 y*m.
-(m - 1)**2*(m + 3)
Let o(c) be the first derivative of 3*c**4/10 + 148*c**3/15 + 36*c**2 + 176*c/5 + 38. Factor o(w).
2*(w + 2)*(w + 22)*(3*w + 2)/5
Let k(m) be the second derivative of 1/66*m**3 - 1/330*m**6 + 0*m**2 - 1/220*m**5 + 0 + 2*m + 1/132*m**4. Factor k(f).
-f*(f - 1)*(f + 1)**2/11
Solve -11/3*v**2 + 2/3*v + 0 - 2*v**3 = 0 for v.
-2, 0, 1/6
Let t = 2196/3685 + 3/737. Let k(d) be the first derivative of 3 + 3/4*d**2 + 3*d + 1/4*d**6 + t*d**5 - 3/4*d**4 - 2*d**3. Determine g so that k(g) = 0.
-2, -1, 1
Let i(o) be the second derivative of -o**9/5040 - 3*o**8/2240 + 3*o**7/280 - o**6/48 + 13*o**4/6 + 30*o. Let q(x) be the third derivative of i(x). Factor q(j).
-3*j*(j - 1)**2*(j + 5)
Factor 60 + 27/2*y**3 + 297*y + 249/2*y**2.
3*(y + 4)*(y + 5)*(9*y + 2)/2
Let b(d) be the third derivative of d**8/448 - 11*d**7/280 + 17*d**6/80 - 7*d**5/40 - 35*d**4/32 + 25*d**3/8 + 174*d**2. Suppose b(r) = 0. What is r?
-1, 1, 5
Let a be 13 - (-12)/(-4)*(-4)/6. Let o = -11 + a. Factor -2/9 - 4/3*t**2 - 8/9*t - 2/9*t**o - 8/9*t**3.
-2*(t + 1)**4/9
Suppose -c + 3*p + 13 = 4, 0 = 2*p + 4. Find w, given that -4*w**3 - w**3 - 15*w**2 + 8*w**c - 9 + 21*w = 0.
1, 3
Let r(c) = -7*c**4 + 3*c**3 - 4*c**2. Let d(y) = 16*y**4 - 6*y**3 + 9*y**2 - y. Let o(z) = -4*d(z) - 9*r(z). Factor o(m).
-m*(m - 1)*(m + 2)**2
Suppose -2*m = 5*a - 49, 4*a - 34 = 2*a + 4*m. Let b = a - 9. Suppose -2*g**2 + 6*g**2 - g**b + 3*g**3 = 0. What is g?
-1, 0
Let p(b) = b**3 - 5*b**2 - 12*b - 12. Let m be p(7). Solve 1/7*x**m + 4/7 - 4/7*x = 0.
2
Let x(p) be the first derivative of p**4/10 - 8*p**3/5 + 9*p**2 - 20*p - 88. Factor x(d).
2*(d - 5)**2*(d - 2)/5
Factor -155*n - 15 + 128*n - 9 - 3*n**2 + 0*n**2.
-3*(n + 1)*(n + 8)
Suppose i + 2*w + 1 = 5*w, -w = -1. Factor 40*t - 40*t + 3*t**i.
3*t**2
Let m(l) be the third derivative of 3*l**7/385 - l**6/66 - 17*l**5/330 + l**4/66 + 160*l**2. Let m(i) = 0. Calculate i.
-1, 0, 1/9, 2
Let z(n) = 2*n**5 + 7*n**4 + 2*n**3 - 8*n**2 - 4*n + 4. Let h(g) = g**5 + g**4 - g. Let l(m) = 3*h(m) - z(m). Suppose l(d) = 0. What is d?
-1, 1, 4
Let u(n) be the third derivative of 0*n**4 + 0*n**3 - 20*n**2 + 0*n + 1/24*n**6 + 0 + 0*n**5 - 1/42*n**7. Factor u(i).
-5*i**3*(i - 1)
Let i be (-38)/(-14) + (-1700)/(-119) + -14. Factor 0 - 1/3*x**2 - 2/9*x**i + 1/9*x**4 + 0*x.
x**2*(x - 3)*(x + 1)/9
Factor 1/4*n**3 + 201/4*n + 25 + 51/2*n**2.
(n + 1)**2*(n + 100)/4
Suppose 6*h - 92 + 80 = 0. Let i(v) be the third derivative of -1/20*v**5 + 0 + 7*v**h - 8/3*v**3 + 0*v - 1/2*v**4 - 1/480*v**6. Factor i(m).
-(m + 4)**3/4
Suppose 89*c - 172 = 46*c. Determine x so that 0*x + 0*x**2 - 2/17*x**5 + 0 - 6/17*x**3 - 8/17*x**c = 0.
