Let h(y) = y**2 - 20*y + 22. Let o be h(19). Factor -q**5 + q**5 + q**5 + 2*q**3 + o*q**4 + 0*q**3.
q**3*(q + 1)*(q + 2)
Let n(f) be the third derivative of -f**9/11340 + f**8/2520 + f**7/1890 - f**6/270 + f**4/8 - 2*f**2. Let x(t) be the second derivative of n(t). Factor x(u).
-4*u*(u - 2)*(u - 1)*(u + 1)/3
Factor -18*m + 70*m + 88*m**2 + 0*m**5 + 28*m**4 + 12 + 4*m**5 + 72*m**3.
4*(m + 1)**4*(m + 3)
Factor -6 - 16*a**2 - 9*a**3 - 3*a + 12*a**3 + 22*a**2.
3*(a - 1)*(a + 1)*(a + 2)
Factor -16/9*i - 2/9*i**3 + 10/9*i**2 + 8/9.
-2*(i - 2)**2*(i - 1)/9
Let s be (-10)/(-40) - (-3)/12. Let s - 1/4*j**2 + 1/4*j = 0. Calculate j.
-1, 2
Let h(t) be the third derivative of -t**7/30 + t**6/20 + 3*t**5/140 - t**4/84 + 324*t**2. Solve h(g) = 0 for g.
-2/7, 0, 1/7, 1
Let s(o) = -11*o**2 - 99*o + 193. Let q(b) = -8*b**2 - 66*b + 129. Let i(h) = -7*q(h) + 5*s(h). Find m, given that i(m) = 0.
2, 31
Let q(m) = -7*m**3 + 50*m**2 + m - 35. Let d(z) = -76*z**3 + 548*z**2 + 12*z - 388. Let b(g) = 3*d(g) - 32*q(g). Let b(c) = 0. Calculate c.
-1, 1, 11
Factor -8754*q + 21332 - 2046*q - q**3 - 360*q**2 - 129332 - 3*q**3.
-4*(q + 30)**3
Let p(t) = t**2 + 28*t + 29. Let g be p(-27). Let b(r) = -r**3 + 10*r**2 - 10*r + 9. Let c be b(9). Factor -2/5 + 2/5*a**g + c*a.
2*(a - 1)*(a + 1)/5
Let h(i) be the third derivative of 0 - 1/30*i**5 + 1/12*i**4 + 37*i**2 + 0*i + 1/672*i**8 - 1/80*i**6 + 0*i**3 + 1/210*i**7. Factor h(t).
t*(t - 1)**2*(t + 2)**2/2
Let a(u) = u**2 + 8*u - 4. Let y be a(-9). Suppose 0 = y*m - 8 - 2. Solve -4/5*r + 0 - 6/5*r**m = 0 for r.
-2/3, 0
Let g(f) be the third derivative of 7/11*f**4 - 49/33*f**3 + 0 - 1/1155*f**7 - 3*f**2 - 1/55*f**6 - 1/15*f**5 + 0*f. Suppose g(t) = 0. Calculate t.
-7, 1
Let u(x) be the first derivative of x**5/80 + x**4/16 + x**3/8 + 6*x**2 - 5. Let r(k) be the second derivative of u(k). Factor r(j).
3*(j + 1)**2/4
Let q = -8 + 26. Let z(y) be the first derivative of -21*y**5/5 - 3*y**4/2 + 6*y**3 + 45. Let r(b) = -b**4 + b**2. Let h(m) = q*r(m) - z(m). Factor h(v).
3*v**3*(v + 2)
Suppose -q + 6*q - 15 = 0. Let d be (3 + -2)*20/40*4/4. Suppose 0*l - d*l**q + 0 + 0*l**2 = 0. What is l?
0
Factor -41*w + 2*w**4 - 8*w**2 + 7*w**3 + 15*w**3 + 9*w - 14*w**3.
2*w*(w - 2)*(w + 2)*(w + 4)
Factor 3708*a**2 + 39*a + 9*a - 3705*a**2 + 45.
3*(a + 1)*(a + 15)
Let v(t) be the second derivative of t**6/30 + 13*t**5/60 + t**4/18 - 4*t**3/9 - 40*t + 1. Suppose v(m) = 0. Calculate m.
-4, -1, 0, 2/3
Let l = 1 + 7. Let q be (1/(-3))/(l/(-48)). Factor -q*r + 3*r**2 + 0*r + 8*r.
3*r*(r + 2)
Let q(c) be the second derivative of -3*c**7/7 + 56*c**6/15 + 3*c**5/2 - 25*c**4 - 76*c**3/3 + 24*c**2 + 34*c - 1. Let q(u) = 0. Calculate u.
