- l**2 - 1/6*l**3 + 1/60*l**5 + 3 - 1/120*l**6. Let m(k) be the second derivative of z(k). Factor m(i).
-(i - 1)**2*(i + 1)
Let r(i) be the third derivative of -i**5/120 - 19*i**4/24 - 361*i**3/12 + 274*i**2. Factor r(m).
-(m + 19)**2/2
Let w(q) = 3986*q**4 + 6897*q**3 - 2072*q**2 + 244*q + 1. Let o(v) = 1329*v**4 + 2299*v**3 - 691*v**2 + 79*v. Let d(m) = -14*o(m) + 4*w(m). Factor d(n).
-2*(n + 2)*(11*n - 1)**3
Let t be 1/2*(-5 + -3) - -10. Let n(m) = -m**3 - m + 1. Let y(a) = -8*a**3 - 4*a**2 - 6*a + 6. Let q(h) = t*n(h) - y(h). Factor q(b).
2*b**2*(b + 2)
Let x(t) be the third derivative of t**5/40 + 7*t**4/16 - 9*t**3/2 - 137*t**2 - 2. Let x(f) = 0. What is f?
-9, 2
Let m(g) = g + 2. Let v be m(1). Let z be 0/(-3) + 0 + 3. Determine q, given that 3*q + 3*q**4 - 12 - 6*q**2 + v*q**5 + 10 + 5 - 6*q**z = 0.
-1, 1
Let n(t) be the third derivative of 2*t**7/35 + 281*t**6/20 + 79521*t**5/80 + 9835*t**4/8 + 1225*t**3/2 - 560*t**2. Factor n(c).
3*(c + 70)**2*(4*c + 1)**2/4
Let c = 60 - -10. Let n = -760/11 + c. Let 18/11*q**2 + 14/11*q**3 + n*q + 2/11 + 4/11*q**4 = 0. Calculate q.
-1, -1/2
Let -5*q**3 + q**2 - 35 + 4*q**2 - 52*q**2 + 22*q**2 + 65*q = 0. Calculate q.
-7, 1
Suppose 1/8*c**3 + 957/8*c - 841/4 - 15/2*c**2 = 0. What is c?
2, 29
Let f(z) be the third derivative of -2*z**7/105 - z**6/2 - 13*z**5/5 - 37*z**4/6 - 8*z**3 + 29*z**2. Factor f(m).
-4*(m + 1)**3*(m + 12)
Let b(d) be the first derivative of d**4/2 - 74*d**3 + 219*d**2 - 218*d - 114. Find m, given that b(m) = 0.
1, 109
Let c(w) be the third derivative of -5*w**8/168 - w**7/6 - 3*w**6/8 - 5*w**5/12 - 5*w**4/24 + 733*w**2. Suppose c(a) = 0. Calculate a.
-1, -1/2, 0
Let j(c) be the second derivative of -c**5/150 - c**4/12 - 4*c**3/15 + 11*c**2 - 12*c. Let q(t) be the first derivative of j(t). Solve q(b) = 0 for b.
-4, -1
Suppose -2*w - 12 = 5*t, 50*w - 2*t + 8 = 54*w. Let 18/7*l**2 + 3/7*l**w - 12/7*l**3 - 12/7*l + 3/7 = 0. What is l?
1
Let y be -2 + (-2)/11 + (-33875)/(-15400). Let h(p) be the third derivative of -1/140*p**5 + 0 + 0*p - y*p**4 - 1/42*p**3 - 1/840*p**6 + 8*p**2. Factor h(r).
-(r + 1)**3/7
Let o(y) = 9*y - 36. Let g be o(-17). Let h = g + 192. Factor 10/3*x**2 + 2/3*x**5 - 2/3*x**4 + 0 - 2*x**h - 4/3*x.
2*x*(x - 1)**3*(x + 2)/3
Let x be 0/((-1)/1)*(-12 + (-525)/(-45)). Factor 4/9*a + 2/9*a**2 + x.
2*a*(a + 2)/9
Let w(c) = -c**3 + c**2 + c - 12. Let x(k) = 3*k**3 - 2*k**2 - 2*k + 35. Let f(d) = 11*w(d) + 4*x(d). Let l(t) be the first derivative of f(t). Factor l(a).
3*(a + 1)**2
Factor -1/4*y + 1/4*y**3 - 1/4*y**2 + 1/4.
(y - 1)**2*(y + 1)/4
Let q be (-3)/((-3)/4)*(4 + -3). Let b = q - 4. Let 2/3*v**4 + 2/3 - 4/3*v**2 + b*v + 0*v**3 = 0. What is v?
