5*(k - 4)*(k - 1)
Let b be (-263)/630 - 39/(-364)*4. Let u(y) be the third derivative of 0 + 0*y + b*y**5 + 0*y**3 + 1/36*y**4 + 5*y**2. Factor u(r).
2*r*(r + 1)/3
Let q(x) be the third derivative of x**6/90 - x**5/30 - x**4/3 + 19*x**3/6 + 17*x**2. Let z(d) be the first derivative of q(d). Solve z(b) = 0.
-1, 2
Let z(p) be the first derivative of 1/4*p**4 + 0*p**2 + 3/20*p**5 + 0*p**3 + 6 - 8*p. Let a(d) be the first derivative of z(d). Find f such that a(f) = 0.
-1, 0
Let u(t) = -t**5 + 14*t**4 - 2*t**3 - 19*t**2 + 23*t + 5. Let m(y) = -y**5 + 8*y**4 - 2*y**3 - 10*y**2 + 11*y + 2. Let i(r) = -5*m(r) + 2*u(r). Factor i(j).
3*j*(j - 3)*(j - 1)**2*(j + 1)
Let u(g) be the first derivative of -2/15*g**3 + 4/5*g**2 - 6/5*g - 1. Factor u(b).
-2*(b - 3)*(b - 1)/5
Let o(q) be the third derivative of q**8/84 - q**7/210 + 2*q**2 + 32. Factor o(p).
p**4*(4*p - 1)
Let a(c) = c**2 + 2*c + 2. Let t = 8 - 11. Let o be a(t). Solve -3*q + 5*q**2 + 3*q - 1 - q + o*q = 0 for q.
-1, 1/5
Let d(g) be the second derivative of g**6/30 + 3*g**5/10 + 11*g**4/12 + g**3 + 18*g - 2. Factor d(h).
h*(h + 1)*(h + 2)*(h + 3)
Let n = -25763 - -128269/5. Let d = n - -110. Suppose 0*r + 0*r**2 + 0 + 3/5*r**4 - 1/5*r**3 + d*r**5 = 0. What is r?
-1, 0, 1/4
Let c(w) = w**3 - w**2 + w - 2. Let k(t) = -40*t**3 + 168*t**2 + 20*t - 8. Let b(v) = 4*c(v) - k(v). Solve b(o) = 0 for o.
-1/11, 0, 4
Let l = -65 + 71. Let k be (-18)/(-5) - 3 - l/10. Factor 2/5*s + 2/5*s**2 + k.
2*s*(s + 1)/5
Suppose -4*m + 220 = -n, 3*m - 2*n + 0*n - 170 = 0. Suppose 20*c = 22*c - m. Find t such that 3*t + c + 8*t - t + 8*t + 3*t**2 = 0.
-3
Let f = -417/5 - -5129/60. Let m = f - -35/3. Find h, given that -39/4*h - 9/4 - 25/4*h**3 - m*h**2 = 0.
-1, -3/5
Let o(c) be the second derivative of c**7/840 + c**6/240 - c**5/80 - 5*c**2 - 2*c. Let n(j) be the first derivative of o(j). Factor n(r).
r**2*(r - 1)*(r + 3)/4
Factor -1/9*x**2 + 25/9 + 0*x.
-(x - 5)*(x + 5)/9
Let c be 8/24*9 + -5 + 2. Let q(u) be the second derivative of 1/33*u**4 + 6*u - 1/165*u**6 - 1/110*u**5 + 0 + c*u**3 + 0*u**2. Factor q(w).
-2*w**2*(w - 1)*(w + 2)/11
Let g = 844/747 - 20/83. Let i = 860 - 7738/9. Factor -g*j + i*j**2 + 8/9.
2*(j - 2)**2/9
Suppose -10/9*w**5 - 4/3*w + 22/9*w**3 + 0 + 26/9*w**2 - 26/9*w**4 = 0. What is w?
-3, -1, 0, 2/5, 1
Let o(d) be the first derivative of 0*d**4 + 0*d**3 - 2 - 5*d - 1/21*d**7 + 0*d**5 + 0*d**2 - 2/135*d**6. Let j(s) be the first derivative of o(s). Factor j(a).
-2*a**4*(9*a + 2)/9
Let v be (6/(-4) - 0)*(-50)/25. Let k(r) be the first derivative of -8 + 0*r**2 - 8/7*r + 2/21*r**v. Factor k(s).
2*(s - 2)*(s + 2)/7
Suppose u = -2*p + 97, 0*p - 443 = -5*u + 4*p. Factor u*l - 47*l + 6 - 49*l - l**2.
-(l - 1)*(l + 6)
Let s(p) be the first derivative of -10*p**6/3 + 19*p**5 - 75*p**4/4 - 125*p**3/3 + 95*p**2/2 + 30*p - 189. Solve s(d) = 0.
