. Let k(a) be the third derivative of n(a). Factor k(y).
y*(y - 1)**2*(3*y - 1)/5
Suppose -13*w + 44 = -2*w. Let m(p) be the first derivative of 0*p**2 + 1/5*p - 1/15*p**3 + w. Factor m(y).
-(y - 1)*(y + 1)/5
Let d(f) be the third derivative of -f**7/280 + f**6/30 - f**5/10 - 7*f**3/6 - 13*f**2. Let g(h) be the first derivative of d(h). Factor g(v).
-3*v*(v - 2)**2
Let v(m) = -m**3 + m**2. Let c(p) = -18*p + 0*p + 28*p**2 - 6*p**2 - 12*p**3. Let z(l) = -c(l) + 10*v(l). Factor z(h).
2*h*(h - 3)**2
Let c(n) be the second derivative of 15/4*n**4 + 13*n + 5/6*n**6 - 5*n**2 + 5/6*n**3 + 0 - 13/4*n**5. Suppose c(m) = 0. Calculate m.
-2/5, 1
Let b = -8 - -15. Factor 12*r - r**4 - 3*r**4 - 4*r**2 - 12*r**3 + 7 + b - 6.
-4*(r - 1)*(r + 1)**2*(r + 2)
Suppose -806 = 7*i - 827. Let m(u) be the third derivative of -1/66*u**4 + 1/330*u**5 + 0 + 1/33*u**i + 0*u - 7*u**2. Factor m(f).
2*(f - 1)**2/11
Let i(h) be the first derivative of h**4/30 - h**3/3 + 4*h**2/5 + 17*h + 22. Let y(j) be the first derivative of i(j). Determine b so that y(b) = 0.
1, 4
Let q = 95/3 + -31. Let y(v) be the first derivative of 5/24*v**4 - v**2 + q*v - 4 + 1/6*v**3. Factor y(d).
(d - 1)*(d + 2)*(5*d - 2)/6
Let d be -106*(-5)/10*1. Factor -4*a + 15*a**2 - 68*a**3 + 5*a**4 + d*a**3 - a.
5*a*(a - 1)**3
Let k(n) be the first derivative of 5*n**3/3 + 195*n**2 + 7605*n + 3. Factor k(h).
5*(h + 39)**2
Let o(h) be the third derivative of -7*h**8/576 + h**7/24 - h**6/16 - 17*h**5/30 + 20*h**2. Let z(x) be the third derivative of o(x). Factor z(t).
-5*(7*t - 3)**2
Let q(a) = 15*a**3 + 130*a**2 + 289*a + 65. Let t(m) = m**3 + 2*m**2 - m - 1. Let y(w) = q(w) + t(w). Factor y(d).
4*(d + 4)**2*(4*d + 1)
Factor 7/4*b**2 - 4 + 1/4*b**3 + 2*b.
(b - 1)*(b + 4)**2/4
Let z = 58 + -58. Let u(t) be the second derivative of 1/10*t**6 + z - 6*t + 0*t**3 + 1/14*t**7 + 0*t**2 + 0*t**5 + 0*t**4. Solve u(s) = 0 for s.
-1, 0
Let q(j) be the second derivative of j**4/12 + 3*j**3 + 81*j**2/2 - 8*j - 3. Solve q(y) = 0.
-9
Let b(u) be the third derivative of -1/180*u**5 + 3*u**2 + 0 + 1/9*u**3 + 0*u + 1/72*u**4. Factor b(z).
-(z - 2)*(z + 1)/3
Find n, given that -69/2*n**4 - 9/2*n**5 - 66*n**3 + 0*n - 30*n**2 + 0 = 0.
-5, -2, -2/3, 0
Let a(l) be the second derivative of 1/130*l**5 + 0*l**3 + 3*l - 1/273*l**7 + 0*l**2 + 0 + 0*l**6 + 0*l**4. Let a(u) = 0. Calculate u.
-1, 0, 1
Let o(k) be the first derivative of -k**6/24 + 13*k**5/20 - 33*k**4/8 + 27*k**3/2 - 189*k**2/8 + 81*k/4 + 69. Solve o(g) = 0 for g.
1, 3
Let p(o) be the third derivative of o**6/40 - o**5/20 - o**4/2 + 2*o**3 + 56*o**2. Determine m so that p(m) = 0.
-2, 1, 2
Let w(a) be the third derivative of -1/42*a**7 - 13*a**2 - 5/12*a**4 - 5/12*a**5 + 0 + 0*a**3 + 0*a - 1/6*a**6. Factor w(k).
-5*k*(k + 1)**2*(k + 2)
Let p be ((-22)/(-77))/((-64)/(-168)). Suppose 4*n = 5*n. Let 0*c**2 + n*c - p*c**5 + 0 - 1/4*c**4 + 0*c**3 = 0. Calculate c.
-1/3, 0
Determine g, given that -35*g**4 - 55*g**2 + 3*g - 9*g - g - 80*g**3 - 3*g = 0.
-1, -2/7, 0
Let m be (-15)/6*((-5)/3 + (-84)/(-180)). Factor -2/3 - 4/3*f**m + 2/3*f**2 + 4/3*f.
-2*(f - 1)*(f + 1)*(2*f - 1)/3
Let q(x) = -41*x + 32. Let l be q(-8). Let f = -2512/7 + l. Determine o so that f*o + 12/7 - 4/7*o**2 = 0.
-1, 3
Let k be (1 + 1/(-6))*18. Let q be (-5)/15*10*(-1)/k. Find o such that 2/9*o**2 + 0 - 2/9*o**3 + q*o - 2/9*o**4 = 0.
-1, 0, 1
Let -3*b**2 - 4 - 71*b + 77*b + 5 + 8 = 0. What is b?
-1, 3
Let s(k) = 4*k**3 - k**2 + 16*k + 6. Let h(c) = 9*c**3 - c**2 + 37*c + 12. Let b(n) = -6*h(n) + 14*s(n). Factor b(x).
2*(x - 3)*(x - 2)*(x + 1)
Let b(z) be the second derivative of -z**4/12 + 2*z**3/3 + 5*z**2/2 - 48*z. Determine v so that b(v) = 0.
-1, 5
Suppose b - 17 = -3*a, a - 127*b + 131*b - 24 = 0. Factor 2/11*f**a + 0 - 6/11*f**3 - 2/11*f + 6/11*f**2.
2*f*(f - 1)**3/11
Let l(d) be the first derivative of -4/3*d + 7/9*d**2 + 2/9*d**3 + 12. Factor l(m).
2*(m + 3)*(3*m - 2)/9
Suppose 0 = -c - 3*g, 4*c - 2*g + 0*g - 42 = 0. Let z = 11 - c. Factor -6 - 20*k**2 - 5*k**2 - 21*k - 9*k**3 + k**z.
-3*(k + 1)**2*(3*k + 2)
Suppose 25*q + 6 = 28*q. Let f(h) be the second derivative of -1/15*h**4 + 1/30*h**3 + 0*h**q + 0 + h. Determine l, given that f(l) = 0.
0, 1/4
Let c(w) be the third derivative of 2*w**8/105 - 8*w**7/105 + w**6/75 + 17*w**5/75 - 11*w**4/30 + 4*w**3/15 + w**2 - 3. Let c(u) = 0. Calculate u.
-1, 1/2, 2
Let p be (-24 + -6)/6 - 117/(-1). Let f be ((-84)/p)/((-6)/16). Factor 