o that t(h) = 0.
-2, 0
Suppose 47*r = -31 + 219. Let l(a) be the second derivative of 1/42*a**r + 2/7*a**2 - 1/7*a**3 + 0 + 4*a. Solve l(x) = 0.
1, 2
Find z, given that 81/7*z - 45/7*z**2 + 3/7*z**3 - 39/7 = 0.
1, 13
Let s(y) = 1527*y - 7635. Let z be s(5). Factor z - 4/3*x**3 + 1/3*x - x**2.
-x*(x + 1)*(4*x - 1)/3
Let v be (7 - 6) + -11 + 12. Factor 9/8 + 3/8*j**v - 3/2*j.
3*(j - 3)*(j - 1)/8
Let y = -3286 - -13145/4. Factor -4*g + y*g**2 + 16.
(g - 8)**2/4
Let o(w) be the second derivative of -w**5/10 - 10*w**4 - 319*w**3 - 1682*w**2 - 60*w. Factor o(a).
-2*(a + 2)*(a + 29)**2
Solve -r**2 + r**3 + 5 - 5*r**3 + 2687*r - 2701*r - 22*r**2 = 0.
-5, -1, 1/4
Let y(k) = 2*k + 30. Let f be y(-14). Factor -2/13 - 4/13*v**f + 6/13*v.
-2*(v - 1)*(2*v - 1)/13
Let c = 2048 - 2045. Factor -3*f**2 - 3/2*f + 3*f**4 + 0 + 3/2*f**5 + 0*f**c.
3*f*(f - 1)*(f + 1)**3/2
Let z(u) = 4*u - 7. Let g(h) = -5*h + 6. Let l(y) = -3*g(y) - 4*z(y). Let p be l(5). Let -r**p + r**3 + r**5 - r**5 = 0. What is r?
-1, 0, 1
Let v(x) = x**2 + 2*x + 13. Let m be v(0). Determine w, given that -3*w + 12*w**3 + 0 - 9 + m*w**3 + 5*w**2 - 26*w**3 = 0.
-1, 3
Let s(r) be the second derivative of -r**4/4 + 18*r**3 - 102*r**2 - 359*r. Factor s(c).
-3*(c - 34)*(c - 2)
Let i be (-12)/(-8) + (-33)/(-6). Suppose i*z = 10*z - 21. Determine f, given that 2*f**4 - 2 - 2*f**2 - 4*f**2 - 3*f**4 + 5*f**3 - 3*f**2 + z*f = 0.
1, 2
Let 5/3*z - 1/6*z**2 + 4 = 0. What is z?
-2, 12
Let r = -64 - -64. Let d(p) be the third derivative of 0*p**3 + 0 + 1/40*p**6 - 1/20*p**5 - 5*p**2 + r*p - 1/4*p**4. Factor d(t).
3*t*(t - 2)*(t + 1)
Let x(k) be the third derivative of -4/15*k**5 - 1/30*k**6 + 0*k + 0 - 2/3*k**4 + 15*k**2 + 0*k**3. Let x(z) = 0. What is z?
-2, 0
Let c = -2/2167 + 39032/28171. Let y = c + -23/26. Determine a, given that -y*a**3 - 2*a + 2*a**2 + 0 = 0.
0, 2
Suppose -20 = -2*x - 4*w, -x + w = -0*x + 5. Suppose -8*l - 3*l + 33 = x. Let 24*t**4 - 9/4 - 9/2*t**2 + 57/4*t - 72*t**l = 0. Calculate t.
-1/2, 1/4, 3
Let j(d) be the second derivative of d**6 - 11*d + 21/10*d**5 + 0 + 13/6*d**4 + d**3 + 0*d**2 + 4/21*d**7. Factor j(o).
2*o*(o + 1)**3*(4*o + 3)
Let s be -3*16/(-12) - -16. Suppose 57*r - 12*r**2 + r**3 + s - 84 - 9*r = 0. Calculate r.
4
Let t(d) be the third derivative of d**6/240 + d**5/120 - 5*d**4/48 + d**3/4 + 45*d**2. Factor t(f).
(f - 1)**2*(f + 3)/2
Factor 0 - 1/3*h**3 + 2/3*h - 1/3*h**2.
-h*(h - 1)*(h + 2)/3
Let s be (-23)/(-3) + 80/(-40) + (-4 - -1). Suppose 0*j + 3*j**5 - 14*j**3 - 25/3*j**4 + 0 - s*j**2 = 0. Calculate j.
-1, -2/9, 0, 4
Let f = 1577/2397 + 7/799. Determine b, given that 4/3*b**2 - f*b + 0 - 2/3*b**3 = 0.
0, 1
Let o = -404 - -16161/40. Let y(z) be the third derivative of 6*z**2 + 0 - 1/12*z**4 - 1/12*z**3 + 0*z - o*z**5. Determine r so that y(r) = 0.
