, given that p(x) = 0.
1, 3
Find s such that 1/2*s - 1/4 - 1/4*s**2 = 0.
1
Let v(b) be the second derivative of 15*b**7/7 - 27*b**6/5 + 21*b**5/5 - 2*b**4/9 - 8*b**3/9 + 3*b - 2. Factor v(k).
2*k*(3*k - 2)**3*(5*k + 1)/3
Let j(u) = 190*u**3 - 2485*u**2 + 8100*u - 7395. Let b(s) = -7*s**3 + 92*s**2 - 300*s + 274. Let x(p) = 55*b(p) + 2*j(p). Factor x(n).
-5*(n - 14)*(n - 2)**2
Let y = -47 + 49. What is z in y*z**4 - 19*z**3 + 41*z**3 - z - 19*z**3 = 0?
-1, 0, 1/2
Let u be 152/38 + 96/(-26). Let f(i) be the first derivative of 2 - 4/39*i**3 - 1/26*i**4 + 1/13*i**2 + u*i. Factor f(q).
-2*(q - 1)*(q + 1)*(q + 2)/13
Let b be (-8*((-6)/4 - -1))/1. Determine w so that 6*w**b + 6*w**2 - 16*w**4 + 5*w - 5*w**3 + w**2 + 3*w**2 = 0.
-1, -1/2, 0, 1
Let h be ((-5 - 7) + 10)*-2. Factor -2/9*p + 2/3*p**2 + 0 - 2/3*p**3 + 2/9*p**h.
2*p*(p - 1)**3/9
Let l = -86 + 91. Let f(q) be the third derivative of 0*q - 4*q**2 + 2/105*q**7 - 1/120*q**6 + 0 + 1/24*q**4 - 1/15*q**l + 0*q**3. Factor f(x).
x*(x - 1)*(x + 1)*(4*x - 1)
Let d(c) = 11*c**3 - 275*c**2 + 3173*c - 2889. Let w(i) = 5*i**3 - 137*i**2 + 1586*i - 1446. Let b(a) = 2*d(a) - 5*w(a). Factor b(s).
-3*(s - 22)**2*(s - 1)
Let i(x) = -222 + 3*x + 9*x**2 + 0*x + 2*x**3 + 213. Let f(d) = -6*d**3 - 28*d**2 - 10*d + 28. Let n(h) = -5*f(h) - 16*i(h). Determine g so that n(g) = 0.
-2, -1, 1
Let b(q) be the third derivative of -q**8/26880 - q**7/960 + 3*q**6/160 - 5*q**5/12 + 58*q**2. Let j(a) be the third derivative of b(a). Factor j(p).
-3*(p - 2)*(p + 9)/4
Let l(f) be the first derivative of -2*f**6/3 - 32*f**5/5 - 18*f**4 - 64*f**3/3 - 10*f**2 + 38. Find a, given that l(a) = 0.
-5, -1, 0
Let -4/9*y**3 + 32/3 + 188/9*y + 88/9*y**2 = 0. What is y?
-1, 24
Let v(b) be the first derivative of b**8/672 + b**7/630 - b**6/720 - 7*b**2/2 - 6. Let c(u) be the second derivative of v(u). Solve c(i) = 0 for i.
-1, 0, 1/3
Let x(i) be the second derivative of 7*i + 3/100*i**5 + 9/5*i**2 - 1/2*i**3 + 0 - 1/10*i**4. Factor x(t).
3*(t - 3)*(t - 1)*(t + 2)/5
Let p(i) = 35*i**2 + 140*i + 80. Let t(j) = -2*j - 18*j**2 - 65*j + 16*j - 40 - 19*j. Let h(c) = -3*p(c) - 5*t(c). Factor h(k).
-5*(k + 4)*(3*k + 2)
Let j(a) be the first derivative of -a**6/2 - 9*a**5/5 - 3*a**4/2 - 8. Factor j(l).
-3*l**3*(l + 1)*(l + 2)
Let b(f) be the first derivative of -f**6/180 + f**5/20 + 2*f**3/3 - f**2 - 43. Let y(z) be the third derivative of b(z). Factor y(o).
-2*o*(o - 3)
Let l(y) = 8*y**3 - 27*y - 5. Let q be 4/(16/(-28)) - -2. Let m(d) = 20*d**3 - 68*d - 12. Let o(f) = q*m(f) + 12*l(f). Factor o(h).
-4*h*(h - 2)*(h + 2)
Suppose 2*b = -2*b. Suppose b = -2*z - z - 3. Let g(t) = -5*t**3 - t**2 + 5*t - 5. Let n(o) = o**3 - o + 1. Let h(i) = z*g(i) - 6*n(i). Solve h(k) = 0.
