*h + 162. Let c(b) = 7*b**2 - 35*b + 54. Let o(n) = 7*c(n) - 2*m(n). Factor o(p).
3*(p - 9)*(p - 2)
Let q(c) be the first derivative of -c**7/315 + c**6/144 + 7*c**5/360 - c**4/72 - 25*c**2/2 + 25. Let a(y) be the second derivative of q(y). Factor a(u).
-u*(u - 2)*(u + 1)*(4*u - 1)/6
Suppose 3*a - 8*a - 10 = -5*r, -25 = -5*r. Factor 0*g**a + 2/9*g**4 + 0*g - 2/9*g**2 + 0.
2*g**2*(g - 1)*(g + 1)/9
Let s be 4 - (337/90 - (-9)/36). Let c(z) be the third derivative of 0*z + s*z**5 - 6*z**2 - 1/9*z**3 + 1/72*z**4 + 0. Suppose c(x) = 0. What is x?
-2, 1
Let j(v) be the third derivative of -2*v**7/945 + 2*v**6/27 - 38*v**5/45 + 2*v**4 + 18*v**3 - 17*v**2 + 3. Find f such that j(f) = 0.
-1, 3, 9
Let t(g) = 24*g**4 + 129*g**3 - 33*g**2 + 33*g. Let q(j) = 3*j**4 + 16*j**3 - 4*j**2 + 4*j. Let m(n) = -33*q(n) + 4*t(n). Find v such that m(v) = 0.
-4, 0
Let c be -12*32/48 - (-33)/4. Factor 0 - 5/4*y**4 - c*y**5 + 2*y + y**2 - 3/2*y**3.
-y*(y - 1)*(y + 2)**3/4
Let y(n) be the second derivative of -2*n**6/3 + 4*n**5/5 + 5*n**4/3 - 8*n**3/3 + 261*n. Factor y(p).
-4*p*(p - 1)*(p + 1)*(5*p - 4)
Let u be ((-10)/(-50) - (-116)/70) + -2. Let m = 55/91 + u. Factor -8/13*f - 2/13 - m*f**2.
-2*(f + 1)*(3*f + 1)/13
Let o(r) be the second derivative of r**4/18 - 14*r**3 - 127*r**2/3 - 2*r - 6. Factor o(b).
2*(b - 127)*(b + 1)/3
Determine n so that 1/2*n + 0 - 1/10*n**2 = 0.
0, 5
Let f(h) be the third derivative of 0*h - 1/525*h**7 + 0 - h**2 - 1/15*h**3 + 0*h**6 + 0*h**4 + 1/75*h**5. Factor f(t).
-2*(t - 1)**2*(t + 1)**2/5
Let v(y) be the third derivative of 3*y**7/70 - y**6/4 + 9*y**5/20 - y**4/4 - 559*y**2. Factor v(c).
3*c*(c - 2)*(c - 1)*(3*c - 1)
Let w(x) = 16*x**4 - 57*x**3 + 72*x**2 - 42*x + 9. Suppose -10 = 2*b - 12. Let h(g) = -g**3 - g**2. Let f(y) = b*w(y) - h(y). Suppose f(p) = 0. What is p?
3/4, 1
Let o = -20 + 43. Factor -o*b + 5 - 25*b + 5*b**2 + 38*b.
5*(b - 1)**2
Let d(x) = 12*x + 3. Let r be d(-1). Let n = 12 + r. Let 8*c**2 + c**n + 4*c - 4*c**3 + 7*c**3 = 0. What is c?
-1, 0
Let z = -6 + 12. Factor -z*g**4 + 4 + 28 + 386*g**2 - 208*g - 48*g**3 - 108*g**3 + 24*g**4.
2*(g - 4)**2*(3*g - 1)**2
Let c be (-4)/(-7*(-60)/(-315)). Suppose -5*g + 7 = -0*x + 3*x, -2*g = 3*x - 1. What is q in 1/3*q**c - 4/3 + q**g + 0*q = 0?
-2, 1
Suppose -5*i - 4 = -14. Suppose -3 = -3*f + i*f. Factor 2*y**3 + 0*y - 3*y + 2 - f*y**2 + 1 + y**3.
3*(y - 1)**2*(y + 1)
Suppose -25*b + 34 = -16. Let k(i) be the second derivative of 1/135*i**6 + 0 + 1/6*i**4 - 1/18*i**5 - 7/27*i**3 + 2/9*i**b - i. Factor k(t).
2*(t - 2)*(t - 1)**3/9
Suppose 396/7*a - 375/7*a**5 + 300*a**4 - 345*a**3 - 1686/7*a**2 + 216/7 = 0. Calculate a.