-1, 1
Suppose 347 = 5*v + 4*r + 32, 4*v - 2*r - 278 = 0. Factor v - 12*t + 20*t**2 - 67.
4*t*(5*t - 3)
Let o(h) be the second derivative of -16/15*h**6 + 5/2*h**4 + 0 + 2/3*h**3 - 18*h + 0*h**2 + 12/5*h**5. Factor o(j).
-2*j*(j - 2)*(4*j + 1)**2
Suppose -4/5*n + 32/5*n**2 + 8/5*n**3 - 16/5 - 4/5*n**5 - 16/5*n**4 = 0. What is n?
-4, -1, 1
Let 69*a**2 - 18*a + 39*a**4 - 6*a**5 + 7358*a**3 - 7442*a**3 + 1 - 1 = 0. What is a?
0, 1/2, 1, 2, 3
Suppose -4*f - 2*d = 142, -3*f + f - 51 = -3*d. Let t = f - -33. Factor 0*r + t - 2/13*r**2 + 2/13*r**3.
2*r**2*(r - 1)/13
Factor 72*k - 22*k**2 - 10*k**2 - 10*k + 10*k**2 + 12.
-2*(k - 3)*(11*k + 2)
Let r(z) be the third derivative of z**7/22680 + z**6/1620 - z**5/216 - 11*z**4/12 + 10*z**2. Let q(s) be the second derivative of r(s). Factor q(j).
(j - 1)*(j + 5)/9
Let h(i) = i**4 + 5*i**3 - 9*i**2 + 3*i + 4. Let l(y) = y**4 - y**3 + 1. Suppose -2*c = -4*c - 8. Let a(s) = c*l(s) + h(s). Factor a(k).
-3*k*(k - 1)**3
Let x(c) be the first derivative of -2*c**5/15 + 34*c**4/3 - 134*c**3/9 - 333. Factor x(v).
-2*v**2*(v - 67)*(v - 1)/3
Let y(x) be the second derivative of -x**5/50 + 34*x**4/15 - 407*x**3/5 + 2178*x**2/5 - 19*x. Factor y(s).
-2*(s - 33)**2*(s - 2)/5
Suppose -q = -3*c, -47*c = -43*c. Let x(f) be the second derivative of -2/9*f**3 - 2/3*f**2 + q + 1/6*f**5 + 7/36*f**4 + 1/30*f**6 - 2*f. Factor x(z).
(z + 1)**2*(z + 2)*(3*z - 2)/3
Determine y, given that 32/7*y - 2/7*y**2 - 30/7 = 0.
1, 15
Let p(z) be the first derivative of z**4/4 - 28*z**3/3 + 53*z**2/2 - 26*z - 36. Determine f, given that p(f) = 0.
1, 26
Let t(x) be the second derivative of -x**8/60480 + x**7/7560 + x**6/1620 - x**4/3 - 29*x. Let z(b) be the third derivative of t(b). Factor z(w).
-w*(w - 4)*(w + 1)/9
Let j(a) be the third derivative of -a**8/4032 + a**7/1008 + a**6/72 + a**5/15 - a**2. Let q(p) be the third derivative of j(p). Let q(n) = 0. Calculate n.
-1, 2
Factor 3/2*w**4 + 11/6*w**3 - 8/3*w**2 + 0 - 2/3*w.
w*(w - 1)*(w + 2)*(9*w + 2)/6
Suppose -5000/11 - 250*w - 10/11*w**3 - 450/11*w**2 + 2/11*w**4 = 0. Calculate w.
-5, 20
Let y(h) = -8*h**2 - 33*h - 34. Suppose 0*k - 30 = -2*k. Let d(t) = -55*t**2 - 230*t - 240. Let f(a) = k*y(a) - 2*d(a). Find w such that f(w) = 0.
-2, -3/2
Suppose -3*o + 85 = -20. Let k be ((-189)/o - -6)/(2/2). Factor -k*l + 2/5 + 1/5*l**2.
(l - 2)*(l - 1)/5
Let n(k) = -7*k**3 - 127*k**2 - 2904*k - 21296. Let a(c) = -8*c**3 - 126*c**2 - 2904*c - 21296. Let d(g) = -5*a(g) + 6*n(g). Factor d(u).
-2*(u + 22)**3
Factor 9/7*w**2 - 33/7*w + 18/7.
3*(w - 3)*(3*w - 2)/7
Let p(u) = 16*u - 50*u + 0*u**2 + 75 + 5*u**2 - 2*u**2. Let o(l) = -21*l**2 + 237*l - 525. Let j(y) = -4*o(y) - 27*p(y). Factor j(a).
3*(a - 5)**2
Let c(w) be the third derivative of -w**5/75 + 7*w**4/30 - 65*w**2. Solve c(o) = 0.