-3, -1, 0
Let o(j) = -10*j - 56. Let u be o(-6). Suppose 4*n = -5*p - 1 - 7, 3*p + 8 = -u*n. Factor 0*d + p - 1/3*d**2 - 1/3*d**3 + 1/3*d**4 + 1/3*d**5.
d**2*(d - 1)*(d + 1)**2/3
Let z = -67 - -66. Let a be (z + 2)/(38/171). Find i such that 0*i - i**2 + a*i**3 + 0 - 7/2*i**4 = 0.
0, 2/7, 1
Suppose -403 = 17*i - 420. Factor -i - 1/4*w**2 - 5/4*w.
-(w + 1)*(w + 4)/4
Let m = 493/365 - 11/73. Factor -12/5*q - 8/5 - 1/5*q**3 - m*q**2.
-(q + 2)**3/5
Let r(y) be the first derivative of y**5 + 65*y**4/2 + 80*y**3 - 642. Factor r(d).
5*d**2*(d + 2)*(d + 24)
Let b(c) be the third derivative of -c**7/105 - c**6/12 - 4*c**5/15 - c**4/3 + 8*c**2 - 3. Suppose b(g) = 0. Calculate g.
-2, -1, 0
Suppose -4*y = -c + 9, 4*c + 4*y - 9 = -13. What is w in -c - 5/4*w - 1/4*w**2 = 0?
-4, -1
Let 0*d - 2/3*d**4 + 0 + 10/9*d**3 - 4/9*d**2 = 0. Calculate d.
0, 2/3, 1
Suppose -4*o + 0 = f - 3, -3*o - f + 3 = 0. Let q(k) be the second derivative of 5*k - 1/6*k**4 - 2*k**3 - 9*k**2 + o. Determine n, given that q(n) = 0.
-3
Let n(d) be the third derivative of -2*d**8/315 - 8*d**7/525 + 11*d**6/180 + 19*d**5/90 + d**4/5 + 4*d**3/45 - d**2 - 82*d. Suppose n(f) = 0. What is f?
-2, -1, -1/4, 2
Factor -15*g - 45 - 5/4*g**2.
-5*(g + 6)**2/4
Let j = 219152/9 + -24350. Suppose 4/9*v - 2/9 - j*v**2 = 0. What is v?
1
Suppose 1/10*g**2 - 6*g + 90 = 0. Calculate g.
30
Let b(u) be the third derivative of -u**7/735 - 5*u**6/252 - 53*u**5/630 - 5*u**4/84 - 182*u**2. Determine p so that b(p) = 0.
-5, -3, -1/3, 0
Factor 130/3*l + 46*l**2 + 2/3*l**4 - 100 + 10*l**3.
2*(l - 1)*(l + 5)**2*(l + 6)/3
Let m(x) = 3*x**2 - 28*x - 148. Let j(s) = -5*s**2 + 55*s + 295. Let b(h) = -4*j(h) - 7*m(h). Factor b(q).
-(q + 12)**2
Let s be 8*((-3)/(-24))/((-35)/(-14)). Suppose 0 = 8*o - 4*o. Let 2/5*f - s*f**3 + o*f**2 + 0 = 0. What is f?
-1, 0, 1
Let h = 39 - 36. Factor 5*j**h + 181*j**2 - 191*j**2 + 1 - 1 + 5*j.
5*j*(j - 1)**2
Let a be (152/70 - 2) + (-520)/(-1300). Find w such that 3/7*w + a - 1/7*w**2 = 0.
-1, 4
Factor -8*y**2 + 10*y**3 - 18218*y**4 - 25 - 44*y**2 + 9 + 72*y - 16 + 18221*y**4 - y**5.
-(y - 2)**3*(y - 1)*(y + 4)
Let d(i) be the first derivative of 0*i**5 + 0*i + 0*i**2 - 2/3*i**6 + 0*i**3 + i**4 + 2. Factor d(p).
-4*p**3*(p - 1)*(p + 1)
Suppose -3*m - n = 21 - 0, 2*n - 6 = 0. Let o be (-10)/m*(-78)/(-130). Suppose -o*z**3 - 3*z**2 - 15/4*z - 3/2 = 0. What is z?
-2, -1
Let a = -20 - -65. Let f(r) be the first derivative of 15*r**2 + 21*r**2 - a*r**2 + r**3 + 12 + 27*r. Determine h so that f(h) = 0.
3
Let j(v) be the third derivative of v**6/40 - 19*v**5/20 + 35*v**4/8 - 17*v**3/2 + v**2 + 27. Suppose j(z) = 0. Calculate z.
1, 17
Suppose 0 = 4*x + 4*v + 4, -4*v + 22 = 5*x + 23. Factor -3/2*i + x*i**4 + 3/2*i**5 + 0*i**3 - 3*i**2 + 0.