-1, -1/3
Let -256/5*b**3 - 108/5 - 468/5*b**2 - 6/5*b**5 - 64/5*b**4 - 378/5*b = 0. Calculate b.
-3, -1, -2/3
Factor -10/9*t + 1/9*t**2 + 0.
t*(t - 10)/9
Factor 2/7*z**5 + 4/7*z**2 + 0 + 0*z + 0*z**4 - 6/7*z**3.
2*z**2*(z - 1)**2*(z + 2)/7
Suppose 2*h - 35 = 9*h. Let p(k) = k**4 - 16*k**3 - 4*k**2 - 6*k - 4. Let o(m) = -m**4 + m**3 - m**2 + m + 1. Let c(b) = h*o(b) - p(b). Factor c(g).
(g + 1)**3*(4*g - 1)
Let a(j) be the first derivative of 6/7*j**2 - 12 + 1/7*j**3 + 12/7*j. Factor a(s).
3*(s + 2)**2/7
Factor -3/8*r + 75/4*r**4 - 15/8*r**3 + 0 - 3*r**2.
3*r*(2*r - 1)*(5*r + 1)**2/8
Let h(g) = 15*g**3 + 4*g - g + 5*g + 32*g**2. Let z(d) be the first derivative of -2*d**4 - 16*d**3/3 - 2*d**2 - 25. Let l(w) = -4*h(w) - 9*z(w). Factor l(r).
4*r*(r + 1)*(3*r + 1)
Let c be (10626/(-13195) - -2)*(0 - 1). Let k = 2/377 - c. Find w, given that 9/5 + k*w + 1/5*w**2 = 0.
-3
Let w(q) be the first derivative of q**3/2 + 42*q**2 + 1176*q - 226. Factor w(a).
3*(a + 28)**2/2
Let s(u) be the first derivative of -u**3/2 + 6*u + 338. Let s(h) = 0. Calculate h.
-2, 2
Suppose 0 = 203*t + 68*t - 813. Solve 1/4*y**t + 0 - 1/2*y**2 + 1/4*y = 0 for y.
0, 1
Let u(b) be the second derivative of 3*b + 0 + 5/6*b**3 + 1/4*b**5 + 0*b**2 - 5/6*b**4. Factor u(y).
5*y*(y - 1)**2
Let y be 2/(-8) - (-19)/(-4). Let m(q) = -2*q - 6. Let v be m(y). Factor -v*w**2 - w**2 + 2*w - 6*w**3 + 1 + 0.
-(w + 1)*(2*w - 1)*(3*w + 1)
Let 24/5 - 2/5*n**2 + 22/5*n = 0. What is n?
-1, 12
Let f(w) be the first derivative of -9 - 15/2*w**2 + 5/4*w**4 - 10/3*w**3 + 0*w. Solve f(i) = 0 for i.
-1, 0, 3
Let m = -69 + 72. Solve g**m + 5*g**2 - 5 + 3 + 8*g**2 - g - 11*g**2 = 0.
-2, -1, 1
Let m(b) be the second derivative of -b**4/66 + 16*b**2/11 - 104*b. Factor m(h).
-2*(h - 4)*(h + 4)/11
Let p(q) be the third derivative of 0 + 0*q**5 + 0*q**7 + 1/32*q**4 + 0*q + 32*q**2 + 1/448*q**8 - 1/80*q**6 + 0*q**3. Factor p(n).
3*n*(n - 1)**2*(n + 1)**2/4
Let b be 0/(135/((-117)/(-13)) + -13). Solve b*l + 6/5*l**3 + 2/5*l**2 + 0 = 0.
-1/3, 0
Let b(l) = 4*l**2 + 2*l + 2. Let v be b(-1). Suppose -55*c**3 + 29*c**2 + 0*c**4 - 5 + 30*c**v + 15*c - 14*c**2 = 0. Calculate c.
-1/2, 1/3, 1
Let v(t) = -t**3 + 4*t**2 - t - 6. Let f be v(3). Let m be (-18)/(-40) - 3/12 - f. Determine n so that 2/5*n**2 + 1/5*n + m*n**3 + 0 = 0.
-1, 0
Let f = -4 + 5. Let w be 2*(-3)/(3/f). Let s(l) = 9*l**3 - 13*l**2 + 4*l + 2. Let x(n) = 36*n**3 - 51*n**2 + 15*n + 9. Let b(d) = w*x(d) + 9*s(d). Factor b(o).
3*o*(o - 1)*(3*o - 2)
Let z(t) = -t**2 + 14*t + 17. Let c be z(15). Factor 54*x**c - 16*x**2 - 7*x**3 - 18*x**2 - 18*x**2.
-x**2*(7*x - 2)
Let q be (-12)/150 + 102/25. Let g be 2/1 - (-3 + 5). Solve 0*z - 1/6*z**q + 0 + 1/6*z**2 + g*z**3 = 0.
