 Calculate n.
-2, 1/4
Let o(w) be the second derivative of -w**6/30 + 29*w**5/10 - 841*w**4/12 + 201*w. Factor o(s).
-s**2*(s - 29)**2
Factor -34*h**3 + 3/2*h**4 + 611/3*h**2 - 374/3*h + 121/6.
(h - 11)**2*(3*h - 1)**2/6
Let m(n) be the second derivative of 3*n**5/100 - 3*n**4/20 + 85*n. Factor m(q).
3*q**2*(q - 3)/5
Let h(t) be the third derivative of 13*t**5/60 - 15*t**4/2 - 14*t**3/3 + 2*t**2 - 70*t. Factor h(x).
(x - 14)*(13*x + 2)
Suppose 209 = 44*q + 121. Let 4*n - 4*n**3 - 32/7 + 36/7*n**q - 4/7*n**4 = 0. What is n?
-8, -1, 1
Suppose 5*p = 4*n - 722, -5*n + 1177 = -4*p + 270. Suppose 13*b - 5*b**2 + n + 17*b - 208 = 0. Calculate b.
1, 5
Let b = 65 + -61. Factor 10*r + 2*r**2 + 0*r**2 - 2*r**b - 10*r.
-2*r**2*(r - 1)*(r + 1)
Let y(b) = -b**2 + 12*b + 2. Let p be y(12). Factor 4*j + 2*j**2 + j**3 + 0*j**p - 3*j**3.
-2*j*(j - 2)*(j + 1)
Suppose -3*t + 2*t = -2. Determine n so that -25*n - n**5 - t*n**4 + 53*n + 2*n**2 - 27*n = 0.
-1, 0, 1
Let d(a) = -20*a**3 - 88*a**2 - 22. Let l(x) = -x**3 - 1. Let p(w) = 2*d(w) - 44*l(w). Factor p(z).
4*z**2*(z - 44)
Let s be -1 + 2 - 3 - -6. Let r(u) be the third derivative of 1/180*u**5 + u**2 + 0 - 1/9*u**3 - 1/72*u**s + 0*u. Factor r(v).
(v - 2)*(v + 1)/3
Suppose -18*b - 13*b + b = 0. Factor -2/3*v + 2/3*v**5 + 0*v**3 - 4/3*v**4 + b + 4/3*v**2.
2*v*(v - 1)**3*(v + 1)/3
Let y(l) be the third derivative of -l**5/30 - l**4/2 - l**2 + 15*l. Let y(q) = 0. What is q?
-6, 0
Let k be 990/(-250) + ((-9)/(-3) - -1). Let g(x) be the first derivative of 0*x - k*x**5 + 1/15*x**3 - 9 + 1/20*x**4 - 1/10*x**2. Find r such that g(r) = 0.
-1, 0, 1
Let t = -89 + 74. Let g be -3*2/10*t. Factor 39/4*c**2 + 3/4*c**4 + 3 - g*c - 9/2*c**3.
3*(c - 2)**2*(c - 1)**2/4
Let m(j) = -3*j**4 - 42*j**3 + 40*j**2 + 229*j + 150. Let v(b) = -2*b**4 - 20*b**3 + 20*b**2 + 113*b + 75. Let d(s) = 3*m(s) - 5*v(s). Factor d(x).
(x - 25)*(x - 3)*(x + 1)**2
Factor 0*q**2 + 2*q + 0*q**2 - 10*q**2 - 68*q + 144 + 7*q**2.
-3*(q - 2)*(q + 24)
Let z(y) = 23*y**2 + 61*y + 46. Let m(c) = -81*c**2 - 213*c - 162. Let i(s) = 5*m(s) + 18*z(s). Factor i(b).
3*(b + 3)*(3*b + 2)
Let p be (-5 + 4)*1*-3. Factor -19*c**3 + 3*c**4 + 0*c**p + 72*c**2 + 46*c**3 + 48*c.
3*c*(c + 1)*(c + 4)**2
Let m = 10 - 6. Determine i, given that 2*i**3 + m*i**3 + 7*i**3 - 3*i**2 - 12*i**3 + 4 = 0.
-1, 2
Let y be (175/(-105))/((-2)/2). Suppose 11/3*x + y + 7/3*x**2 + 1/3*x**3 = 0. Calculate x.
-5, -1
Let c(o) be the second derivative of 1/21*o**4 - 2/147*o**7 + 0*o**3 - 2/105*o**6 - 3 + o + 1/35*o**5 + 0*o**2. Factor c(k).
-4*k**2*(k - 1)*(k + 1)**2/7
Let u(m) be the third derivative of 7*m**8/12 + 184*m**7/5 + 9242*m**6/15 - 736*m**5 + 800*m**4/3 + 2*m**2 - 751. Suppose u(l) = 0. What is l?
