- 2*o(r). Factor f(l).
-3*(l + 1)**2
Let r(o) = -11*o**2 + 49*o - 226. Let i(v) = -5*v**2 + 25*v - 111. Let n(x) = -7*i(x) + 3*r(x). Let t be n(6). Factor -2/5 - 3/5*f**t + f + 4/5*f**2.
-(f - 2)*(f + 1)*(3*f - 1)/5
Let q be (-120)/(-78)*(-7)/(-4). Let n = q + -219/91. Factor n*v**2 + 10/7 - 12/7*v.
2*(v - 5)*(v - 1)/7
Let l(p) be the third derivative of -p**5/140 + 11*p**4/56 + 40*p**3/7 - 2656*p**2. Factor l(q).
-3*(q - 16)*(q + 5)/7
Suppose 413*t + 877*t + 70 - 1501 = 5019. Suppose 4/7*n**t - 72/7*n + 4*n**4 - 12/7*n**2 + 0 + 52/7*n**3 = 0. Calculate n.
-3, -2, 0, 1
Let a(z) be the third derivative of 0*z - 2/25*z**5 - 1/175*z**7 - 83*z**2 + 0*z**4 - 1/25*z**6 + 0 + 0*z**3. Factor a(s).
-6*s**2*(s + 2)**2/5
Factor 78*x**2 + 383*x + 72*x**2 - 48*x**2 - 4*x**3 + 486 + 202*x + 7*x**3.
3*(x + 1)*(x + 6)*(x + 27)
Let f(m) be the first derivative of -m**5/5 - 3*m**4/4 + 14*m**3/3 + 6*m**2 - 40*m + 1830. Solve f(w) = 0.
-5, -2, 2
Let q be (-33)/(-4) - (-3)/4. Suppose q*g - 2 = 8*g. Factor 3 + 33/8*s**3 - 3/4*s**g + 3/8*s**5 - 9/4*s**4 - 9/2*s.
3*(s - 2)**3*(s - 1)*(s + 1)/8
Let o = 1061684 - 1061682. Determine v so that 12/5*v + 8/5 + 6/5*v**o + 1/5*v**3 = 0.
-2
Suppose -14*d + 2 = -5*p - 18*d, 1 = -7*p - 5*d. Let r be (-648)/(-210) + (6/7)/(-3). Find j such that 2/5*j**p + r + 16/5*j = 0.
-7, -1
Let j be (4 + 0)*135/180. Factor 31027 + j*s**2 - 9*s - 31027.
3*s*(s - 3)
Factor -57*f**2 - 186473*f + 187577*f + 53*f**2.
-4*f*(f - 276)
Factor -141/7*v**2 + 36/7*v**3 + 0 - 3/7*v**4 + 180/7*v.
-3*v*(v - 5)*(v - 4)*(v - 3)/7
Let l(h) be the first derivative of h**6/30 - 7*h**5/15 + 11*h**4/6 - 10*h**3/3 + 14*h**2 - 2*h - 46. Let c(z) be the second derivative of l(z). Factor c(x).
4*(x - 5)*(x - 1)**2
Let y(r) = -r**2 - 4*r + 0*r + 4*r - 3*r. Let d be y(-3). Factor -4*l**2 - 2*l + 0*l + d*l + 8*l.
-2*l*(2*l - 3)
Let d(x) = 5*x + 22*x**2 - 3*x - 26*x**2 + 17*x. Let n(g) = -4*g**2 + 18*g. Let v(i) = 2*d(i) - 3*n(i). Factor v(h).
4*h*(h - 4)
Let c(r) be the third derivative of 0*r**3 + 0*r - 13/20*r**6 - 2/21*r**7 + 0 + 4*r**2 - 1/336*r**8 - 121/24*r**4 + 11/3*r**5. Suppose c(n) = 0. Calculate n.
-11, 0, 1
Determine l, given that 781250/3 - 2500/3*l + 2/3*l**2 = 0.
625
Let r(s) be the first derivative of s**6/165 + s**5/66 + s**4/132 - 46*s**2 + 82. Let k(y) be the second derivative of r(y). Factor k(m).
2*m*(m + 1)*(4*m + 1)/11
Let l(a) = a**4 + a**3 + a**2 + a - 1. Let u(o) = -6*o**4 - 48*o**3 - 50*o**2 - 8*o + 8. Let h be 56/7*1/(-2) - -3. Let d(k) = h*u(k) - 8*l(k). Factor d(s).
-2*s**2*(s - 21)*(s + 1)
Suppose 2*h + t - 166 = 0, -2*t = -4*h - 0*t + 316. Suppose 5*a - 2*a = h. Factor 5*w**4 - 15*w - 12*w + a*w + 5*w**3.
5*w**3*(w + 1)
Suppose 5*n + 11 = 3*v, -4*v + 9 = -7*n + 6*n. What is a in -2*a**v + 0*a**2 - a**2 - 8*a + 6 + 5*a = 0?