-1, -1/4, 1, 2, 3
Let j be (2 + -2)/(3 - -3). Let d(c) be the third derivative of 1/36*c**4 + 4*c**2 + 0 + 0*c**3 - 1/18*c**5 + 5/144*c**6 + j*c. What is n in d(n) = 0?
0, 2/5
Let i be (0/(-1))/(2 + -4). Let s(h) be the third derivative of i + 4*h**3 + 7/2*h**5 + 0*h + 7*h**2 - 5/8*h**6 - 11/2*h**4. Factor s(z).
-3*(z - 2)*(5*z - 2)**2
Let c(o) be the second derivative of -5*o**4/66 + o**3/33 + 6*o**2/11 - 145*o. Factor c(h).
-2*(h + 1)*(5*h - 6)/11
Let i = 72218 + -72213. Let t(p) = -p**2 - 2*p + 3. Let b be t(-3). Let -1/5*n - 6/5*n**3 - 4/5*n**4 + b - 4/5*n**2 - 1/5*n**i = 0. What is n?
-1, 0
Let c(g) = -2*g**2 + 12*g - 2. Let r(o) = -o - 1. Suppose -1 = 4*b - 17. Let d(s) = b*r(s) + c(s). Factor d(z).
-2*(z - 3)*(z - 1)
Let u be 4/(16/26)*2. Find d such that u*d**3 - 12*d + 3*d**3 - 4*d**5 - 8*d**4 - 2*d**2 + 10*d**2 = 0.
-3, -1, 0, 1
Let c(s) = -17*s**2 - 126*s. Let j(r) = -15*r**2 - 125*r. Let l(i) = 5*c(i) - 6*j(i). Suppose l(f) = 0. What is f?
-24, 0
Let w(h) be the first derivative of -h**6/810 + h**5/135 - h**4/54 + 4*h**3/3 + 3*h**2/2 + 18. Let n(p) be the third derivative of w(p). Factor n(m).
-4*(m - 1)**2/9
Suppose -1/2*k**2 + 1/2*k**5 + 3/2*k**3 + 0 + 0*k - 3/2*k**4 = 0. Calculate k.
0, 1
Let h(k) be the first derivative of k**6/30 - 4*k**5/15 + k**4/2 + 7*k**2/2 - 7. Let m(g) be the second derivative of h(g). Find l such that m(l) = 0.
0, 1, 3
Let v(q) be the third derivative of -1/5*q**5 + 0*q + 4/3*q**3 + 2/105*q**7 + 1/6*q**4 - 1/30*q**6 + 0 + 58*q**2. Determine x, given that v(x) = 0.
-1, 1, 2
Suppose 2*j = 5*s + 23 - 31, -2*s - 3*j - 12 = 0. Let -2/13*z**4 + 0 + 2/13*z**3 + s*z + 0*z**2 = 0. What is z?
0, 1
Let z be (13/(-39))/(2*(-3)/126). Let l(u) be the third derivative of 3*u**2 + 0*u - 1/270*u**5 + 0*u**4 + 0*u**3 - 1/945*u**z + 0 + 1/270*u**6. Factor l(a).
-2*a**2*(a - 1)**2/9
Let x(b) be the third derivative of -5/24*b**4 + 0*b + 1/2*b**3 + 0 + 12*b**2 + 1/120*b**6 + 1/60*b**5. Determine l, given that x(l) = 0.
-3, 1
Let p(s) be the second derivative of -s**7/84 - 7*s**6/15 - 221*s**5/40 - 169*s**4/12 + 1124*s. Factor p(w).
-w**2*(w + 2)*(w + 13)**2/2
Let o be 36/27 + (-5)/(-3). Factor 7*t**2 + 8*t**2 - 34*t**2 + 16*t**2 + o*t + 6.
-3*(t - 2)*(t + 1)
Factor -48/5 - 46/5*y + 2/5*y**2.
2*(y - 24)*(y + 1)/5
Factor -1/4*j**2 + 3/4*j + 10.
-(j - 8)*(j + 5)/4
Let b be (-322)/(-77) + 4/(-22). Let 9*p**5 + 3*p**5 - 49*p**3 - 26*p**4 - b*p**2 + 67*p**3 = 0. Calculate p.
0, 1/2, 2/3, 1
Let l be ((6/(-30))/(6/5))/(-42). Let m = l - -167/252. Find b, given that -2/3*b**4 + 0*b**3 + 0*b + 0 + 0*b**2 - m*b**5 = 0.
-1, 0
Let f = 59 - 48. Suppose -6*l = -f*l + 10. Factor 0*x**l + 0 + 2/9*x**3 - 2/9*x.