-1, 2/9, 2, 6
Let h(x) be the first derivative of -8*x**3 - 11 + 2*x**2 + 39/4*x**4 + 8*x + 169/20*x**5. Let y(t) be the first derivative of h(t). Factor y(w).
(w + 1)*(13*w - 2)**2
Let o(x) = 7*x - 67. Let i be o(10). Let s(z) be the second derivative of -1/2*z**5 + 2*z - 9*z**3 - 27/2*z**2 + 0 - i*z**4 - 1/30*z**6. Factor s(d).
-(d + 1)*(d + 3)**3
Let x be (13/(-2) - -6)*-6. Let p(o) be the second derivative of 3*o + 0 - x*o**2 - 1/4*o**4 + 3/2*o**3. Determine w, given that p(w) = 0.
1, 2
Suppose 0 = 5*m + 2*q - 15, -4*m - q + 12 = 2*q. Suppose -3 = -m*n + 3. Factor n + 5*g**2 + 6*g**2 + 9*g**3 + 2*g**4 - 9 + 3.
(g + 1)*(g + 2)**2*(2*g - 1)
Let b(i) = -284*i + 4. Let y be b(0). Factor 0*u - 2/5*u**y + 0 + 2/5*u**3 + 4/5*u**2.
-2*u**2*(u - 2)*(u + 1)/5
Let m(g) = 647*g**2 - 73*g + 1. Let p(t) = -t**2 - t - 1. Let u(d) = -m(d) + p(d). Find v such that u(v) = 0.
1/18
What is f in -28*f - 1/4*f**4 - 39/2*f**2 - 49/4 - 4*f**3 = 0?
-7, -1
Let p(z) = -19*z**3 - 43*z**2 + 91*z - 29. Let y(l) = 9*l**3 + 21*l**2 + 1 - 45*l + 12 + 2. Let a(s) = 6*p(s) + 13*y(s). Determine m so that a(m) = 0.
-7, 1
Let 3/8*o**2 + 0 + 69/8*o = 0. What is o?
-23, 0
Factor 3*h - 32*h**2 - 9*h - 33 - 62*h - 4*h**3 - 7.
-4*(h + 1)*(h + 2)*(h + 5)
Let c be 1292/304 - 20/16. Factor -6/5*h + 2/5*h**c + 0 - 4/5*h**2.
2*h*(h - 3)*(h + 1)/5
Let n(g) be the second derivative of g**5/120 + g**4/9 + 4*g**3/9 + 11*g + 8. Factor n(o).
o*(o + 4)**2/6
Let n = -197 - -197. Let p(w) be the first derivative of -1/10*w**2 + n*w - 1/5*w**3 + 1/15*w**6 - 1/20*w**4 + 3/25*w**5 - 4. What is a in p(a) = 0?
-1, -1/2, 0, 1
Let i(x) = 3*x**3 + 18*x**2 + x - 22. Let j(w) = -6*w**3 - 36*w**2 - 3*w + 45. Let h(a) = -9*i(a) - 4*j(a). Solve h(d) = 0 for d.
-6, -1, 1
Suppose 22 = 5*t + 7. Factor -2*n**3 - 44*n**2 - t*n**3 + 0*n**3 + 29*n**2.
-5*n**2*(n + 3)
Let d(t) be the second derivative of -t**7/2520 - 13*t**6/360 - 169*t**5/120 - 11*t**4/6 + 29*t. Let r(z) be the third derivative of d(z). Factor r(n).
-(n + 13)**2
Let j be ((-634)/4)/(58/16 - 4). Let u = j - 413. Find z, given that -7/3*z**5 - u*z**2 + 5/3*z**4 + 4/3*z + 23/3*z**3 + 4/3 = 0.
-2, -2/7, 1
Let b = -20 - -11. Let w = b - -15. Factor 4*u - 34*u**2 + 8 + 0*u - w*u**2.
-4*(2*u - 1)*(5*u + 2)
Let y = 7222 - 79306/11. Determine u so that 372/11*u**2 + 98/11*u**4 + y*u + 350/11*u**3 + 16/11 = 0.
-2, -1, -2/7
Let q = -2213/8 + 277. Let n(i) be the second derivative of 1/8*i**3 - 3/80*i**5 + 0 - 5*i + 1/16*i**4 - q*i**2. Factor n(r).
-3*(r - 1)**2*(r + 1)/4
Let f(d) = -d**3 - d**2 - 2*d + 2. Let l(u) = 6*u**3 + 5*u**2 + 10*u - 11. Let r(t) = t**2 - 7*t + 3. Let q be r(8). Let k(i) = q*f(i) + 2*l(i). Factor k(w).
w*(w - 2)*(w + 1)
Let w be 12*9/162*3. Factor 20/3*r + 4/3*r**w + 16/3.