-1, 1
Let v(h) be the third derivative of 31*h**2 - 1/120*h**6 + 0*h**5 + 1/24*h**4 + 0 + 0*h + 0*h**3. Suppose v(f) = 0. Calculate f.
-1, 0, 1
Let o(l) be the second derivative of 1/72*l**4 + 0*l**2 + 0 + 1/12*l**3 + 6*l. Find u such that o(u) = 0.
-3, 0
Let s be 184/56 - 4/14. Suppose 0 = s*h + 2*h - 10. Factor -5*i**2 + 3*i**2 + i**2 + 3*i**h.
2*i**2
Factor 0*y - 4/3*y**4 - 4/3*y**2 - 8/3*y**3 + 0.
-4*y**2*(y + 1)**2/3
Let x(h) = 28*h**3 - h**2 + 2*h - 2. Let u be x(1). Factor -27*l - l**3 - 8*l**2 - l**2 + 0*l - u.
-(l + 3)**3
Suppose -7225/4 + 85/2*p - 1/4*p**2 = 0. What is p?
85
Let l be 7/14*8*3/2. Factor -6*i**2 + 2*i - 5*i + 0*i + 3*i**3 + l.
3*(i - 2)*(i - 1)*(i + 1)
Suppose -4*z - 4*o = -3*o - 15, 4*z - o = 17. Suppose -9*h**3 - 18*h + 6 + 39/2*h**2 + 3/2*h**z = 0. Calculate h.
1, 2
Let m be (33/(-18) - -2)/((-6)/585). Let v = 17 + m. Suppose -v*b + 0 + 3/4*b**2 = 0. Calculate b.
0, 1
Let i = 34 - 54. Let p be ((-1)/(-2))/(i/24*-1). Find g, given that 15*g**3 + 21/5*g + 57/5*g**2 + p + 12/5*g**5 + 48/5*g**4 = 0.
-1, -1/2
Suppose 0 = 2*o - 5*i + i - 6, 3*i + 9 = 3*o. Suppose -b = x - 4 + 1, 0 = -2*x - 3*b + 7. Factor -h**3 - h**o + x*h**4 + 0*h**3.
2*h**3*(h - 1)
Let p(f) = 10*f**2 + 4 + 16*f - f**2 + 15*f**2 + 9*f**3. Let y(b) = b**3 + b**2 - b + 1. Let l(z) = p(z) - 4*y(z). Factor l(c).
5*c*(c + 2)**2
Let d(y) be the first derivative of -676/3*y**3 - 16*y + 104*y**2 - 16. Factor d(l).
-4*(13*l - 2)**2
Factor -88*t - 26*t**3 + 5/2*t**4 + 80*t**2 + 24.
(t - 6)*(t - 2)**2*(5*t - 2)/2
Let h(k) = 6*k + 44. Let d be h(-7). Let 3*i + i**2 - 2*i**2 - 9*i**d = 0. Calculate i.
0, 3/10
Let t(q) = 8*q - 6. Let i be t(1). Let y be (2 - (4 - 4)) + i/(-4). Factor -m**2 - y*m**3 + 0 + 0*m - 1/2*m**4.
-m**2*(m + 1)*(m + 2)/2
Factor -3/2 - 3/2*k + 3/2*k**2 + 3/2*k**3.
3*(k - 1)*(k + 1)**2/2
Let u(f) = -20*f**3 + 177*f. Let p(a) = 7*a**3 - 60*a. Let r(w) = 11*p(w) + 4*u(w). Suppose r(h) = 0. What is h?
-4, 0, 4
Let l = -8 + 10. Suppose -l*x - 5*j + 4 = 0, -2 + 6 = 2*x + 4*j. Determine r, given that 0*r**2 - 5*r**2 + 15*r - 10 + 0*r**x = 0.
1, 2
Let r(v) be the first derivative of v**8/560 + v**7/70 + v**6/24 + v**5/20 - 4*v**3 + 10. Let t(y) be the third derivative of r(y). Let t(a) = 0. What is a?
-2, -1, 0
Suppose 4*s - 10 = -2. Factor 4*v**2 + v**4 + 4*v**3 - 2*v**2 + 3*v**2 - v**s.
v**2*(v + 2)**2
Let u(t) be the second derivative of t**5/20 - 7*t**4/4 + 20*t**3 - 50*t**2 + 327*t. Factor u(j).
(j - 10)**2*(j - 1)
Let m(y) = -6*y**2 + 64*y - 216. Let h(i) = -2*i**2 + 21*i - 72. Let s be -5 + (-27)/(-5) + 84/(-10). Let v(w) = s*h(w) + 3*m(w). Suppose v(z) = 0. What is z?
6
Let g(n) = -14*n**5 - 4*n**4 - 10*n**3 - 4*n**2 + 24. Let i(t) = -2*t**5 - t**4 + 2*t**2 - t + 1. Let h(a) = g(a) - 8*i(a). Determine p so that h(p) = 0.
