Let c(i) = 11*i**3 - 67*i**2 + 61*i + 53. Let u(x) = -17*x**3 + 101*x**2 - 91*x - 79. Let b(d) = 7*c(d) + 5*u(d). Factor b(z).
-4*(z - 3)*(z - 2)*(2*z + 1)
Determine s, given that 14*s**2 + 4*s**4 + 22309*s - 32*s**3 - 22277*s + 46*s**2 - 64 = 0.
-1, 1, 4
Let j be ((-141)/(-235))/(1/5). Let n(t) be the second derivative of -8*t + 1/4*t**j + 0*t**2 + 1/24*t**4 + 0. Find u, given that n(u) = 0.
-3, 0
Suppose 22/3 - 1/3*y**2 + 3*y = 0. What is y?
-2, 11
Let p = 13828 + -13825. Factor -16/7*n**p - 528/7*n + 144/7 - 188/7*n**2.
-4*(n + 6)**2*(4*n - 1)/7
Let u = -8329/149280 + 18/311. Let b(o) be the third derivative of 0 + o**2 + 0*o + 0*o**3 - 1/96*o**4 - 1/120*o**5 - u*o**6. Let b(a) = 0. Calculate a.
-1, 0
Let n(v) be the first derivative of v**4/10 - 4*v**3/15 + v**2/5 - 139. What is x in n(x) = 0?
0, 1
Let c be (-9)/(180/(-100)) - -1. Factor -3/2*l**3 + c*l**2 + 3/2*l - 6.
-3*(l - 4)*(l - 1)*(l + 1)/2
Suppose 0*p - 6 = -p. Factor -q - 8*q**3 + p*q**3 + 3*q.
-2*q*(q - 1)*(q + 1)
Let b be 5 + 1 - ((-48)/112 + (-124)/(-28)). Factor 3/2*a**4 + 0*a + 0 - 15/2*a**3 + 6*a**b.
3*a**2*(a - 4)*(a - 1)/2
Determine k, given that 16/7 - 12/7*k**4 - 24/7*k + 22/7*k**3 + 2/7*k**5 - 4/7*k**2 = 0.
-1, 1, 2
Factor 4/11*y + 0 + 80/11*y**3 + 38/11*y**4 + 46/11*y**2.
2*y*(y + 1)**2*(19*y + 2)/11
Let d = 556 + -556. Let a(w) be the second derivative of -6*w - 1/15*w**4 + 4/15*w**3 + d + 0*w**2. Determine n, given that a(n) = 0.
0, 2
Let w be (5/15)/((-2)/(-102)). Factor w*h**3 + h**2 - 7*h**3 - 9*h**3.
h**2*(h + 1)
Determine o, given that 12*o**2 - 12*o**4 - 8914*o**3 + 8906*o**3 - 8*o**4 = 0.
-1, 0, 3/5
Let y be (-16*(-1)/10)/(2/5). Suppose 114*k**y + 27 + 22*k - 730*k**2 - 2*k + 13 + 66*k**4 - 5*k**3 = 0. Calculate k.
-2, -2/9, 1/4, 2
Let a(s) be the first derivative of -4/5*s**5 + 0*s**2 + 0*s**3 + 14 - 1/2*s**4 + 0*s - 1/3*s**6. Solve a(o) = 0.
-1, 0
Let t(i) = i**2 - 34*i + 124. Let x be t(4). Let b(d) be the first derivative of 1/2*d**3 + 8 - 3/4*d**x + 0*d - 1/8*d**6 - 1/8*d**2 + 1/2*d**5. Factor b(r).
-r*(r - 1)**3*(3*r - 1)/4
Let h(g) be the third derivative of -g**8/5376 - g**7/2016 + g**6/288 - g**4/4 - 8*g**2. Let p(c) be the second derivative of h(c). Solve p(o) = 0 for o.
-2, 0, 1
Suppose 74*p - 4 + 4 = 0. Determine s so that 0*s - 2/7*s**5 - 2/7*s**4 + 2/7*s**2 + p + 2/7*s**3 = 0.
-1, 0, 1
Let n be (-4 - 55/(-10)) + (-33)/(-6). Let z be ((-90)/(-21))/(-3)*(-7)/n. Factor 2/7*d**3 + 2/7*d**2 + 0*d + 6/7*d**5 - z*d**4 + 0.
2*d**2*(d - 1)**2*(3*d + 1)/7
Let y(j) = -4*j**3 - 2*j**2 + 4*j + 2. Let w(i) = i**3 + 5*i**2 + 6*i + 10. Let u be w(-4). Let x(m) = m**3 - m. Let r(h) = u*y(h) - 6*x(h). Factor r(n).
-2*(n - 1)*(n + 1)*(7*n + 2)
Let p(m) be the first derivative of -7/3*m**3 + 0*m**4 + 1/540*m**5 + 0*m**2 + 0*m + 1 + 1/1620*m**6. Let g(w) be the third derivative of p(w). Factor g(z).
