 2/11*k**4 + 12/11*k**3 + w*k.
-2*(k - 2)**2*(k - 1)**2/11
Let o = 52 + -48. Let l be ((-2)/3)/((-12)/18). Let d(u) = 5*u**2 - 2*u + 5. Let b(t) = -t**2 + t - 1. Let w(v) = l*d(v) + o*b(v). Factor w(x).
(x + 1)**2
Let j(h) be the first derivative of -6*h**5/5 - 9*h**4/4 + 2*h**3 + 9*h**2/2 + 159. Factor j(u).
-3*u*(u - 1)*(u + 1)*(2*u + 3)
Let l(b) be the third derivative of b**7/945 + 74*b**6/135 + 11099*b**5/135 + 3626*b**4/9 + 2401*b**3/3 + 82*b**2. Determine a, given that l(a) = 0.
-147, -1
Let r(n) = 7*n**5 - n**4 + 2*n**3 + 6*n**2 + n. Let h(s) = -s**5 - s**4 - s. Let b(c) = 5*h(c) + r(c). Factor b(m).
2*m*(m - 2)*(m - 1)**2*(m + 1)
Let j(o) be the second derivative of 1/15*o**6 + 2/3*o**2 + 0 - 1/2*o**4 - 1/30*o**5 - 1/3*o**3 - 41*o. Let j(z) = 0. Calculate z.
-1, 1/3, 2
Let l(d) be the second derivative of 1/60*d**4 - 16*d + 0*d**2 + 0 + 1/30*d**3. Factor l(n).
n*(n + 1)/5
Let k = 20 - -1. Factor -27*x + 8*x**3 - 14*x**3 - 63*x**2 - 21*x**3 - k*x - 12.
-3*(x + 1)*(3*x + 2)**2
Let w = 347/1113 - 14/53. Let x(q) be the second derivative of w*q**7 + 0*q**2 + 1/3*q**4 - 1/10*q**5 + 3*q + 0*q**3 + 0 - 2/15*q**6. Factor x(u).
2*u**2*(u - 2)*(u - 1)*(u + 1)
Let w = -9794 + 9796. Suppose 9/7*y**w - 12/7*y**3 + 0*y + 3/7*y**4 + 0 = 0. What is y?
0, 1, 3
Let g(n) be the first derivative of n**6/360 - n**5/30 + n**4/8 + 11*n**3/3 + 6. Let l(r) be the third derivative of g(r). Factor l(m).
(m - 3)*(m - 1)
Suppose -6925*d + 6893*d + 160 = 0. Find l, given that 17/4*l**2 - 1/2*l - 39/4*l**3 - 11/4*l**d + 0 + 35/4*l**4 = 0.
0, 2/11, 1
Let u be -7 + -10 + 3 - -3 - -13. Factor 3/8*x**u - x + 1/2.
(x - 2)*(3*x - 2)/8
Suppose -4*y + 3*y + 3 = 0. Factor -4*n - n + 15*n - 10*n**y - 5*n**2 + 5*n**4.
5*n*(n - 2)*(n - 1)*(n + 1)
Let f(m) be the first derivative of -m**8/1008 + m**6/180 - m**4/72 - 17*m**2/2 - 14. Let q(x) be the second derivative of f(x). Find v such that q(v) = 0.
-1, 0, 1
Let i be (39/12 - 4)*-4. Factor 2*o**3 + 3*o**i - 4*o**3 - o + 0*o**3.
o*(o - 1)*(o + 1)
Let v(b) be the first derivative of b**3 - 87*b**2/2 + 84*b - 342. Find s, given that v(s) = 0.
1, 28
Let 6/13*v**2 + 0 + 0*v - 2/13*v**3 = 0. What is v?
0, 3
Let m(n) be the third derivative of -5/336*n**8 + 4/3*n**5 - 4*n**2 + 20/3*n**4 + 0 + 0*n + 40/3*n**3 - 1/6*n**6 - 5/42*n**7. Factor m(f).
-5*(f - 2)*(f + 1)*(f + 2)**3
Suppose -y - 4*g = 5, -3*y - 2*g - 10 = -5*y. Determine k, given that -2*k**4 + 0*k**4 - 15*k**2 - y*k**4 + 20*k + 20 - 20*k**3 = 0.
-2, -1, 1
Let z(s) be the second derivative of 0 - 12*s + 0*s**2 + 0*s**4 - 1/48*s**3 + 1/160*s**5. Factor z(u).
u*(u - 1)*(u + 1)/8
Let p be ((-5)/15)/(1 - 2). Let w(x) be the first derivative of 0*x - 1/3*x**2 + p*x**3 - 1/12*x**4 + 5. Factor w(o).