4*(r + 1)*(r + 4)/3
Let f(j) = 6*j**3 + 2*j + 8. Let l = 175 - 172. Let q(c) = -5*c**3 + c**2 - 7 + 3*c + 0*c - 4*c. Let s(g) = l*f(g) + 4*q(g). Factor s(o).
-2*(o - 2)*(o - 1)*(o + 1)
Let l be ((-30)/12)/(15/(-12)). Let c(o) be the second derivative of -3*o - 1/15*o**3 + 0*o**l - 3/100*o**5 + 0 + 1/12*o**4. Factor c(b).
-b*(b - 1)*(3*b - 2)/5
Let i(g) = g**3 - g**2 - g. Let x(k) = -49*k**4 - 603*k**3 - 724*k**2 + 558*k - 88. Let z(w) = 6*i(w) - x(w). Solve z(h) = 0 for h.
-11, -2, 2/7
Suppose 0 = -86*x - 52*x + 276. Factor 2*o**4 + 0*o + 0 - 5/3*o**3 - 1/3*o**x.
o**2*(o - 1)*(6*o + 1)/3
Let h be 39 - 40*42/112. Factor -8*v + h + 2/3*v**2.
2*(v - 6)**2/3
Let r = 2/147 + 194/147. Factor r*k**2 + 2/3*k**3 + 0*k + 0.
2*k**2*(k + 2)/3
Let z(n) be the first derivative of -n**4/18 + 16*n**3/27 - n**2 - 4*n - 251. Factor z(d).
-2*(d - 6)*(d - 3)*(d + 1)/9
Let r(n) = -n**5 - 32*n**4 + 84*n**3 - 46*n**2 - 75*n + 86. Let d(g) = -16*g**4 + 42*g**3 - 24*g**2 - 38*g + 44. Let b(o) = 10*d(o) - 4*r(o). Factor b(s).
4*(s - 3)*(s - 2)**3*(s + 1)
Let y(v) = 13*v**3 - 37*v**2 + 47*v + 105. Let i(s) = -115*s**3 + 335*s**2 - 425*s - 945. Let r(p) = 4*i(p) + 35*y(p). Factor r(x).
-5*(x - 7)*(x - 3)*(x + 1)
Let y(c) be the second derivative of 0*c**2 - 2/25*c**6 + 0*c**3 + 0 - 3/100*c**5 + 1/30*c**4 - 1/30*c**7 + 18*c. Determine m, given that y(m) = 0.
-1, 0, 2/7
Suppose 4*m = m + 18. Let y be (2/3)/(8/m). Factor y - 3/8*n - 1/8*n**2.
-(n - 1)*(n + 4)/8
Let m = -10 - -4. Let g(k) = -8*k + 6. Let f be g(m). Factor -n**2 - 54*n + f*n + n**4.
n**2*(n - 1)*(n + 1)
Suppose 0 = 4*d + 2*b - 10, 10*b = 2*d + 13*b - 7. Solve 8/3*c**d + 28/3*c - 4/3*c**5 + 4 - 20/3*c**4 - 8*c**3 = 0.
-3, -1, 1
Let p(h) = -3*h - 28. Let f be p(9). Let r(g) = 45*g**2 + 215*g + 350. Let q(y) = -5*y**2 - 24*y - 39. Let i(s) = f*q(s) - 6*r(s). Factor i(n).
5*(n + 3)**2
Let c(d) = d**3 - 10*d**2 + d - 11. Let u be c(10). Let b(q) = -8*q**3 - 3*q**2 - 3. Let x(o) = o**3 + o**2 + 1. Let i(p) = u*b(p) - 3*x(p). Factor i(m).
5*m**3
Determine o so that 15706 + 4*o**2 + 19672 + 499*o - 2*o**2 + 33*o = 0.
-133
Let s(w) be the second derivative of 9*w**5/5 - 7*w**4/3 - 112*w**3/3 - 24*w**2 + 2*w - 31. Factor s(n).
4*(n - 3)*(n + 2)*(9*n + 2)
Let n(t) be the third derivative of t**5/150 - 7*t**4/20 - 11*t**2 + 35*t. Factor n(f).
2*f*(f - 21)/5
Let y(d) be the first derivative of 0*d**2 + 5/3*d**3 + 4 + 0*d + 3/4*d**4. Let m(z) = z**2. Let k(l) = -2*m(l) + y(l). Solve k(n) = 0.
-1, 0
Let l(j) be the first derivative of 5*j**3/3 + 165*j**2 + 5445*j - 26. Factor l(p).
5*(p + 33)**2
Let g(d) be the third derivative of d**6/240 - d**5/20 + 5*d**4/48 - 146*d**2. Find a, given that g(a) = 0.
0, 1, 5
Let g(h) be the second derivative of -1/15*h**3 - 20*h - 1/210*h**7 - 1/30*h**6 + 0 - 9/100*h**5 + 0*h**2 - 7/60*h**4