 7/6*p**b - 1/3*p.
-(p + 1)**2*(4*p - 1)/6
Let f = -486 - -487. Let h be 340/150 - (6/10 - f). Factor 4/3*g**2 - 14/3*g + 2/3*g**3 + h.
2*(g - 1)**2*(g + 4)/3
Factor -332*k - 19*k + 5*k**2 - 14*k - 75*k - 900.
5*(k - 90)*(k + 2)
Suppose -591*i + 212 + 331 = -639. Suppose 0 + 1/2*q**3 - i*q - 2*q**2 + 1/2*q**4 = 0. Calculate q.
-2, -1, 0, 2
Let m(f) = f**2 + 1093 + 513 + 163 + 89*f. Let y(z) = -z**2 - 90*z - 1770. Let t(g) = -6*m(g) - 5*y(g). Suppose t(v) = 0. Calculate v.
-42
Let u(s) be the first derivative of -60*s - 1 + 5/3*s**3 + 10*s**2. Suppose u(c) = 0. Calculate c.
-6, 2
Suppose 1078*l = 1458*l - 1520. Factor 0*a + 20/3*a**3 - 2/3*a**l - 6*a**2 + 0.
-2*a**2*(a - 9)*(a - 1)/3
Let p(w) = 2*w**2 - 2*w - 1. Let x(g) = 15*g**2 + 636*g + 639. Let h(s) = -6*p(s) + x(s). Solve h(d) = 0 for d.
-215, -1
Factor -8*n - 25*n**3 - 235*n + 6*n**3 - n**5 + 6*n**3 + n**3 - 14*n**4 + 270*n**2.
-n*(n - 3)*(n - 1)*(n + 9)**2
Factor 5/6*q**2 - 2/3 - 1/2*q**3 + 1/2*q - 1/6*q**4.
-(q - 1)**2*(q + 1)*(q + 4)/6
Suppose 36*z = -6 + 114. Find v, given that -71*v**3 + 7*v**2 + 75*v**z + 5*v**2 = 0.
-3, 0
Let o(m) = -m**3 + 6*m**2 + 14*m + 9. Let f be o(8). Let x be (73/6 - 5) + f. Find w, given that x*w**3 - 5/6*w**2 + 1/2*w + 1/6*w**4 + 0 = 0.
-3, 0, 1
Let i(x) be the first derivative of 5*x**3/3 + 105*x**2/2 - 500*x + 2201. Let i(j) = 0. What is j?
-25, 4
Factor 620356 + 2069300 + 5601*c**2 + 239948*c + 657883*c - 78189 + 3*c**3 + 1719234*c.
3*(c + 1)*(c + 933)**2
Let c = -5505 + 5508. Let h(t) be the first derivative of -6 - 2/3*t**c - 3/2*t + 1/16*t**4 + 13/8*t**2. Factor h(m).
(m - 6)*(m - 1)**2/4
Let b(w) be the first derivative of -w**4/9 + 56*w**3/9 - 18*w**2 + 339*w - 87. Let p(u) be the first derivative of b(u). Determine m, given that p(m) = 0.
1, 27
Suppose -6*i + 4 = -4*i. Factor 15*c**3 + i*c**2 + 150*c + 3*c**4 - 5*c**2 - 39*c**3 + 18*c**2.
3*c*(c - 5)**2*(c + 2)
Suppose 30 = 5*d - 170. Let v(y) be the third derivative of -5/36*y**4 + 0 - 1/45*y**5 - d*y**2 - 4/9*y**3 - 1/720*y**6 + 0*y. Determine q, given that v(q) = 0.
-4, -2
Let g(z) be the second derivative of -z**4/6 + 23*z**3/3 + 210*z**2 + 4412*z. Factor g(c).
-2*(c - 30)*(c + 7)
Let f(i) be the third derivative of -1/75*i**5 + 1/900*i**6 - 2/15*i**3 - 31*i**2 + 11/180*i**4 + 1 + 0*i. Determine l so that f(l) = 0.
1, 2, 3
Let x(i) be the second derivative of 0 + 0*i**4 + 1/378*i**7 + 1/135*i**6 + 1/180*i**5 + 0*i**2 + 0*i**3 + 63*i. Factor x(l).
l**3*(l + 1)**2/9
Let x(i) = -9*i - 142. Let j be x(-16). Suppose -38*b + 6*b**2 - 3*b**4 + 56*b + 3*b**5 - 3*b**j - 4*b**3 - 17*b**3 = 0. What is b?
-2, -1, 0, 1, 3
Let z(k) be the third derivative of 0 + 0*k - 12*k**2 + 19/108*k**4 - 1/270*k**5 + 0*k**3. Factor z(m).
