2/3
Let m = -31414 - -31417. Factor -2/5*p**5 + 2/5*p - 4/5*p**4 + 0 + 0*p**m + 4/5*p**2.
-2*p*(p - 1)*(p + 1)**3/5
Factor 162 + 7/2*c**4 + 1/4*c**5 - 81/2*c**2 + 39/4*c**3 - 135*c.
(c - 3)*(c - 1)*(c + 6)**3/4
Factor -7*n**3 - 75*n - 5*n**3 - 40*n**2 + 2*n**3 - 8*n**2 + 126 + 7*n**3.
-3*(n - 1)*(n + 3)*(n + 14)
Let s(t) be the second derivative of t**5/170 - 287*t**4/34 + 573*t**3/17 - 859*t**2/17 - 328*t + 4. Factor s(v).
2*(v - 859)*(v - 1)**2/17
Let m(b) be the second derivative of b**7/1680 - b**6/480 - 38*b**2 + b - 27. Let h(g) be the first derivative of m(g). What is i in h(i) = 0?
0, 2
Let p be (-9)/12*(-7 + (-12)/(-4)). Suppose 8 = 2*u + 4, -4*u + 11 = l. Solve -2*f**p + 32*f**2 - 28*f - 9 + 17 - f**l + 4*f**5 - 5*f**3 - 8*f**4 = 0 for f.
-2, 1
Suppose -2*d = 1 - 9. Let o be 39 + -51 + 10 + ((-10)/4)/5*-10. Factor 0*l + 2/3*l**o + 2/9*l**5 + 0 + 2/9*l**2 + 2/3*l**d.
2*l**2*(l + 1)**3/9
Factor 3*a**2 - 246*a - 20796 + 9341 + 10423.
3*(a - 86)*(a + 4)
Suppose -4*h - 54 = -5*p, 5*h + p + 0*p + 82 = 0. Let d be h/32*(1 - 1). Solve -4/15 - 2/15*i**3 + 2/5*i + d*i**2 = 0 for i.
-2, 1
Factor 13286/3*i**2 + 360 - 7568/3*i - 98/3*i**3.
-2*(i - 135)*(7*i - 2)**2/3
Let h(b) = 83*b**2 + 7953*b + 3152219. Let t(l) = -32*l**2 - 3181*l - 1260887. Let v(s) = 10*h(s) + 26*t(s). Let v(a) = 0. What is a?
-794
Let w(y) be the third derivative of 5*y**8/336 - y**7/42 - y**6/2 - y**5/3 + 10*y**4/3 - 1245*y**2. Factor w(j).
5*j*(j - 4)*(j - 1)*(j + 2)**2
Let k(g) be the third derivative of g**7/280 + 7*g**6/60 + 3*g**5/2 + 9*g**4 - 5*g**3/2 - 131*g**2. Let s(y) be the first derivative of k(y). Factor s(q).
3*(q + 2)*(q + 6)**2
Let q be (0 + 0)*1/3. Let c = -6/3421 + 10275/6842. Let q + c*r**3 + 0*r**2 - 3/2*r = 0. What is r?
-1, 0, 1
Suppose -13*i - 11 = 2. Let u be 4/i + -7 + (-4 - -17). Factor -2/5*j + 0 - 2/5*j**u.
-2*j*(j + 1)/5
Let g(i) = 19*i - 5900 + i + 5896 + 4*i**2. Let y(w) = -2 + w + 1 + 0*w. Let z(d) = -g(d) + 4*y(d). Factor z(u).
-4*u*(u + 4)
Let j(p) be the second derivative of -p**4/72 + 23*p**3/12 - 33*p**2/2 - 2*p - 8137. Factor j(a).
-(a - 66)*(a - 3)/6
Suppose 10*p - 1129 + 189 = 0. Factor -8*u**2 + 95*u**4 + 12*u**3 - 193*u**4 + p*u**4.
-4*u**2*(u - 2)*(u - 1)
Factor -192*o**3 - 4*o**4 - 162*o**2 - 537*o + 863*o**2 + 815*o**2 - 783*o.
-4*o*(o - 6)*(o - 1)*(o + 55)
Let n(m) = 3*m**3 - 40*m**2 - 31*m. Let b(f) = -2*f**3 + 40*f**2 + 33*f. Let h(x) = -4*b(x) - 3*n(x). Factor h(o).
-o*(o + 1)*(o + 39)
Let d(k) = 7*k**3 + 122*k**2 + 375*k. Let x(t) = -2*t**3 - 22*t**2. Let q(u) = -d(u) - x(u). Suppose q(y) = 0. Calculate y.
-15, -5, 0
Solve 240*z - 223*z - 774*z - 1900 + 18*z**2 - 183*z - 13*z**2 = 0.
