*2*(j + 2)/4
Let k(u) be the second derivative of 3*u**5/2 + 101*u**4/6 + 164*u**3/3 + 44*u**2 - 199*u. Factor k(j).
2*(j + 2)*(3*j + 1)*(5*j + 22)
Let a be 6/7*-7*(-7)/21. Let v(b) be the first derivative of -7 - 4/5*b**5 - 4*b**3 + a*b**2 + 0*b + 3*b**4. Factor v(i).
-4*i*(i - 1)**3
Let q(u) be the first derivative of 10 - 2/3*u**3 - 3*u + 5/2*u**2. Factor q(g).
-(g - 1)*(2*g - 3)
Let a(n) = n**3 - 5*n + 4. Let h be a(4). Suppose -19*l - 145 = -h*l. Factor -2/3*j + 0*j**4 + 0*j**2 - 2/3*j**l + 4/3*j**3 + 0.
-2*j*(j - 1)**2*(j + 1)**2/3
Let r(l) be the second derivative of -38*l**6/75 + 36*l**5/25 - l**4 - 4*l**3/15 - 48*l. Find n such that r(n) = 0.
-2/19, 0, 1
Suppose -n = -5*d + 24, -2*d + 32 = 2*n + 20. Find q such that -3/2 - 39/2*q**4 - 27*q**2 - 33*q**3 - 9/2*q**d - 21/2*q = 0.
-1, -1/3
Let f(j) = -2*j**2 - j - 7. Let s(t) = -6*t**2 - 2*t - 21. Let g(m) = 7*f(m) - 2*s(m). Let l(a) = -a**2 - 1. Let b(w) = -2*g(w) + 6*l(w). Factor b(c).
-2*(c - 4)*(c + 1)
Let g be (-2)/4 - (4 - (-15)/(-2)). Let w(k) be the third derivative of 0 + 2*k**2 - 5/144*k**4 + 0*k - 1/18*k**g - 1/180*k**5. Factor w(m).
-(m + 2)*(2*m + 1)/6
Let d(s) be the third derivative of -1/45*s**4 + 12*s**2 + 0*s + 2/45*s**5 + 0 + 0*s**3 - 1/100*s**6. Let d(q) = 0. What is q?
0, 2/9, 2
Let p be (6/84)/(-3*6/(-144)). Factor -p*j**4 - 1/7*j**2 + 0 + 0*j + 5/7*j**3.
-j**2*(j - 1)*(4*j - 1)/7
Let f = -174 + 178. Factor 0*k**2 + 2/9*k**f - 4/9*k + 4/9*k**3 - 2/9.
2*(k - 1)*(k + 1)**3/9
Let o(u) be the first derivative of -3*u**5/10 - 63*u**4/8 - 39*u**3/2 - 57*u**2/4 + 71. Factor o(x).
-3*x*(x + 1)**2*(x + 19)/2
Solve 11280*k + 5966*k**4 - 2785*k**4 - 75*k**5 - 11184*k**2 - 5592*k**3 - 1771*k**4 - 2400 = 0.
-2, 2/5, 10
Let b(g) be the third derivative of 1/9*g**4 + 0*g**3 + 0 + 0*g - 1/45*g**5 + 13*g**2. Factor b(y).
-4*y*(y - 2)/3
Suppose -l + 13 = -11. Let x be 6/(-16)*l/(-18). Solve -y**2 + 0 + x*y**3 - 3/2*y = 0 for y.
-1, 0, 3
Suppose -2*y + 1 + 57 = s, -123 = -5*y + 3*s. Factor -5 + 65*f**3 - 28*f**3 + 5*f**4 - 10*f - y*f**3.
5*(f - 1)*(f + 1)**3
Factor -60*r - 9/2*r**2 + 0 + 3/2*r**3.
3*r*(r - 8)*(r + 5)/2
Let t(l) = 26*l**3 - 156*l**2 + 32*l - 16. Let q(z) = -5*z**3 + 31*z**2 - 6*z + 3. Let o(r) = 16*q(r) + 3*t(r). What is u in o(u) = 0?
0, 14
Let h(o) = 4*o**4 + 4. Let q(v) = v**5 - 8*v**4 - 7. Let i(y) = -y**2 + 9*y + 18. Let a be i(11). Let p(w) = a*q(w) - 7*h(w). Find t, given that p(t) = 0.
0, 1
Find z, given that -4/5*z**3 + 12/5*z**2 + 0 - 8/5*z = 0.
0, 1, 2
Suppose -2/5*q**2 + 512/5*q - 32768/5 = 0. What is q?
128
Let o(y) be the first derivative of y**3/3 + y**2 - 63*y - 1004. What is s in o(s) = 0?