0, 7
Suppose -2*p + 8 - 2 = 0. Suppose 47 + 85*x**4 + 111*x**4 - 357*x**p - 43 - 48*x + 205*x**2 = 0. Calculate x.
1/4, 2/7, 1
Suppose 0 = 4*d - 5*o - 31, 24 = 6*d - 3*d - 4*o. Determine g, given that 0*g + 0*g**3 + 2/13*g**d + 0 - 2/13*g**2 = 0.
-1, 0, 1
Factor -7/2*a + 1/2*a**2 + 6.
(a - 4)*(a - 3)/2
Suppose 0 = 5*k - 2*f - 10, k + 3*f + 53 = 38. Let o(y) be the third derivative of k*y + 0 - 1/48*y**4 + 0*y**3 + 1/240*y**5 - y**2. Factor o(w).
w*(w - 2)/4
Let d(o) be the first derivative of -1/30*o**6 + 0*o**2 - 4 + 1/10*o**4 + 0*o + 1/25*o**5 + 0*o**3. Solve d(g) = 0.
-1, 0, 2
Let q(x) be the first derivative of 1/2*x**6 + 0*x**2 - 16 - 3/4*x**4 + 2*x**3 - 6/5*x**5 + 0*x. Find m, given that q(m) = 0.
-1, 0, 1, 2
Let i(h) be the second derivative of 5/2*h**2 + 3*h + 5/36*h**4 - 25/18*h**3 + 0 + 1/12*h**5. Factor i(k).
5*(k - 1)**2*(k + 3)/3
Let q(m) be the second derivative of -92/5*m**3 + 0 - 12167/50*m**5 - 529/5*m**4 + 17*m - 8/5*m**2. Find t, given that q(t) = 0.
-2/23
Let y be 15 + -12 + -2 + 1. Factor 0*g + 0 + 1/5*g**y.
g**2/5
Let z(v) be the second derivative of 315/2*v**4 + 343/10*v**6 + 588/5*v**5 + 81/2*v**2 + 0 + 108*v**3 + 10*v. Factor z(s).
3*(s + 1)*(7*s + 3)**3
Let g(t) be the first derivative of -t**7/490 + t**6/35 - 6*t**5/35 + 4*t**4/7 - 8*t**3/7 + 17*t**2 - 2. Let k(c) be the second derivative of g(c). Factor k(f).
-3*(f - 2)**4/7
Let g = -27 + 63. Factor -156*u**2 - 85*u - 1 - 19 - 31*u + g*u**3.
4*(u - 5)*(3*u + 1)**2
Factor -1/3*w - 1/3*w**3 - 2 + 4/3*w**2.
-(w - 3)*(w - 2)*(w + 1)/3
Let p(r) be the first derivative of -3*r**4/4 + 35*r**3 - 741*r**2/2 - 3249*r - 21. Suppose p(q) = 0. What is q?
-3, 19
Let n(a) be the third derivative of -a**8/4032 + 11*a**5/60 + 9*a**2. Let b(r) be the third derivative of n(r). Factor b(w).
-5*w**2
Let r(u) be the second derivative of -u**6/150 + 11*u**5/100 - 7*u**4/12 + 5*u**3/6 - 4*u + 7. Let r(b) = 0. Calculate b.
0, 1, 5
Let q(b) be the third derivative of 0 + 1/42*b**4 + 0*b - 1/14*b**3 - 28*b**2 - 1/420*b**5. Factor q(s).
-(s - 3)*(s - 1)/7
Let d(f) be the second derivative of f**5/5 - 11*f**4/3 + 56*f**3/3 - 106*f. Factor d(w).
4*w*(w - 7)*(w - 4)
Let n(j) be the first derivative of -5*j**3/3 - 10*j**2 - 20*j - 16. Let n(k) = 0. What is k?
-2
Let j be 168*((-4)/(-8))/((-2)/(-2)). Factor -18*v**2 + 96*v**2 + 42 + 9*v**3 + 195*v - j*v.
3*(v + 1)*(v + 7)*(3*v + 2)
Suppose 5*y + 4 = -2*w, -2*w - 3*w - 10 = 4*y. Suppose -9*s + 5 + 13 = y. Factor -5/2*r + 7/2*r**s - 1.
(r - 1)*(7*r + 2)/2
Let d = -22/21 + 359/336. Let u(g) be the second derivative of 0 + d*g**4 + 1/8*g**2 + 1/12*g**3 - 2*g. Suppose u(s) = 0. Calculate s.
-1
Let o(r) be the second derivative of 0 + 6*r - 3/8*r**4 + 9/2*r**2 + 1/20*r**5 + 0*r**3. Let h(a) be the first deriva