-2, 190
Let w(c) be the second derivative of -3*c**5/4 + 1135*c**4/36 - 125*c**3/9 - 368*c - 4. Factor w(f).
-5*f*(f - 25)*(9*f - 2)/3
Let k(q) be the third derivative of 15*q**2 + 0*q - 1/630*q**7 + 0*q**3 + 1/180*q**5 + 5/72*q**4 + 0 - 1/72*q**6. Let k(t) = 0. Calculate t.
-5, -1, 0, 1
Let r(m) be the second derivative of -12/7*m**2 - 66*m + 0 + 19/21*m**3 - 5/42*m**4. Determine i, given that r(i) = 0.
4/5, 3
Solve -1/3*m**4 - 44/3*m**3 - 89*m**2 + 5044/3*m - 4732/3 = 0 for m.
-26, 1, 7
Let t(z) be the second derivative of -5*z**4/12 - 65*z**3/2 + 675*z**2 - 414*z - 6. Factor t(m).
-5*(m - 6)*(m + 45)
Suppose 504 - 84 = -30*a. Let p be ((-2)/a + 0)/(30/240). What is k in 0 + 12/7*k**2 + 4/7*k**5 + 4/7*k**3 - p*k - 12/7*k**4 = 0?
-1, 0, 1, 2
Let j(q) = q**3 - 22*q**2 - 81*q - 22. Let c be j(26). Determine r so that -r**2 - c - 118*r - 91*r + 161*r = 0.
-24
Determine f so that 2484/5*f + 582/5*f**2 + 1944/5 + 43/5*f**3 + 1/5*f**4 = 0.
-18, -6, -1
Let h(j) be the first derivative of 12/5*j**5 - 2*j**3 + 15/2*j**2 - 6*j - 110 - 1/2*j**6 - 3*j**4. Factor h(y).
-3*(y - 2)*(y - 1)**3*(y + 1)
Let w(j) = -11*j**2 + 7*j + 4. Let x(k) = -42*k**2 + 32*k + 18. Let z(l) = 9*w(l) - 2*x(l). Factor z(t).
-t*(15*t + 1)
Suppose 5*x + z - 15 = 0, -3*x + x + 3*z = -23. Suppose -2*s + 4 = -x. Factor 16 + 6*d - s*d**4 + 26*d + 12*d**2 - 3*d**3 - 5*d**3.
-4*(d - 2)*(d + 1)**2*(d + 2)
Let m(f) be the first derivative of f**6/4 + 27*f**5/5 - 123*f**4/4 + 64*f**3 - 261*f**2/4 + 33*f + 220. Factor m(s).
3*(s - 1)**4*(s + 22)/2
Suppose 2*l - 58*l = 42*l. Let i(m) be the first derivative of l*m**3 + 0*m - 1/27*m**6 - 14 - 2/9*m**4 + 0*m**2 - 8/45*m**5. Suppose i(o) = 0. Calculate o.
-2, 0
Let j(u) be the third derivative of -u**5/15 - 457*u**4/6 - 304*u**3 - 23*u**2. Factor j(o).
-4*(o + 1)*(o + 456)
Factor -31/3*r**3 + 1/3*r**5 - 79/3*r**2 + 9*r**4 + 46*r - 56/3.
(r - 1)**3*(r + 2)*(r + 28)/3
Let v be (-15)/7*70/(-175)*14/9. Let w(m) be the second derivative of 1/5*m**5 + v*m**3 + 0*m**2 - 19*m + 0 + m**4. Determine b, given that w(b) = 0.
-2, -1, 0
Let c(p) be the second derivative of -p**3/3 - 16*p**2 + 123*p. Let l be c(-18). Determine t so that -2/13*t**3 - 6/13*t**l + 2/13*t + 6/13*t**2 + 0 = 0.
-1, -1/3, 0, 1
Let g = -40/7269 - -184268/21807. Factor -160/9*j**2 + 0 - 16/9*j - g*j**3.
-4*j*(j + 2)*(19*j + 2)/9
Factor -10/11*v**2 + 42/11 + 34/11*v - 2/11*v**3.
-2*(v - 3)*(v + 1)*(v + 7)/11
Let l(j) be the second derivative of -j**4/4 + 635*j**3 - 1209675*j**2/2 + 2078*j. Let l(c) = 0. What is c?
635
Suppose 0 = z - 5*v + 23, -5*v + 3*v = -3*z - 4. Factor -143*c + 41*c + 24 + 34*c**z - 106*c.
2*(c - 6)*(17*c - 2)
Let v be -2 + 40/15 + (-8)/(-6). Suppose -v*z - 4*s - 6 + 16 = 0, 4*z = s + 56. Determine w so that -12*w**3 - 5*w**4 - z*w**3 + 15*w**3 + 5*w**5 = 0.