2*x*(x - 1)*(x + 1)/9
Let s(d) be the first derivative of 14/3*d**2 + 4 - 8/3*d - 4/3*d**3. Factor s(i).
-4*(i - 2)*(3*i - 1)/3
Suppose 3*m + 6 = 2*m. Let w(i) = 4*i**2 + 17*i + 2. Let s(q) be the first derivative of 2*q**3/3 + 9*q**2/2 + q - 1. Let h(c) = m*w(c) + 11*s(c). Factor h(l).
-(l + 1)*(2*l + 1)
Let n = 57/20 + -11/60. Let h(d) be the first derivative of 0*d**2 - 4/5*d**5 + d**4 + 4 + 0*d + n*d**3. Factor h(j).
-4*j**2*(j - 2)*(j + 1)
Let n(x) = x + 13. Let i be n(-15). Let h be 6 + i + -5 + 3. Factor -9*t**h + t**4 - 12*t**3 - 3*t**4 - 8 - 17*t**2 - 9*t - 15*t.
-2*(t + 1)**2*(t + 2)**2
Let g(o) = o**2 - 20*o + 40. Let w be g(2). Let h(p) be the third derivative of -1/30*p**5 + 4*p**2 + 0*p + 0*p**3 + 0*p**w - 1/120*p**6 + 0. Factor h(d).
-d**2*(d + 2)
Let p(w) be the first derivative of -w**5/510 + w**4/204 + w**2 - 3. Let l(c) be the second derivative of p(c). Factor l(s).
-2*s*(s - 1)/17
Find t, given that 18*t**2 - 26 - 9 + 7*t**2 + 170*t = 0.
-7, 1/5
Let u(w) be the first derivative of w**3/7 + 3*w**2/7 - 9*w/7 + 286. Let u(r) = 0. Calculate r.
-3, 1
Let j(m) be the first derivative of -m**6/6 + 2*m**5 - 31*m**4/4 + 22*m**3/3 + 16*m**2 - 32*m - 46. Solve j(v) = 0.
-1, 1, 2, 4
Let b(k) be the second derivative of 1/10*k**4 + 0*k**2 - 2*k - 1/50*k**5 - 2/15*k**3 + 0. Suppose b(v) = 0. What is v?
0, 1, 2
Let b be 9/30 + (-876)/(-730). Find j such that -15/4*j**2 - b - 3/4*j**3 - 17/4*j + 1/4*j**4 = 0.
-1, 6
Let a(t) = -3*t**4 - 33*t**3 - 18*t**2 + 12*t + 30. Let n(m) = 3*m**4 + 30*m**3 + 18*m**2 - 12*m - 29. Let k(u) = 5*a(u) + 6*n(u). Factor k(l).
3*(l - 1)*(l + 2)**3
Let b(m) = -27*m**2 + 162*m + 72. Let u(i) = 25*i**2 - 161*i - 72. Let n(x) = 2*b(x) + 3*u(x). What is v in n(v) = 0?
-3/7, 8
Let g = 959/1938 - -5/969. Determine q so that -7/6*q**2 + g*q - 1/6*q**4 + 5/6*q**3 + 0 = 0.
0, 1, 3
Let u = 19092/5 + -3812. Let k be (2*-1)/((-8)/12). Solve -2/5*i - 2/5*i**2 + u*i**k + 0 + 32/5*i**4 = 0 for i.
-1, -1/4, 0, 1/4
Let w(g) be the first derivative of -1/2*g**2 + 1 + 0*g - 2/3*g**3 + 3/4*g**4. Determine m so that w(m) = 0.
-1/3, 0, 1
Let i(o) = 67*o + 338. Let m be i(-5). Factor -3/2*h**2 - m*h - 3/2.
-3*(h + 1)**2/2
Let m = -785 + 62803/80. Let b(z) be the second derivative of -5*z + 0*z**2 + 1/60*z**6 + 0 + 0*z**3 + m*z**5 + 1/48*z**4. Factor b(x).
x**2*(x + 1)*(2*x + 1)/4
Let o = 4116841/780 - 5278. Let i(p) be the third derivative of 0*p**5 + 0*p**3 + 0 - o*p**6 + 0*p - 8*p**2 + 1/156*p**4. Factor i(v).
-2*v*(v - 1)*(v + 1)/13
Suppose h - 3*o + 0*o = 44, 5*h + 5*o = 160. Suppose 10*z + 15 = h. Factor -1/2*c**3 + 1/4*c**4 + 0*c**z + 0 + 0*c.
c**3*(c - 2)/4
Suppose -23*o + 92 + 0 = 0. Let g(b) be the second derivative of 0 + 1/4*b**2 + 1/8*b