-2/5, 2/5, 3
Suppose 4*q - 126 = -2*h, 5*h = q - 9 - 6. Suppose -12 = -4*i, -p - p - 2*i = -q. Factor 3*g**5 + 5*g**2 - 9*g**2 - g**4 + p*g**3 - 10*g**4.
g**2*(g - 2)*(g - 1)*(3*g - 2)
Let -10/9*l**4 + 4/9*l**3 + 0*l + 2/9*l**5 + 0 + 16/9*l**2 = 0. What is l?
-1, 0, 2, 4
Let 0 - 2/7*u**2 + 2/7*u**3 + 0*u - 2/7*u**5 + 2/7*u**4 = 0. Calculate u.
-1, 0, 1
Suppose -t = -5*h + 2*h + 9, h = 2*t + 8. Factor 0 + h*k**2 + 18/7*k**3 - 4/7*k.
2*k*(k + 1)*(9*k - 2)/7
Let u(y) = 13*y**3 + 19*y**2 - 23*y - 24. Let l(z) = -45*z**3 - 66*z**2 + 81*z + 84. Suppose -3*d - 80 + 65 = 0. Let a(c) = d*l(c) - 18*u(c). Factor a(h).
-3*(h - 1)*(h + 1)*(3*h + 4)
Suppose 18 = -3*o - 3. Let z be (12/21)/((-2)/o). Factor 4 + 2*h**3 - 4*h**2 + 8*h + 12*h**2 + z*h.
2*(h + 1)**2*(h + 2)
Let j(w) = w. Let r(k) = 5*k**2 - 20*k. Suppose 2*a - 19 = 21. Let c(q) = a*j(q) + r(q). Let c(m) = 0. Calculate m.
0
Let k(i) = -3*i + 15. Let n be k(4). Find s such that -616*s**n + 0*s + 617*s**3 - s = 0.
-1, 0, 1
Let c(k) be the third derivative of 22*k**2 + 0*k + 1/480*k**5 - 1/8*k**3 + 0 + 5/192*k**4. Determine b so that c(b) = 0.
-6, 1
Suppose 0 = -9*x + 4 + 14. Let 0*p**4 + 3*p**3 - 3*p**x - 13*p**5 + 10*p**5 + 3*p**4 = 0. What is p?
-1, 0, 1
Let j(s) be the first derivative of 2*s**5/5 + s**4 - 2*s**3/3 - 2*s**2 - 4*s - 1. Let i(o) = 4 + 7 + 9 - 23 + 4. Let p(r) = 4*i(r) + j(r). Factor p(m).
2*m*(m - 1)*(m + 1)*(m + 2)
Solve -2/9*g**2 - 28/9*g + 64/9 = 0 for g.
-16, 2
Let s(n) = -2*n + 43. Let i be s(9). Let r = i - 22. Solve 2/3*v**r - 2*v - 4/3 + 0*v**2 = 0 for v.
-1, 2
Let t(c) be the third derivative of -c**5/240 + c**4/8 - 167*c**2 - 2*c. Determine i, given that t(i) = 0.
0, 12
Let w(j) be the second derivative of j**7/210 - j**6/75 - j**5/20 + j**4/10 + 189*j. Suppose w(v) = 0. Calculate v.
-2, 0, 1, 3
Let d(r) be the second derivative of -r**7/3780 - r**6/540 - r**4/2 - 9*r. Let m(k) be the third derivative of d(k). Factor m(p).
-2*p*(p + 2)/3
Suppose 9*w**2 - w + 12*w + 9*w**3 - 8*w + 3*w**4 = 0. Calculate w.
-1, 0
Suppose -6*f - 80 = -11*f. Solve 40*a**2 - 31 + 10*a**3 + 25 + f - 5*a**5 - 10*a**4 + 35*a = 0 for a.
-1, 2
Let o(b) be the third derivative of 0*b**3 - 15*b**2 + 0 + 0*b + 1/20*b**4 - 1/50*b**5. Find s such that o(s) = 0.
0, 1
Suppose 2*s - 3*n + 1 = 5, s - 2*n = 3. Let p be (s/(-3))/(15/9). Factor 1/5*g**3 + 1/5*g**2 + 0 - 1/5*g - p*g**4.
-g*(g - 1)**2*(g + 1)/5
Let c be -2 + (7 - 5) - 6/57. Let l = 25/57 + c. Find w such that l - 1/3*w**3 + 1/3*w - 1/3*w**2 = 0.
-1, 1
Let v(f) = -21*f**2 + 4. Let d be v(-2). Let i be (2/(-2))/(10/d). Solve -2*j + 6*j**3 - 6*j**4 + i*j**3 - 4*j**2 - 2*j**4 = 0 for j.
-1/4, 0, 1
Let b be (0 + -10)/(-5) + 0/(-1). Let q be 4/3*b/((-56)/(-18)). Factor q*m + 3/7*m**2 + 3/7.
3*(m + 1)**2/7
Let u(j) be the first derivative of 4*j**5/5 - 2*j**4 + 4*j**3/3 + 210. Solve u(y) = 0.