-o*(o - 2)*(o - 1)/3
Let f(g) be the third derivative of 0*g + 0 + 0*g**3 + g**2 + 0*g**6 - 1/24*g**4 + 1/30*g**5 + 1/336*g**8 - 1/105*g**7. Factor f(t).
t*(t - 1)**3*(t + 1)
Let m = 18862/7 + -2704. Let u = 734/63 + m. Find s such that -2*s - u*s**2 - 4/9 = 0.
-1/2, -2/5
Let r be 11 + (-2 - 4/4). Suppose -f + r - 2 = 2*i, -f - 5*i + 12 = 0. Factor -6/7*a**f - 2/7*a**3 - 2/7 - 6/7*a.
-2*(a + 1)**3/7
Suppose o - 3 = c, -4*o + 10 + 2 = 5*c. Factor 2*p**2 + p**4 + 27*p**o - 3*p**2 - 2*p - 25*p**3.
p*(p - 1)*(p + 1)*(p + 2)
Let z = -212 + 206. Let y be -1*(18/36)/(7/z). Determine t, given that 12/7 + y*t**2 - 15/7*t = 0.
1, 4
Suppose 0 = -0*x - x. Factor -t**2 + 0*t**2 + x*t**2 - 3*t**3 - 6*t - 8*t**2.
-3*t*(t + 1)*(t + 2)
Solve -103*w + 2*w**2 - 5*w**3 - 7*w**4 + 103*w = 0 for w.
-1, 0, 2/7
Let b(j) be the second derivative of j**3/2 - 6*j**2 + 11*j. Let r be b(5). Factor 8*i**3 - r*i + 7*i**3 - 12*i**3.
3*i*(i - 1)*(i + 1)
Suppose 34*f - 88*f - 3*f**3 - 20*f - 36 + 35*f**2 - 22*f = 0. What is f?
-1/3, 6
Let q(c) be the first derivative of 4*c**3/3 - 30*c**2 + 56*c - 237. Find x, given that q(x) = 0.
1, 14
Let c(w) be the third derivative of -w**7/5880 + w**6/1680 + 11*w**4/24 + 17*w**2. Let z(l) be the second derivative of c(l). Factor z(d).
-3*d*(d - 1)/7
Let y(u) be the third derivative of 1/15*u**4 + 6*u**2 - 1/75*u**5 + 0*u - 1/150*u**6 + 0*u**3 + 0. Factor y(b).
-4*b*(b - 1)*(b + 2)/5
Let y(b) be the second derivative of -3*b + 0 + 5/6*b**4 + 1/4*b**5 - 5/6*b**3 - 5*b**2. Solve y(z) = 0 for z.
-2, -1, 1
Suppose 1/8*d**3 + 11/4*d**2 - 47/8*d + 3 = 0. Calculate d.
-24, 1
Let r be 8/((-2)/(8/(-4))*2). What is n in -7*n**3 + 5*n**3 - 12*n**2 - r*n**2 - 32*n = 0?
-4, 0
Let 3/5*m**3 + 21/5*m - 9 + 21/5*m**2 = 0. Calculate m.
-5, -3, 1
Let i be 24/6 - 33/9. Suppose -2*m = 5*j - 26 - 5, 0 = 3*m - 2*j + 1. Factor -5/3*c**2 - i*c**3 + m - c.
-(c - 1)*(c + 3)**2/3
Let u = 31 + -32. Let z be 3/u + (-77)/(-21). Factor z*m - 1/3*m**2 - 1/3.
-(m - 1)**2/3
Let m = 27 + -20. Let a be 8/30 - (74/(-10) + m). Suppose 1/6*r**2 + a + 2/3*r = 0. What is r?
-2
Let b be 83/65 - 15/195. Let q(o) be the first derivative of -8/5*o - 3 + 8/15*o**3 - b*o**2. Factor q(m).
4*(m - 2)*(2*m + 1)/5
Let v = -2104 + 2106. Suppose -4/7 - 1/7*r**v + 4/7*r = 0. Calculate r.
2
Let f(u) = 13*u**3 - 87*u**2 + 245*u - 161. Let j(p) = 24*p**3 - 174*p**2 + 489*p - 321. Let k(z) = 9*f(z) - 5*j(z). Solve k(w) = 0.
1, 2, 26
Let m(q) be the third derivative of q**7/630 + q**6/90 + q**5/30 - 19*q**4/24 + 16*q**2. Let v(g) be the second derivative of m(g). Factor v(u).
4*(u + 1)**2
Let p be 20/((-3)/(-18)*2). Let f = 63 - p. Factor -2/5*n**f + 16/5 - 24/5*n + 12/5*n**2.