2*z*(z + 1)/9
Let q(m) be the first derivative of m**8/2520 + m**7/630 - m**6/540 - m**5/90 - 2*m**3/3 + 20. Let z(p) be the third derivative of q(p). Solve z(d) = 0.
-2, -1, 0, 1
Find i such that -3/4 - 6*i**4 - 9/4*i**2 - 71/4*i**3 + 4*i**5 + 19/4*i = 0.
-1, 1/4, 3
Factor 4*y - 2*y - 211*y**5 + y - 4*y**4 - 2*y**3 + 210*y**5 + 4*y**2.
-y*(y - 1)*(y + 1)**2*(y + 3)
Suppose 4*o**2 + o**3 - 8 + 6*o**2 + o**2 - 10*o - 17*o**2 + 5*o**2 = 0. What is o?
-2, -1, 4
Let j be 2 + (-16)/(-4) + -1. Factor 6*y**2 - 3*y**3 - j + 5 + 0 - 3*y.
-3*y*(y - 1)**2
Let r(s) be the third derivative of -2*s**7/525 - 2*s**6/75 + 4*s**5/25 - 5*s**2 - 7. Suppose r(w) = 0. What is w?
-6, 0, 2
Let p be (-1*1)/((-6)/30). Factor 32*x**4 - 20*x**p - 26*x**5 - 24*x**5 + 74*x**5.
4*x**4*(x + 8)
Let z(m) be the third derivative of m**7/105 + m**6/60 - m**5/10 - m**4/12 + 2*m**3/3 + 77*m**2. Factor z(u).
2*(u - 1)**2*(u + 1)*(u + 2)
Let p(t) be the second derivative of 0*t**3 + 1/220*t**5 + 0 + 0*t**2 - 5/132*t**4 + 31*t. Factor p(z).
z**2*(z - 5)/11
Let k(t) be the second derivative of -3/7*t**3 - 8*t + 27/14*t**2 + 1/28*t**4 + 0. Factor k(d).
3*(d - 3)**2/7
Let i(j) be the first derivative of j**6/15 - 14*j**5/25 + 900. What is p in i(p) = 0?
0, 7
Let q be 4 + (-3 - 9/(-3)) - 2. Suppose 5*o = q*z + 27, 2*o - 5*z - 23 = -8. Factor -1/4*x**o + 1/4*x**4 + 1/4*x**3 + 0 + 0*x - 1/4*x**2.
-x**2*(x - 1)**2*(x + 1)/4
Let r(v) = -2*v**5 - 7*v**4 + 17*v**3 + 5*v**2 + 5*v + 5. Let u(a) = a**5 + 4*a**4 - 9*a**3 - 3*a**2 - 3*a - 3. Let o(j) = -3*r(j) - 5*u(j). Factor o(w).
w**3*(w - 2)*(w + 3)
Let s(b) = -b**3 - 11*b**2 + 43*b + 17. Let w be s(-14). Factor 0*l**2 + 0 - 8/13*l + 2/13*l**w.
2*l*(l - 2)*(l + 2)/13
Let v(k) = k - 16. Let o be v(17). Let h be -5 + o + (-20)/(-5). Determine i, given that -2/3*i**2 + 0 + h*i = 0.
0
Let 2/5*o**4 - 16/15*o - 56/15*o**3 + 22/5*o**2 + 0 = 0. Calculate o.
0, 1/3, 1, 8
Let i = -17 + 20. Suppose 0 = -p + 3*u + 16, 2*p + 6*u - 2*u = -8. Factor -3/4*m - 9/2*m**i + 3*m**2 + 0 + 3*m**p - 3/4*m**5.
-3*m*(m - 1)**4/4
Let k be ((-33)/110)/(21/(-14)). Factor 0*h + 0 - 6/5*h**2 - k*h**3.
-h**2*(h + 6)/5
Suppose 4/9*b**4 + 0 + 0*b - 8/3*b**3 + 32/9*b**2 = 0. What is b?
0, 2, 4
Let u(n) be the second derivative of -n**4/24 + n**3/6 + 61*n. Factor u(s).
-s*(s - 2)/2
Suppose 15 = -h - 2*h. Let c(j) = -j - 2. Let x be c(h). Factor 8/7 + 6/7*z**2 - 12/7*z - 1/7*z**x.
-(z - 2)**3/7
Let c(h) be the third derivative of h**8/1260 + h**7/1575 - h**6/150 + h**5/450 + h**4/90 + 138*h**2 + 2. Solve c(v) = 0 for v.
-2, -1/2, 0, 1
Let g be ((-44)/33)/((-1)/3). Suppose -26*p**5 - 9*p**3 - 3*p**2 + 29*p**5 + 5*p**3 - 5*p**3 + 3*p**g + 6*p = 0. What is p?