-9, 7
Let c = 10 - -4. Let d be 2 - 2/(16/c). Factor d*w**5 + 1/4*w**2 - 1/4*w**4 + 0 - 1/4*w**3 + 0*w.
w**2*(w - 1)**2*(w + 1)/4
Let d(u) be the second derivative of -u**7/14 + 9*u**5/10 + 2*u**4 + 3*u**3/2 - 4*u - 63. Solve d(t) = 0 for t.
-1, 0, 3
Let a(i) be the second derivative of i**5/4 + 65*i**4/6 + 845*i**3/6 - 4*i - 5. Factor a(o).
5*o*(o + 13)**2
Let i(r) be the first derivative of r**6/1440 + r**5/60 + r**4/6 - 5*r**3/3 + 6. Let l(v) be the third derivative of i(v). Suppose l(t) = 0. What is t?
-4
Factor 0 - 93/4*t**2 - 3/2*t.
-3*t*(31*t + 2)/4
Factor 0*k + 8/3*k**3 - 5/3*k**4 + 0 + 1/3*k**5 - 4/3*k**2.
k**2*(k - 2)**2*(k - 1)/3
Let g(h) be the second derivative of 21*h**5/5 - 5*h**4 - h**3/2 + 3*h**2 + 2*h - 6. Factor g(t).
3*(2*t - 1)**2*(7*t + 2)
Let v = -59 + 23. Let h be 0 - (10/45 - (-26)/v). Factor -1/2*b**2 + h*b + 0.
-b*(b - 1)/2
Let a(k) be the third derivative of 1/120*k**5 + 0 + 0*k + 1/3*k**3 + 1/12*k**4 + 16*k**2. Factor a(d).
(d + 2)**2/2
Suppose 3 = c - 1. Let r be 3*2*(5/(-12))/(285/(-152)). Factor -4/3*m**c - 1/3*m**2 + r*m**3 + 0 + 0*m.
-m**2*(2*m - 1)**2/3
Suppose 0 = -q + 3*p + 17, -4*p + 13 = -q - 7*p. Factor 0*r - 2/15*r**4 + 0 + 0*r**q - 2/15*r**3.
-2*r**3*(r + 1)/15
Let q(s) be the second derivative of -s**7/252 - s**6/30 + s**5/30 + 17*s**4/36 - 17*s**3/12 + 5*s**2/3 + 99*s. Factor q(x).
-(x - 1)**3*(x + 4)*(x + 5)/6
Let u(y) = -2*y**5 - y**4 + 2*y**2 + y + 1. Let b(q) = -6*q**5 - 18*q**4 + 22*q**3 - 2*q**2 + 4*q + 4. Let n(s) = b(s) - 4*u(s). Find z, given that n(z) = 0.
0, 1, 5
Suppose -2*x - x - 9 = 0. Let r be x/4*(-2 + -2). Find i such that -i - 8*i**3 + 8*i**3 + i**r = 0.
-1, 0, 1
Let x be 5*(-3 + 72/20). Factor -26*t - 24*t**2 - x*t**3 - 1 - 17 - 13*t.
-3*(t + 1)**2*(t + 6)
Let v(y) be the first derivative of 7*y**6/480 - y**5/80 - 11*y**3/3 + 11. Let g(b) be the third derivative of v(b). Factor g(k).
3*k*(7*k - 2)/4
Let g = 121/4 - 359/12. Let j(o) be the first derivative of -2/27*o**3 - 4/9*o - g*o**2 - 3. Find h, given that j(h) = 0.
-2, -1
Factor 22*d - 43/2 - 1/2*d**2.
-(d - 43)*(d - 1)/2
Let 1398 - 1432 + 22*x + 2*x**2 + 10*x = 0. What is x?
-17, 1
Suppose 46 = -4*z + 6. Let x be 6/z*(-125)/100. Factor 1/4*c**2 + x*c + 1/2.
(c + 1)*(c + 2)/4
Let u(i) = i + 1. Let y(k) = -2*k**2 + 8*k + 8. Let v be (4/10)/(4/80). Let m be (-1)/1 + (8 - v). Let h(s) = m*y(s) + 8*u(s). Solve h(t) = 0.
0
Suppose -20 = -5*w + d, -251 = 4*w + 4*d - 267. Determine j, given that -w*j**2 + 10/9*j**3 + 14/9*j + 4/3 = 0.
-2/5, 1, 3
Let b(c) be the third derivative of -7*c**5/120 - 3*c**4/16 - c**3/6 + 14*c**2 - c. Factor b(h).
-(h + 1)*(7*h + 2)/2
Determine d, given that -15*d**5 - 4/3 + 19/3*d**2 + 11*d**4 - 16/3*d + 109/3*d**3 = 0.
-1, -1/3, 2/5, 2
Let u = 77581/4 - 19395. Factor -2 - 3/2*g**2 - u*g**3 - 3*g.