-1, 0, 2
Let u(h) be the second derivative of 0 + 223*h - 19/6*h**6 - 20/3*h**3 + 175/6*h**4 + 59/4*h**5 + 0*h**2. Suppose u(i) = 0. What is i?
-1, 0, 2/19, 4
Let o be (-35 + 1843/57)/((-8)/6). Suppose -5*q = -q. Factor q - 2/3*d + 2/3*d**o.
2*d*(d - 1)/3
Let v(y) be the third derivative of -y**6/720 - y**5/24 - y**4/3 - 11*y**3/9 - 99*y**2. Factor v(a).
-(a + 2)**2*(a + 11)/6
Determine d, given that 89/7*d - 5/7*d**2 - 68/7 = 0.
4/5, 17
Let l(q) be the second derivative of -2*q**3 + 3*q + 9/20*q**5 + 0*q**2 - 2 - q**4. Factor l(f).
3*f*(f - 2)*(3*f + 2)
Suppose -610 = -72*a + 11*a. Let l(w) = -w**2 - 10*w - 1. Let b be l(-7). Suppose -b*m**5 + a*m**2 + 0 + 51*m**3 + 15*m**4 - 6*m**3 + 0 = 0. What is m?
-1, -1/4, 0, 2
Let k(t) be the first derivative of 26 - 4/3*t**3 + 0*t + 19/5*t**5 - 2*t**4 + 0*t**2 - 7/6*t**6. Solve k(q) = 0 for q.
-2/7, 0, 1, 2
Let d(z) be the first derivative of -z**6/9 + 22*z**5/3 - 667*z**4/6 - 1682*z**3/3 + 3638. Factor d(t).
-2*t**2*(t - 29)**2*(t + 3)/3
Suppose 3*b + q + 34 = 0, 5*b - 17*q + 18*q + 56 = 0. Let r be 48/(-264) - 2/b. Factor 0*x - 2/11*x**2 - 3/11*x**3 + r + 0*x**4 + 1/11*x**5.
x**2*(x - 2)*(x + 1)**2/11
Suppose -4*m + 3*t - 50 - 6 = 0, -2*m + 2*t - 30 = 0. Let n be m/(165/(-10))*(2 - -2251). Factor -n - 15*f**2 + 6*f - 5*f**3 - f + 5*f**4 + 1512.
5*(f - 2)*(f - 1)*(f + 1)**2
Factor 18*o + 3*o**2 + 59*o + 2*o**2 - 47*o.
5*o*(o + 6)
Let x(w) be the second derivative of -5*w**3 + 0 + 35/24*w**4 - 1/6*w**5 + 30*w + 29/2*w**2. Let k(u) be the first derivative of x(u). Solve k(v) = 0.
3/2, 2
Let c(t) = -37*t**2 + 2*t - 1. Let w be c(1). Let l = w - -39. Determine z, given that -12*z**3 + 3*z**l + z**4 + z**4 + 4*z**2 + 3*z**3 = 0.
0, 1, 2
What is b in 80*b**3 - 297*b**2 + 135*b**5 - 136*b + 46*b + 75*b**4 - 155*b**5 - 48*b**2 = 0?
-2, -1/4, 0, 3
Suppose -2*j = 2*p - 0*j - 16, j = -4*p + 41. Let t = 37 - p. Find x, given that -11*x**2 + t*x**2 + 25*x**2 - 100*x - 7*x**3 + 3*x**3 = 0.
0, 5
Find b, given that 0 + 494/9*b**4 - 368/9*b + 1480/9*b**2 - 10/9*b**5 - 532/3*b**3 = 0.
0, 2/5, 1, 2, 46
Factor -771/5*w - 153*w**2 - 6/5.
-3*(w + 1)*(255*w + 2)/5
Let f be (-2)/3*-45 - (-3)/3. Let g = f - 7. Determine p so that -51 - 58 + 24*p - 35 - 4*p**2 + g*p = 0.
6
Let b(u) be the second derivative of u**5/20 - 13*u**4/4 + 169*u**3/2 - 25*u**2 - 67*u. Let y(f) be the first derivative of b(f). Let y(p) = 0. Calculate p.
13
Suppose 2*z = 5 + 5. Let q(m) be the third derivative of 0*m**3 + 1/420*m**6 - 13*m**2 + 1/252*m**4 + 1/210*m**z + 0*m + 1/2205*m**7 + 0. Factor q(c).
2*c*(c + 1)**3/21
Let m = -10714/3 + 3673. Let a = m - 304/3. Solve 1/3*g - a*g**4 + 0 + g**3 - g**2 = 0.
0, 1
Let o(y) be the third derivative of -y**7/5040 - y**6/720 + y**5/72 + 185*y**3/6 + 64*y**2 + 2. Let q(i