-20, 0, 2/7
Let h(m) be the second derivative of m**5/20 - 5*m**4/6 + 14*m**3/3 - 12*m**2 - 260*m. Factor h(w).
(w - 6)*(w - 2)**2
Let l(m) be the third derivative of 0*m + 4/3*m**3 + 0 - 1/3*m**4 - 34*m**2 + 1/30*m**5. Factor l(w).
2*(w - 2)**2
Suppose 1 + 27*b**2 + 5*b - 1 + 271*b**4 - 274*b**4 + 22*b - 3*b**3 = 0. Calculate b.
-3, -1, 0, 3
Let h(f) = 3*f**2 - 141*f + 936. Let l be h(39). Let 0*t + 1/8*t**4 + l - 1/2*t**2 + 1/8*t**5 - 1/2*t**3 = 0. Calculate t.
-2, -1, 0, 2
Solve m**3 - 823875 + 2*m**3 - 177*m**2 - 408*m**2 + 38025*m = 0.
65
Let t(j) be the third derivative of -1/12*j**4 + 1/24*j**5 + 0 + 22*j**2 - 1/240*j**6 + 0*j + 0*j**3. Let t(y) = 0. What is y?
0, 1, 4
Suppose 3*x + 22 = 31. Factor -9*p**2 - 4 + 0*p**3 - x*p**2 - 4*p**3 - 7*p - 5*p.
-4*(p + 1)**3
Suppose 0 = -22*o + 20*o + 22. Solve -o*u**2 + 75*u**3 - 183*u**2 + 48 + 25*u**3 - 26*u**2 + 16*u = 0.
-2/5, 3/5, 2
Let o be (-2)/(-6) - 8/36. Let m = o - -13/45. Factor 4/5 - 2/5*n**2 - m*n.
-2*(n - 1)*(n + 2)/5
Suppose 44 = 4*n - 4*h, -2*n - 4*h - 3 = 5. Let q(y) be the first derivative of -9/4*y**4 + 0*y - 3*y**2 - 3/5*y**5 - 6 + 5*y**3 + 1/2*y**n. Factor q(i).
3*i*(i - 1)**3*(i + 2)
Factor 0 + 82/11*g**3 + 0*g + 2/11*g**5 + 4*g**4 + 40/11*g**2.
2*g**2*(g + 1)**2*(g + 20)/11
Let t(d) be the first derivative of 5*d**3 + 3/5*d**5 - 3*d**4 + 0*d + 23 - 3*d**2. Factor t(c).
3*c*(c - 2)*(c - 1)**2
Let r(q) be the first derivative of -3*q**4/22 - 2*q**3/3 - 8*q**2/11 - 107. Solve r(w) = 0.
-8/3, -1, 0
Let l(k) = 2*k - 9. Let y be l(7). Suppose 4*t - m = y - 0, 0 = m + 1. Let 0 - 3*x**2 + t + 2*x**2 = 0. Calculate x.
-1, 1
Let x(v) = 454*v + 5451. Let l be x(-12). Solve -2/3*t**l + 0*t + 0 + 2/3*t**2 = 0 for t.
0, 1
Let h(n) = 5*n**4 - 35*n**3 + 131*n**2 + 3. Let d(p) = -p**4 + p**3 - p**2 - 1. Let j be (24/84)/(1/7) + 1. Let u(o) = j*d(o) + h(o). Factor u(g).
2*g**2*(g - 8)**2
Factor 41*k**2 + 47*k**2 + 37*k**2 - 123*k**2 + 10*k + 12.
2*(k + 2)*(k + 3)
Let f(h) be the first derivative of h**6/15 + 36*h**5/25 + 31*h**4/5 + 176*h**3/15 + 57*h**2/5 + 28*h/5 + 135. Determine m so that f(m) = 0.
-14, -1
Factor -2*h**3 + 120*h**2 - 229*h**2 + 105*h**2.
-2*h**2*(h + 2)
Let x(h) be the first derivative of 1/30*h**6 + 0*h + 5 + 0*h**5 - 3/2*h**2 + 0*h**3 + 0*h**4. Let a(z) be the second derivative of x(z). Factor a(r).
4*r**3
Suppose 3*j = 2*z + 16, -5*j + 7*j = 5*z + 29. Let v(r) be the first derivative of 0*r + j - 2*r**3 + 3/4*r**4 + 0*r**2. Suppose v(i) = 0. What is i?
0, 2
Find l, given that 99*l**2 + 20*l - 51*l**2 - 46*l**2 = 0.
-10, 0
Factor 13/5 + 1/5*d**2 - 14/5*d.
(d - 13)*(d - 1)/5
Let a = -94/3 - -488/15. Let m(g) = -g**2 + 32*g + 233. Let k be m(38). Find s such that 0 - 1/5*s**k - 4/5*s - 12/5*s**2 - a*s**4 - 13/5*s**3 = 0.