-(g + 2)**3/4
Let p(s) be the first derivative of s**4/10 - 6*s**3/5 - 48*s**2/5 - 104*s/5 - 112. Factor p(r).
2*(r - 13)*(r + 2)**2/5
Suppose 0 = -4*j + 19 + 13. Factor 2*i**4 + 2*i**4 + 1 - j*i**2 + 3.
4*(i - 1)**2*(i + 1)**2
Let z(q) be the third derivative of -q**6/210 + 17*q**5/105 - 31*q**4/42 + 10*q**3/7 - 244*q**2. Factor z(o).
-4*(o - 15)*(o - 1)**2/7
Let u(r) be the third derivative of r**7/3360 + r**6/480 + r**5/240 - 11*r**3/6 + 13*r**2. Let p(x) be the first derivative of u(x). Find j such that p(j) = 0.
-2, -1, 0
Let k(j) = -5*j**3 - 68*j**2 + 58*j. Let x(g) = -52*g**3 - 748*g**2 + 640*g. Let h(m) = -32*k(m) + 3*x(m). Factor h(f).
4*f*(f - 16)*(f - 1)
Let q(d) = d**3 + 7*d**2 - 26*d - 72. Let c be q(-9). Let k = 1 - -1. Factor c*r + 2/3*r**3 - 2/3*r**k + 0.
2*r**2*(r - 1)/3
Suppose -z + 1 = 2. Let j be 1 + (-3 - -6) + z. Determine d so that -d**4 + d**2 - 2*d - 16*d**3 + 10*d**j + 8*d**3 = 0.
-1, 0, 1, 2
Let s be (-6)/(-108)*(-9)/(-2). Let n(m) be the first derivative of 9/4*m + 3/2*m**2 + s*m**3 + 6. Factor n(j).
3*(j + 1)*(j + 3)/4
Let o = 257941/180 + -1433. Let m(k) be the third derivative of -1/360*k**6 + 6*k**2 + 1/6*k**3 + 5/72*k**4 + 0*k + o*k**5 + 0. Let m(x) = 0. What is x?
-1, 3
Factor 2/5*s**5 + 12/5 + 16/5*s**4 + 48/5*s**3 + 68/5*s**2 + 46/5*s.
2*(s + 1)**3*(s + 2)*(s + 3)/5
Let y(x) be the first derivative of 2*x**5/5 + x**4 - 10*x**3/3 - 6*x**2 + 126. Factor y(j).
2*j*(j - 2)*(j + 1)*(j + 3)
Let c(v) be the second derivative of -1/6*v**4 - 49*v**2 - 14/3*v**3 + 0 - 13*v. Suppose c(n) = 0. Calculate n.
-7
Suppose -5*p = -r + 3*r + 11, 0 = -5*r - 5*p - 35. Let d = r - -11. Determine t so that t**2 + 0*t - 2*t**2 - d*t + t = 0.
-2, 0
Let z = -2702 - -2705. Factor 3*g**z + 3/2*g**2 + 9 - 39/2*g.
3*(g - 2)*(g + 3)*(2*g - 1)/2
Suppose 170*d = 168*d. Let b(m) be the second derivative of -2*m + 1/15*m**6 + 1/63*m**7 + 1/10*m**5 + 0*m**2 + 1/18*m**4 + d*m**3 + 0. Factor b(i).
2*i**2*(i + 1)**3/3
Let q be (-5)/2*17/(-51). Factor -1/2*d**3 - 1/6*d**5 + 3/2*d**2 + 0 - q*d**4 + 0*d.
-d**2*(d - 1)*(d + 3)**2/6
Suppose -1/2*b**5 - 4*b**4 + 128*b**2 - 512*b + 24*b**3 + 0 = 0. Calculate b.
-8, 0, 4
Let a(x) be the third derivative of x**5/12 - x**4/12 - 2*x**3 - 6*x**2. Let o(l) = 6*l**2 - 2*l - 12. Let w(y) = -4*a(y) + 3*o(y). Factor w(g).
-2*(g - 3)*(g + 2)
Suppose 2*r - 2*k - 16 = 0, -2*r + 12 = -0*k - k. Let g = 4 - 2. Factor r*y**3 + y**4 - 3*y**4 - 4*y**2 - g*y**3 - y**5 + 2 - y + 4*y**4.
-(y - 2)*(y - 1)**2*(y + 1)**2
Suppose -214*f + 219*f - 22 = 4*t, 5*f = -2*t + 34. What is r in -3/4*r**3 + 0 + 0*r**t + 3/4*r = 0?
-1, 0, 1
Let z(u) = u**2 - 5*u - 4. Let c be z(6). Let 4*g**2 + c*g - 7*g + 2 + 6 - 7*g = 0. What is g?
1, 2
Suppose -9*a = -3*a. Let p(i) be the third derivative of 0*i**3 + a - 1/3*i**4 + 3*i**2 - 1/