3*i*(i - 1)*(i + 1)**3/2
Let t(b) be the second derivative of b**4/12 + b**2/2 - 2*b. Let n(z) = 8*z**2 - 8*z + 9. Let q = -152 - -155. Let m(i) = q*n(i) - 15*t(i). Factor m(p).
3*(p - 2)*(3*p - 2)
Let x(l) = -2*l**4 + l**3 + l**2 - l. Let n(s) = -6*s**4 + 10*s**3 - 4*s**2 - 10*s + 8. Let w(a) = -n(a) + 2*x(a). Determine r so that w(r) = 0.
-1, 1, 2
Factor 0 - 17/2*v**2 + 9/2*v + 7/2*v**3 + 1/2*v**4.
v*(v - 1)**2*(v + 9)/2
Let i(a) = -80*a**4 - 2785*a**3 - 8100*a**2. Let n(l) = -3*l**4 - 103*l**3 - 300*l**2. Let b(d) = 2*i(d) - 55*n(d). Factor b(c).
5*c**2*(c + 4)*(c + 15)
Let q(y) be the second derivative of y**4/6 + 2*y**3 + 8*y**2 + 52*y. Factor q(r).
2*(r + 2)*(r + 4)
Let j(r) = 4*r**3 + 765*r**2 + 49152*r + 1048576. Let q(h) = -12*h**3 - 2296*h**2 - 147456*h - 3145728. Let i(z) = 8*j(z) + 3*q(z). Find u, given that i(u) = 0.
-64
Let n = -56 - -60. Factor -t**3 + 7*t**3 - 2*t**n - 6*t**2 - 27*t + 29*t.
-2*t*(t - 1)**3
Suppose -15 = 4*d - 9*d. Suppose l**3 - 2*l**3 - 2*l**2 + 0*l + 0*l**d - l = 0. Calculate l.
-1, 0
Let y be (4 + 292/(-84))*3. Let c = y - 9/7. What is w in 0*w**2 + 0*w + 0 - 6/7*w**4 - 4/7*w**5 - c*w**3 = 0?
-1, -1/2, 0
Let v be 15/(-60) + (-90)/(-8). Suppose 14*b = v*b + 27. Factor -g - 4*g**2 - 12*g**3 + 7*g**4 + 8 + 13*g - b*g**4 - 2*g**4.
-4*(g - 1)*(g + 1)**2*(g + 2)
Let r = 1351/8866 - -1/682. Factor -r + 12/13*m + 14/13*m**2.
2*(m + 1)*(7*m - 1)/13
Let m = -30 + 37. Suppose -6*l + 5 + m = 0. Determine i so that -3*i + 2*i**l - 2*i**2 - 2*i**2 + 5*i**2 = 0.
0, 1
Let k be 0/1 - (-1 + -1). Let x be (-3 - 47/(-15)) + (-64)/600*-10. Determine j, given that 21/5*j**k - 27/5*j + x = 0.
2/7, 1
Let g = 89 - 88. Let n be -2*(g/9)/(4/(-12)). Factor 0 + 0*h + 2/3*h**3 + n*h**2.
2*h**2*(h + 1)/3
Let y(w) be the first derivative of -1/14*w**4 + 1/7*w**2 - 19 + 0*w + 0*w**3. Factor y(r).
-2*r*(r - 1)*(r + 1)/7
Let j = 22373 - 22371. Factor 81/5 - 72/5*c + 16/5*c**j.
(4*c - 9)**2/5
Suppose 0 = o + 4*f - 22, 2*o + 32 = 4*o + 5*f. Let i(g) be the third derivative of -1/3*g**5 + 0 - 2*g**3 - 1/30*g**o - 5*g**2 - 7/6*g**4 + 0*g. Factor i(c).
-4*(c + 1)**2*(c + 3)
Let y(k) be the second derivative of -k**4/16 + 7*k**3/8 + 27*k**2/4 - 2*k + 145. Find t such that y(t) = 0.
-2, 9
Suppose -2 = -b - b, b = -2*t + 67. Determine f, given that -50*f**3 - 15*f**4 - 16*f**2 + 58*f + 20 - 31*f + f**2 + t*f = 0.
-2, -1/3, 1
Let q(i) be the third derivative of i**6/24 + 3*i**5/4 - 35*i**4/8 + 55*i**3/6 + 59*i**2. Factor q(n).
5*(n - 1)**2*(n + 11)
Let l(o) be the third derivative of o**5/30 - 53*o**4/60 - 22*o**3/15 - o**2 + 12. Determine d, given that l(d) = 0.
-2/5, 11
Suppose 2*v + 1/4*v**2 - 7/4*v**3 + 1 - 5/4*v**4 - 1/4*v**5 = 0. Calculate v.
-2, -1, 1
Let d = 9045 - 9041. Factor 0*u + 0*u**2 + 12/7*u**3 + 22/7*u**d + 6/7*u**5 + 0.
2*u**3*(u + 3)*(3*u + 2)/7
Let