-2, -1, 0
Suppose -3*m - 2*c + 1 = -1, -m = -2*c - 6. Factor 0*v**3 + 2*v**3 + 8*v**m - 8*v - 136*v**4 + 134*v**4.
-2*v*(v - 2)*(v - 1)*(v + 2)
Let s be 22 + 4560/(-135) + 12. Determine v so that 0 + 2/3*v**5 + 0*v**2 - s*v**3 + 4/9*v**4 + 0*v = 0.
-1, 0, 1/3
Let v(g) be the third derivative of g**5/100 + 9*g**4/40 + 9*g**3/5 - g**2 - 3*g. Solve v(b) = 0 for b.
-6, -3
Let k(i) be the third derivative of i**8/2352 + i**7/147 + 29*i**6/840 + 8*i**5/105 + i**4/14 + 10*i**2 - 18*i. Factor k(u).
u*(u + 1)**2*(u + 2)*(u + 6)/7
Let w(b) be the first derivative of -b**7/490 - b**6/56 - 2*b**5/35 - b**4/14 + 3*b**2 + 1. Let i(g) be the second derivative of w(g). Factor i(d).
-3*d*(d + 1)*(d + 2)**2/7
Let v(w) be the second derivative of 1/12*w**4 + 18*w + 0 + 0*w**2 + 2/3*w**3. Factor v(u).
u*(u + 4)
What is w in -21/5*w**3 - 6/5*w + 6/5*w**4 + 0 + 21/5*w**2 = 0?
0, 1/2, 1, 2
Let k(l) = -80*l**4 + 88*l**3 + 3*l**2 - 16*l - 1. Let o(j) = -j - 1. Suppose b = -3*a - 10, -4*a - 6 = 6. Let v(n) = b*k(n) + 3*o(n). Factor v(z).
(z - 1)*(4*z - 1)**2*(5*z + 2)
Let h(v) = -10*v + 3. Let c be h(0). Let u be ((-16)/168)/(c/(-18)). Factor -8/7 + u*b**2 - 4/7*b.
4*(b - 2)*(b + 1)/7
Let z = 22 + -12. Suppose 5 - 25 = -z*l. Solve -1/3*m**5 + 0*m**l + 0 + 0*m + 2/3*m**4 - 1/3*m**3 = 0.
0, 1
Let x(m) = -1 - 8*m - m**4 - m**2 + m**3 - m**2 + 9*m + 3*m**2. Let r(w) = 12*w**4 - 30*w**3 + 26*w**2 - 18*w + 6. Let b(k) = r(k) + 4*x(k). Factor b(i).
2*(i - 1)**3*(4*i - 1)
Let d be (-268)/(-84) - (4 + (-88)/24). Find x, given that 18/7*x**5 + 0 + 0*x + d*x**3 - 6*x**4 + 0*x**2 = 0.
0, 2/3, 5/3
Factor -14/11*x**2 + 10/11*x**3 - 2/11*x**4 + 6/11*x + 0.
-2*x*(x - 3)*(x - 1)**2/11
Determine g so that 99*g**2 + 588*g**2 + 60 - 237*g**2 - 66*g**2 + 560*g**2 + 32*g**3 - 478*g = 0.
-30, 1/4
Let a(q) = -6*q**3 + 78*q**2 - 162*q + 75. Let r(x) = 7*x**3 - 77*x**2 + 165*x - 75. Let w(b) = 4*a(b) + 3*r(b). Factor w(l).
-3*(l - 25)*(l - 1)**2
Let u(s) be the third derivative of -1/60*s**6 - 1/10*s**5 + 1/105*s**7 + 0 + 0*s + 1/12*s**4 - 16*s**2 + 2/3*s**3. Factor u(f).
2*(f - 2)*(f - 1)*(f + 1)**2
Let o(v) be the first derivative of -v**4/2 + 16*v**3/3 - 20*v**2 + 32*v + 68. Let o(i) = 0. What is i?
2, 4
Let y be ((-4)/(-12))/(-1)*-42. Suppose 2*w = 3*w + 3*g + 10, -5*w = -g - y. Find a such that w*a**2 - 5*a**4 + 3*a**2 - 9*a**2 - 15*a**3 - 6*a**2 = 0.
-2, -1, 0
Let v(k) be the first derivative of -1/10*k**4 + 0*k + 0*k**2 + 5 - 2/15*k**3. Let v(y) = 0. Calculate y.
-1, 0
Let g(w) be the third derivative of -w**6/720 + 11*w**5/360 + w**4/144 - 11*w**3/36 + 181*w**2. Factor g(t).
-(t - 11)*(t - 1)*(t + 1)/6
Let p = 22748/221 - 1332/13. Suppose 0 - 2/17*v**4 - 16/17*v**2 + 10/17*v**3 + p*v = 0. Calculate v.
0, 1, 2
Determine u so that 36/5*u + 0*u*