-2*(n - 2)**3/5
Let g(l) = -108*l + 1193. Let t be g(11). Factor 1/2*p**t + 0 + 0*p + 0*p**2 + 3/2*p**4 + p**3.
p**3*(p + 1)*(p + 2)/2
Let g(t) be the third derivative of t**8/1176 - 4*t**7/735 - t**6/420 + 2*t**5/105 - 2*t**2 + t. Determine j so that g(j) = 0.
-1, 0, 1, 4
Let n(l) = 2*l**2 + 27*l + 28. Let z be n(-1). Factor -z*d**2 + 7/3*d**3 + 0 + 2/3*d.
d*(d - 1)*(7*d - 2)/3
Let c(y) be the third derivative of -y**6/420 - 4*y**5/105 - 5*y**4/84 + 50*y**3/21 - 55*y**2. What is k in c(k) = 0?
-5, 2
Let s(m) be the second derivative of 1/336*m**7 + 0*m**2 - 5/96*m**4 + 1/240*m**6 - 1/24*m**3 + 0 - 3/160*m**5 - 10*m. Factor s(x).
x*(x - 2)*(x + 1)**3/8
Let l(b) be the third derivative of b**6/840 - 3*b**5/140 + 9*b**4/56 - b**3/3 - 19*b**2. Let z(h) be the first derivative of l(h). Solve z(j) = 0 for j.
3
Determine k so that -1/2*k**2 + 0*k + 2*k**3 + 0 = 0.
0, 1/4
Let o(l) be the second derivative of -8*l**7/21 + l**6/15 + 4*l**5/5 - l**4/6 + l + 16. Determine r so that o(r) = 0.
-1, 0, 1/8, 1
Let p(v) be the first derivative of 9*v**3/4 - 141*v**2/8 + 15*v/2 - 82. Factor p(y).
3*(y - 5)*(9*y - 2)/4
Let d = -24077489/35541 + 7/3231. Let w = d + 678. Factor w*h + 2/11 + 6/11*h**2 + 2/11*h**3.
2*(h + 1)**3/11
Suppose 4*m + 5*f = -5, -3*f - 5 = -2*f. Factor -7*r**2 + 0 + 12*r**2 - 2 - m*r + 7*r**2.
(3*r - 2)*(4*r + 1)
Suppose -2/21*f**2 + 2/7*f + 0 = 0. Calculate f.
0, 3
Let t(i) be the third derivative of i**6/24 - 47*i**5/30 + 91*i**4/30 - 12*i**3/5 + i**2 + 74*i. Factor t(b).
(b - 18)*(5*b - 2)**2/5
Let s(g) be the second derivative of -g**4/6 + 5*g**3/3 + 14*g**2 - 4*g + 4. Factor s(v).
-2*(v - 7)*(v + 2)
Let y = -1 + -6. Let q = 7 + y. Factor 9 + 7*k - 18*k - 3 + 3*k**2 + q.
(k - 3)*(3*k - 2)
Suppose d + s + 0 = 3, d - 3*s = -1. Factor -50/13*v**d - 40/13*v - 8/13.
-2*(5*v + 2)**2/13
Let o(z) be the third derivative of z**8/40320 + z**7/2016 + z**6/360 - 9*z**5/20 + 4*z**2. Let y(v) be the third derivative of o(v). Find d such that y(d) = 0.
-4, -1
Suppose -4*z = t - 125 - 206, -3*z - t = -249. Let p = z + -80. Let 0 - 6/5*w + 2/5*w**p = 0. What is w?
0, 3
Let i be ((-12)/15 - -2)/(33/110). Determine s so that -2*s**i - 3 - 3 - 8*s + 6*s**3 + 6 = 0.
-1, 0, 2
Let k(u) be the third derivative of -5/3*u**3 - 1/24*u**6 + 0*u + 0 - 17*u**2 - 25/24*u**4 - 1/3*u**5. Factor k(d).
-5*(d + 1)**2*(d + 2)
Let l(t) be the third derivative of -9*t**8/112 - 17*t**7/35 - 19*t**6/40 + 21*t**5/10 + 7*t**4/2 - 4*t**3 + 3*t**2 - 125*t. Find z such that l(z) = 0.
-2, -1, 2/9, 1
Let h(a) = 2*a**4 - a**3 + a**2 - a - 1. Let w(u) = 28*u**4 - 8*u**3 - 12*u**2 - 28*u + 20. Let d(v) = -12*h(v) + w(v). Suppose d(i) = 0. What is i?
-2, 1, 2
Let i(y) = -17*y - 18. Let r be i(-11). Factor 8*k**2 - r*k + 86*k + 87*k + 5*k**3 + k**4.
k*(k + 1)*(k + 2)**2
Let d be 6080/10450 + 2/(-11). Solve -16/