-2, -1, 1, 2
Suppose f - 63 + 55 = 0. Let t be f/6 - (4 + (0 - 4)). Factor 2*n**2 - 2/3*n**3 - 2/3*n**4 + t + 10/3*n.
-2*(n - 2)*(n + 1)**3/3
Let b(f) be the second derivative of f**6/45 + 4*f**5/5 + 92*f**4/9 + 160*f**3/3 + 400*f**2/3 - 33*f. Determine p, given that b(p) = 0.
-10, -2
Let u(y) be the first derivative of -2/5*y**5 + 0*y**2 + 0*y + 1/6*y**6 - y**4 - 22 + 8/3*y**3. Find c, given that u(c) = 0.
-2, 0, 2
Let b(g) be the third derivative of -125/336*g**8 + 0 - 5/42*g**7 + 0*g - 1/3*g**5 + 2/3*g**6 + 0*g**3 - 4*g**2 + 0*g**4. Factor b(f).
-5*f**2*(f + 1)*(5*f - 2)**2
Let v(f) = 6*f**4 + 6*f**3 - 10*f**2 - 2*f + 4. Let x(a) = 7*a**4 + 5*a**3 - 9*a**2 - 3*a + 6. Let i(j) = -3*v(j) + 2*x(j). Factor i(r).
-4*r**2*(r - 1)*(r + 3)
Let k(r) be the third derivative of -r**10/30240 + r**9/7560 - r**8/20160 - r**7/2520 + r**5/30 - 4*r**2. Let p(w) be the third derivative of k(w). Factor p(t).
-t*(t - 1)**2*(5*t + 2)
Let w = -116 + 120. Let x(k) be the first derivative of 1/2*k**4 + 2/3*k**3 - w - k**2 + 0*k - 2/5*k**5. Factor x(m).
-2*m*(m - 1)**2*(m + 1)
Suppose 94*w = 89*w + 20. Factor 95*u**2 + 68*u**3 + 19*u**w - 8 + 16*u - 21*u**2 - u**4.
2*(u + 1)**2*(u + 2)*(9*u - 2)
Let m(i) be the second derivative of 23*i**4/4 + 24*i**3 + 6*i**2 - 245*i. Factor m(x).
3*(x + 2)*(23*x + 2)
Let l(y) be the second derivative of -y**6/255 - y**5/170 + y**4/51 - 9*y + 1. Let l(u) = 0. What is u?
-2, 0, 1
Factor 2/13 - 6/13*z - 2/13*z**2 + 6/13*z**3.
2*(z - 1)*(z + 1)*(3*z - 1)/13
Let z(c) be the third derivative of 0 + 1/18*c**4 + 1/180*c**5 - 13*c**2 - 5/18*c**3 + 0*c. Factor z(f).
(f - 1)*(f + 5)/3
Suppose 4*g = g. Let k(r) = r**3 - r**2 + r + 5. Let m be k(g). Factor 27*f**m + 9*f**3 + 2 - 2 + 18*f**4 - 6*f**3.
3*f**3*(3*f + 1)**2
Let l(w) = -w**2 - 4*w + 47. Let y be l(5). Solve -15/7*s**y - 24/7*s - 12/7 - 3/7*s**3 = 0 for s.
-2, -1
Let r(a) be the third derivative of 1/24*a**6 + 0*a - 1/12*a**3 - 1/12*a**5 + 1/672*a**8 + 5/48*a**4 + 4*a**2 + 0 - 1/84*a**7. Find p, given that r(p) = 0.
1
Let w(l) = 4*l**2 + 9*l - 85. Let z(k) = 4*k**2 + 8*k - 92. Let d(n) = 4*w(n) - 5*z(n). Factor d(q).
-4*(q - 5)*(q + 6)
Let x(q) = -41*q - 6*q**2 - 2 + 37*q + 2*q**2. Let m(b) = 13*b**2 + 11*b + 5. Suppose 0*y + 20 = 5*y. Let o(v) = y*m(v) + 14*x(v). Factor o(r).
-4*(r + 1)*(r + 2)
Let h = -177 - -180. Let b(t) be the first derivative of -21/2*t**2 + 4*t**h - 6*t - 4. Find i, given that b(i) = 0.
-1/4, 2
Factor 765*c - 798 + 99*c**2 + 2*c**3 + 14 - 83 + c**3.
3*(c - 1)*(c + 17)**2
Let c be ((-70)/(-25) + -4)/((-8)/20). Let i(m) be the first derivative of -1/12*m**4 + 1/3*m**2 - 1/9*m**c - 2 + 0*m. Solve i(v) = 0.
-2, 0, 1
Suppose -6 = -3*d + 2*u, -4*d + 2 = -3*d + 2*u. Factor 8*m + 32*m*