-2, -1, 0, 1
Let h(f) be the first derivative of -3*f**4/28 + 65*f**3/7 + 3*f**2/14 - 195*f/7 - 458. Find c such that h(c) = 0.
-1, 1, 65
Factor -13 + 16*y + 2566*y**2 - 3 - 2570*y**2.
-4*(y - 2)**2
Let s(l) be the first derivative of 0*l - 1/2*l**4 - 4/15*l**5 - 1/18*l**6 - 4/9*l**3 + 18 - 1/6*l**2. Solve s(w) = 0.
-1, 0
Let c(z) be the second derivative of 0 + 0*z**2 + 0*z**3 + 1/6*z**6 + 5/3*z**4 + z**5 - 3*z. Factor c(g).
5*g**2*(g + 2)**2
Let d be (2/6)/(-14 - 1778/(-126)). Determine v so that -12 - 18*v + 21/2*v**3 + d*v**2 - 3/2*v**5 + 0*v**4 = 0.
-2, -1, 2
Let r(n) be the first derivative of 2*n**2 - 8*n - 1 - 1/6*n**3. Determine a, given that r(a) = 0.
4
Suppose -5*h + 26 = 5*v - 2*v, -4*h + 12 = -2*v. Let s be 10/(-35) + -17*(-6)/357. What is x in 12/7*x**v - 8/7*x + s - 4/7*x**3 = 0?
0, 1, 2
Let d(c) = 255 + 70*c**3 + 79*c + c**4 - 130 - 161*c**2 - 136. Let y(a) = a**4 + 35*a**3 - 81*a**2 + 39*a - 6. Let s(m) = -6*d(m) + 11*y(m). Factor s(b).
5*b*(b - 3)**2*(b - 1)
Let z(j) be the first derivative of 5*j**3/3 + 30*j**2 - 369. Factor z(m).
5*m*(m + 12)
Let o be 62/22 + (-42)/(-231). Let m(l) be the third derivative of -1/90*l**5 + 5*l**2 + 1/9*l**o + 0*l + 0*l**4 + 0. Factor m(u).
-2*(u - 1)*(u + 1)/3
Let j(v) be the third derivative of 0*v + 0 - 16*v**2 + 4/9*v**3 + 1/6*v**4 + 1/45*v**5. Factor j(b).
4*(b + 1)*(b + 2)/3
Let b(s) = -4*s - 1. Let y(m) = -m. Let p(d) = -b(d) + 3*y(d). Let v(f) = -3*f**2 - 5*f - 2. Let k(a) = 2*p(a) + v(a). Solve k(j) = 0.
-1, 0
Let p = -961 - -962. Determine d so that 1/2*d - 1/2*d**3 - p + d**2 = 0.
-1, 1, 2
Let n(d) = -d. Let i be n(-7). Let b be (-3 + i)*(1 + 0). What is a in -16*a**4 + 34*a**b - 15*a**4 + 6*a**2 - 9*a**3 = 0?
0, 1, 2
Let u(q) be the first derivative of 0*q + 0*q**3 + 1/18*q**4 - 2/45*q**5 + 0*q**2 - 10. Let u(v) = 0. What is v?
0, 1
Let l be 2/(-8)*(-15 + 17)*0. Factor l*b**2 + 2/7 - 3/7*b + 1/7*b**3.
(b - 1)**2*(b + 2)/7
Let p(l) = 5*l**4 + 9*l**3 + 4. Let g(m) = 10*m**4 - 5*m + 5*m + 3*m**3 + 14*m**3 + 7. Let d(z) = 4*g(z) - 7*p(z). Determine v, given that d(v) = 0.
-1, 0
Let d = -2/5211 - -15637/10422. Let c(l) be the first derivative of 7 + 0*l**3 + d*l**2 + 0*l - 3/4*l**4. Factor c(z).
-3*z*(z - 1)*(z + 1)
Factor 363/2 - 33*a + 3/2*a**2.
3*(a - 11)**2/2
Let u = 18 + -14. Suppose -u*m = 6*m. Find j, given that -4/11*j**3 + 4/11*j - 2/11 + 2/11*j**4 + m*j**2 = 0.
-1, 1
Factor 1035*b**5 - 76*b**4 + 707*b**3 - 1033*b**5 + 15*b**3.
2*b**3*(b - 19)**2
Let a(d) = 25*d**4 - 7*d**3 + 9*d**2 + 41*d. Let q(m) = -3*m**4 + m**3 - m**2 - 5*m. Let n(p) = -6*a(p) - 51*q(p). Suppose n(f) = 0. Calculate f.
-1, 0, 1, 3
Find n, given that -36 - 112/3*n - 4/3*n**2 = 0.
-27, -1
Let l(s) be the third derivat