-2*m*(m - 19)/9
Let y be (-693)/54 + 13 + 2/(-18). Let f(g) be the first derivative of 18 - 1/27*g**3 + y*g**2 + 0*g. What is z in f(z) = 0?
0, 1
Solve -54/7*k + 2/7*k**2 + 36 = 0.
6, 21
Let n = -33 - -27. Let k(c) = -8*c**3 + 89*c**2 - 188*c + 73. Let h(p) = -3*p**3 + 30*p**2 - 63*p + 24. Let r(w) = n*k(w) + 17*h(w). What is d in r(d) = 0?
-10, 1
Determine c so that -41*c - 259*c + 59923 + 0*c**4 - 60103 + 5*c**4 - 125*c**2 = 0.
-3, -2, -1, 6
Let j(h) be the third derivative of -105*h**2 + 0*h - 1/60*h**5 + 3/4*h**4 + 19/6*h**3 + 0. Factor j(f).
-(f - 19)*(f + 1)
Solve -26/3 - 34/9*d**2 + 2/9*d**3 + 110/9*d = 0.
1, 3, 13
Let g(s) = 136*s + 42*s - 8*s - 9075 + 25*s + 135*s - 20*s**2. Let l(t) = 7*t**2 - 110*t + 3025. Let h(p) = 6*g(p) + 17*l(p). Determine v, given that h(v) = 0.
55
Let m(g) = -135*g**3 - 155*g**2 + 185*g + 455. Let j(o) = -11*o**3 - 13*o**2 + 16*o + 38. Let s(x) = 25*j(x) - 2*m(x). Factor s(d).
-5*(d - 2)*(d + 1)*(d + 4)
Let p = 5215/2 + -2607. Let l(u) be the first derivative of p*u**4 - 4/5*u**5 + 10/3*u**3 + 14 + 2*u**2 + 0*u. Factor l(f).
-2*f*(f - 2)*(f + 1)*(2*f + 1)
Let q(s) be the second derivative of -5*s**7/42 - 2*s**6/5 + 5136*s. Factor q(m).
-m**4*(5*m + 12)
Let c be 3763/1278 - 5/2. Let u(r) be the first derivative of 2/27*r**3 - c*r - 1/9*r**2 + 24. Let u(q) = 0. Calculate q.
-1, 2
Solve -2/3*b**3 - 34*b + 50/3 + 18*b**2 = 0.
1, 25
Factor -7986 + 1837/6*n**2 + 1/6*n**5 + 1/2*n**3 - 484*n - 7/2*n**4.
(n - 11)**3*(n + 6)**2/6
Let x(v) be the second derivative of -20*v**7/7 - 703*v**6/15 - 407*v**5/2 - 350*v**4 - 740*v**3/3 - 32*v**2 - 937*v. Solve x(j) = 0.
-8, -2, -1, -2/3, -1/20
Suppose -8 = -h + 3*k - 7, -5*k = -4*h + 11. Let n(b) be the first derivative of 0*b + 2*b**2 - 4/3*b**3 + h. Solve n(t) = 0.
0, 1
Let y(b) be the first derivative of b**3/3 + 109*b**2/2 - 110*b - 1201. Factor y(u).
(u - 1)*(u + 110)
Suppose 39 = 15*a + 84. Let s be -3 - (a + 15/(-5)). Determine i, given that 2/5*i**s + 0 + 2/5*i**4 + 0*i**2 + 0*i = 0.
-1, 0
Let w = 73 - 56. Suppose 0 = 2*i - m - w, -2*m = -5*i - 3*m + 46. Factor 7*k**4 - 15*k - i*k**3 + 24*k**3 + 0*k**4 - 2*k**4 - 5*k**2.
5*k*(k - 1)*(k + 1)*(k + 3)
Let a(y) be the first derivative of 7*y**3/5 + 81*y**2/10 - 12*y/5 - 245. Determine l, given that a(l) = 0.
-4, 1/7
Suppose 19*f - 3*f = 3936. Let -3*i**2 + 0*i**2 - 196*i + f*i + i**2 = 0. Calculate i.
0, 25
Let w(z) = -25*z**4 - 16*z**3 - 34*z**2 + 149*z - 85. Let o(v) = -11*v**4 - 8*v**3 - 18*v**2 + 75*v - 43. Let d(i) = -11*o(i) + 5*w(i). Solve d(k) = 0.
-3, 1, 2
Let n(u) be the first derivative of -4*u**3/3 + 1730*u**2/3 - 384*u - 4242. Let n(w) = 0. Calculate w.
1/3, 288
Let u(t) = -23*t**3 + 16*t**2 + 728*t + 704. Let h(r) = -56*r**3 + 40*r**2 + 1820*r + 1760. Let s(p) = 5*h(p) - 12*u(p). Factor s(w).