0, 1
Let f = -5/5384 - -3031/2692. Let 1/4*b**3 + 3/8*b - f*b**2 + 1/2 = 0. Calculate b.
-1/2, 1, 4
Determine w so that -253/3*w**2 - 108 - 34/3*w**3 + 204*w - 1/3*w**4 = 0.
-18, 1
Let f(x) = -15*x**2 - 1182*x - 1167. Let v(s) = 6*s**2 + 473*s + 467. Let i(u) = -5*f(u) - 12*v(u). Determine w so that i(w) = 0.
-77, -1
Let k(p) be the third derivative of p**8/840 - p**6/180 + 3*p**3/2 + p**2. Let z(f) be the first derivative of k(f). What is i in z(i) = 0?
-1, 0, 1
Let t(h) = 12*h + 3. Let k(p) = p**2 - 13*p - 2. Suppose 4*l + 2 = -2*v + 4*v, 11 = 3*l + v. Let u(d) = l*t(d) + 3*k(d). Factor u(n).
3*n*(n - 5)
Let w be 0 + (1 - -1) - (6 + -8). Factor -2*j**2 + 0*j**3 - 2*j**3 + w*j**3 - 2*j**5 + 2*j**4 + 0*j**2.
-2*j**2*(j - 1)**2*(j + 1)
Let k be 2266/143 - (-4)/26. Determine u so that -268*u**3 + 171*u**2 + 116*u**4 + 16 - 54*u + 237*u**2 - 62*u - 140*u**2 - k*u**5 = 0.
1/4, 1, 4
Let q(f) = 6*f**2 - f + 2. Let z be q(2). Let g = -22 + z. Factor -8*y**3 + 10*y**2 + 4 + 3*y**5 - 18*y**g + 0*y**4 + 4*y + 4*y**4 + y**5.
4*(y - 1)**2*(y + 1)**3
Let g(f) be the third derivative of 0 - 4*f**2 + 1/30*f**5 + 1/2*f**3 + 0*f - 1/24*f**4. Let p(r) = r**2 - r + 2. Let i(y) = 2*g(y) - 3*p(y). Factor i(b).
b*(b + 1)
Let a(b) be the second derivative of -b**5/40 - b**4/8 + 3*b**3/4 - 5*b**2/4 + 144*b. Let a(r) = 0. Calculate r.
-5, 1
Let x = 257/11844 - -2/329. Let w(o) be the second derivative of -1/18*o**3 + x*o**4 + 2*o + 0*o**2 + 0. Determine t, given that w(t) = 0.
0, 1
Let z(y) be the third derivative of -1/30*y**6 + 1/504*y**8 + 0*y - 11/36*y**4 - 1/315*y**7 + 1/3*y**3 + 0 + 4*y**2 + 7/45*y**5. Factor z(i).
2*(i - 1)**4*(i + 3)/3
Let i(b) be the third derivative of b**5/12 + 5*b**4/6 - 25*b**3/6 - 80*b**2. Determine d, given that i(d) = 0.
-5, 1
Let j(x) be the first derivative of 2*x**2 + 0*x - 26 - 4/21*x**3. Find v, given that j(v) = 0.
0, 7
Let l be (-17)/(-4) - (54/(-8) - -6). Let c(j) = -6*j**2 - 48*j - 144. Let o(q) = -13*q**2 - 96*q - 288. Let v(n) = l*c(n) - 2*o(n). Let v(b) = 0. Calculate b.
-6
Factor -1/4*q**2 + 0 + 1/4*q.
-q*(q - 1)/4
Suppose -2*g + 4*g - 16 = 0. Let q = g - 7. Solve 0 + o**2 + 2*o - q - 2*o**2 = 0 for o.
1
Let y(m) be the first derivative of -7/8*m**2 - 1/2*m - 5/12*m**3 - 14. Find k such that y(k) = 0.
-1, -2/5
Let z be ((-2)/91)/(10/(-70)). Factor -z*u**3 + 10/13*u**2 - 8/13*u + 0.
-2*u*(u - 4)*(u - 1)/13
Let l be ((-10)/(-3))/(4/6). Suppose -25 = -l*g, z - 3*z - 2*g = -18. Factor c**3 + 3/2*c**z + 0*c + 0*c**2 + 0 + 1/2*c**5.
c**3*(c + 1)*(c + 2)/2
Suppose 4*t - 5*r - 3 = 5*t, 0 = 4*t - 3*r - 11. Suppose -t*b = b. Factor -10*z**3 - 4*z**5 - 2*z**2 + 2*z**5 + 16*z + 4*z**5 - 8 + 2*z**4 + b*z**3.
2*(z - 1)**3*(z + 2)**2
Solve 6/7*u + 40/7 - 1/7*u**2 = 0 for u.
-