-1, 0, 1
Let g(s) be the second derivative of s**4/24 - 27*s**3 + 6561*s**2 + 438*s. Find b, given that g(b) = 0.
162
Let b(c) = -28*c**3 + 168*c**2 - 112*c + 8. Let g(k) = -19*k**3 + 112*k**2 - 74*k + 5. Let t(z) = -5*b(z) + 8*g(z). Factor t(o).
-4*o*(o - 4)*(3*o - 2)
Let u(d) = -2*d**3 - d**2 - d. Let o(s) = -7*s**3 - 7*s**2 - 2*s. Let g(n) = 5*o(n) - 20*u(n). Factor g(j).
5*j*(j - 2)*(j - 1)
Let q = 5601 - 22261/4. Let b = 36 - q. Factor 0 - 3/4*a**2 - b*a**4 - 1/4*a - 3/4*a**3.
-a*(a + 1)**3/4
Suppose -5*r - 3 = -6*r. Factor 3*a**2 + 8*a - 2*a**3 + 7 - a**4 + r - 6.
-(a - 2)*(a + 1)**2*(a + 2)
Factor -21/5*u - 1/10*u**2 - 441/10.
-(u + 21)**2/10
Let u(y) be the first derivative of 0*y + 0*y**2 + 0*y**3 - 1/26*y**4 - 2/65*y**5 + 15. Factor u(i).
-2*i**3*(i + 1)/13
Let l be ((-8)/12*12)/(-2). Suppose f = -l*f + 85. Suppose 6 - 24*y**2 + 4*y**3 + f*y**3 - 21*y + 18*y**2 = 0. Calculate y.
-1, 2/7, 1
Suppose -45*z**4 - 219*z**3 - 300 - 720*z - 30*z**3 - 3*z**5 - 663*z**2 + 36*z**2 = 0. Calculate z.
-5, -2, -1
Let j be (1 - (-167)/11) + 10/(-55). Suppose -x = -3*q - q + 4, 3*q - 4*x - j = 0. Determine v, given that 1/4*v**3 - 1/4*v**5 + 0*v**2 + q*v + 0*v**4 + 0 = 0.
-1, 0, 1
Solve -2/13*l**2 + 40/13 - 2/13*l = 0 for l.
-5, 4
Let -a**4 - 15*a**2 + 16*a**2 + 0*a**2 - 6*a**3 + 26*a**2 = 0. What is a?
-9, 0, 3
Let p(s) be the second derivative of 0*s**2 + s + 0*s**4 - 1/10*s**6 + 1/21*s**7 + 0 + 0*s**3 + 1/20*s**5. Find r such that p(r) = 0.
0, 1/2, 1
Let v be -10 + ((-90)/(-40) - -10). Factor -6*k**3 + 0*k - v*k**4 + 27/4*k**5 + 3*k**2 + 0.
3*k**2*(k + 1)*(3*k - 2)**2/4
Let p = -1205 - -1210. Let n(u) be the second derivative of 1/45*u**3 - 5*u - 1/90*u**4 - 1/150*u**p + 0 + 1/15*u**2. Suppose n(i) = 0. Calculate i.
-1, 1
Find c such that 4/5*c**3 - 268/5*c + 0 + 264/5*c**2 = 0.
-67, 0, 1
Let x(s) be the second derivative of -s**4/48 - 21*s**3/4 - 3969*s**2/8 + 361*s. Solve x(m) = 0.
-63
Suppose -3*i = -3 - 3. Let x = -12205/12 + 4071/4. Solve 0*v - x*v**2 + 0 + i*v**3 - 4/3*v**4 = 0.
0, 1/2, 1
Let w be (-172)/(-36) + 3/(-81)*-6. Let g(m) be the third derivative of -w*m**2 + 2/7*m**3 + 0*m + 0 - 1/105*m**5 + 1/21*m**4. Determine c so that g(c) = 0.
-1, 3
Suppose 0*m + 2*m = l + 45, -2*l = 4*m - 102. Solve -65*t**2 + m*t**2 - 36*t**3 + 20*t**2 - 3*t = 0 for t.
-1/3, -1/4, 0
Solve 6/7*s**2 + 2/7*s**3 + 162/7 - 90/7*s = 0 for s.
-9, 3
Let i(k) be the third derivative of -k**5/90 - 8*k**4/3 - 256*k**3 - 186*k**2. Factor i(o).
-2*(o + 48)**2/3
Factor 2*h**3 + 12*h**2 + 11*h**4 - h**3 + 2*h**3 - 14*h**4 - 12*h.
-3*h*(h - 2)*(h - 1)*(h + 2)
Let i(a) = a**3 + 8*a**2 + 6*a + 6. Suppose 4*y - 8 - 8 = 4*n, 0 = 2*y + 6. Let u be i(n). Determine r so that -3*r**2 - u*r + 15*r + 5*r**2 =