-4*(w - 11)*(w + 1)*(w + 8)
Let y be ((-4)/120)/(131/(-1572)). Find t such that 6/5 - y*t**4 - 8/5*t + 8/5*t**3 - 4/5*t**2 = 0.
-1, 1, 3
Let k be 5 + 54 + (35 - 92). Factor k - 1/8*r**2 + 15/8*r.
-(r - 16)*(r + 1)/8
Let l(r) = -13100*r - 209598. Let u be l(-16). Factor -6/5*h**2 - 14/15*h**4 + 0 + 0*h - 2/15*h**5 - u*h**3.
-2*h**2*(h + 1)*(h + 3)**2/15
Let s be -12*33/(-44) - 0/2. Factor -44 - 4*i**3 + 4*i + 16 + s*i**2 + 19*i**2.
-4*(i - 7)*(i - 1)*(i + 1)
Let a(j) = 3*j + 4. Suppose q + 3*b = -4*q + 4, 3*q + 4*b = 9. Let d be a(q). Let -5*y**2 + 7 + 8*y**2 - d - 9*y = 0. Calculate y.
1, 2
Suppose 0 = -2*a - 150 + 160. Suppose -a*q = q - 12. Factor 6 + 1/6*l**2 - q*l.
(l - 6)**2/6
Factor 348/7*i**2 + 60/7 - 222/7*i**3 + 48/7*i**4 + 3/7*i**5 - 237/7*i.
3*(i - 1)**4*(i + 20)/7
Let f(o) be the third derivative of 2*o**7/105 + 3*o**6/10 - 17*o**5/15 - 63*o**4/2 + 392*o**3/3 + 422*o**2 + 2*o - 4. Factor f(n).
4*(n - 4)*(n - 1)*(n + 7)**2
Let i(z) be the second derivative of 5*z**4/12 + 283*z**3/6 + 84*z**2 + 951*z. Determine x so that i(x) = 0.
-56, -3/5
Let g(q) be the third derivative of q**6/420 - 13*q**5/70 + 83*q**4/21 + 276*q**3/7 + 5*q**2 - q - 663. Factor g(j).
2*(j - 23)*(j - 18)*(j + 2)/7
Let a(s) be the first derivative of -s**6/4 - 21*s**5/10 + 57*s**4/4 - 31*s**3 + 129*s**2/4 - 33*s/2 - 1839. Factor a(m).
-3*(m - 1)**4*(m + 11)/2
Let v(a) be the third derivative of 11/6*a**4 - 968/3*a**3 - 72*a - 1/240*a**5 + 3*a**2 + 0. Factor v(b).
-(b - 88)**2/4
Let v(i) be the third derivative of -73/570*i**5 + 0*i + 0*i**3 + 0 + 1/228*i**6 + 312*i**2 - 5/38*i**4. Factor v(h).
2*h*(h - 15)*(5*h + 2)/19
Let t(z) be the second derivative of 13/45*z**4 + 0*z**2 + 43*z + 0 + 1/150*z**5 + 0*z**3. Find a, given that t(a) = 0.
-26, 0
Let j be (-16)/(-24) - (-24)/12. Let k(c) be the third derivative of 1/30*c**6 + 0*c + 0 - 1/15*c**5 - 2/3*c**4 + j*c**3 + 9*c**2. Find i such that k(i) = 0.
-2, 1, 2
Suppose -4*c + 0*c - 4*a + 8 = 0, -3*a = -c + 10. Let v be c + (5 - 1) + 5/2. Factor -v*f**2 - 3/2*f + 0 - 147/8*f**3.
-3*f*(7*f + 2)**2/8
Let v be (4/110)/((2/(-10))/(-1)). Let x = 186/451 - 2/41. Factor v + 2/11*w**2 - x*w.
2*(w - 1)**2/11
Let c(z) be the second derivative of z**4/4 - 26*z**3 + 2025*z**2/2 + 448*z - 1. Factor c(s).
3*(s - 27)*(s - 25)
Suppose -5*v + 4*m - 7*m = -42, v - 10 = -m. Factor 31*f - 88*f + 31*f + v - 3*f**2 + 29*f.
-3*(f - 2)*(f + 1)
Let y(l) be the third derivative of 5/48*l**4 + 1/3*l**3 + 0 + 0*l + 35*l**2 + 1/120*l**5. Factor y(f).
(f + 1)*(f + 4)/2
Let o = -3160 - -22136/7. Factor 38/7*h + 24/7 + 2/7*h**3 + o*h**2.
2*(h + 1)*(h + 3)*(h + 4)/7
Solve 385*x - 186*x + 483*x**4 - 199*x - 484*x**3 + 3*x**5 - 2*x**5 = 0.
-484, 0, 1
Factor 40 + 2/5*a*