-2, 1
Let t be (-2321)/(-13926)*(-1 - 69/(-15)). Factor 54/5 + t*g**3 - 9/5*g - 12/5*g**2.
3*(g - 3)**2*(g + 2)/5
Suppose -14*b + 107 = -243. What is n in 15*n + 8*n + 100*n**2 - 3*n + 110*n**2 - 215*n**2 + b = 0?
-1, 5
Let i(k) be the second derivative of -k**7/42 + 7*k**6/6 - 261*k**5/20 + 733*k**4/12 - 409*k**3/3 + 156*k**2 - 6*k + 89. Find a, given that i(a) = 0.
1, 3, 4, 26
Let x(h) = -3*h**4 - 26*h**3 - 17*h**2 + 20*h + 28. Let d(u) = 80*u**4 + 705*u**3 + 460*u**2 - 540*u - 760. Let c(i) = -2*d(i) - 55*x(i). Factor c(g).
5*(g - 1)*(g + 1)*(g + 2)**2
Let s = 190240/3 - 63413. Determine r, given that s - 5/3*r - 2*r**2 = 0.
-1, 1/6
Let c(f) = -22916*f - 91657. Let i be c(-4). Determine p so that 6 + 8/3*p**2 + i*p + 1/3*p**3 = 0.
-3, -2
Suppose 224 = 6*f + 10*f. Suppose -f*i + 60 = -2*i. Factor -23 - 150*u**4 + 20*u + 23 + 185*u**3 - 100*u**2 - 10*u**i + 55*u**5.
5*u*(u - 1)**2*(3*u - 2)**2
Let v = -5276 + 5280. Let o(m) be the second derivative of 4/7*m**2 + 18*m + 1/42*m**v + 0 - 4/21*m**3. What is l in o(l) = 0?
2
Let w(g) be the second derivative of g**6/15 + 177*g**5/10 - 179*g**4/6 - 59*g**3 + 178*g**2 + 1746*g. Factor w(h).
2*(h - 1)**2*(h + 1)*(h + 178)
Let i(z) = 802*z**3 - z**2 + z - 2. Let a be i(2). Factor -a*k - 421*k - 78732 - 4*k**3 - 1915*k - 324*k**2.
-4*(k + 27)**3
Suppose 2*w = -b + 3*b - 14, 0 = 4*w. Suppose b*a + 5 = 8*a. Let -2/9*x**4 - 1/9*x**a + 0 + 1/9*x + 0*x**3 + 2/9*x**2 = 0. Calculate x.
-1, 0, 1
Let f(y) be the third derivative of y**5/90 - 185*y**4/18 + 34225*y**3/9 - 3*y**2 - 41*y. Determine z so that f(z) = 0.
185
Let f(k) be the third derivative of -k**7/5040 - k**6/4320 - 31*k**4/12 + 32*k**2. Let o(b) be the second derivative of f(b). Factor o(q).
-q*(3*q + 1)/6
Let c(w) be the third derivative of -5*w**7/42 + 31*w**6/75 - 121*w**5/300 - w**4/60 - 21*w**2 + 31. Factor c(k).
-k*(k - 1)**2*(125*k + 2)/5
Factor 3/4*l**2 + 131043 - 627*l.
3*(l - 418)**2/4
Let o = 158 + -154. Factor -4*l - 10*l**2 - 21*l**4 + 22*l**4 + l**o + 2*l**5 - 6*l**3.
2*l*(l - 2)*(l + 1)**3
Suppose 0 - 1/2*x**5 - 400158*x**3 - 68694048*x + 1549/2*x**4 + 69093432*x**2 = 0. What is x?
0, 1, 516
Let l = 61 + -37. Suppose 2*i - 5*y - l = 0, 4*y = 5*i - y - 30. Determine r so that -4*r**i - 280*r + 554*r - 278*r = 0.
-1, 0
Let x(p) be the third derivative of -p**5/12 + 505*p**4/12 - 980*p**3 + 8233*p**2. Suppose x(g) = 0. What is g?
6, 196
Factor -206*m**2 + 6*m**3 + 10846874*m + 78*m**2 + 2*m**4 - 10846754*m.
2*m*(m - 6)*(m - 1)*(m + 10)
Let x(v) be the first derivative of v**4/11 - 10*v**3/33 - 4*v**2/11 + 6*v/11 - 1023. Let x(m) = 0. Calculate m.
-1, 1/2, 3
Let b(w) be the first derivative of -105*w**6/2 + 136*w**5 + 115*w**4/4 - 380*w**3/3 - 50*w**2 - 802. What is f in b(f) = 0?
-5/9, -2/7, 0, 1, 2
Let d(r) be the first derivative of 4*r**5/25 + 286*r**4/5 + 81796*r**3/15 - 2672. Find p, given that d(p) = 0.
-143, 0
Let s(m) be the first derivative of m**3 + 906*m**2 + 273612*m + 171. Factor s(f).
3*(f + 302)**2
Let c(j) be the second derivative of j**7/42 - j**6/15 - 13*j**5/20 - 5*j**4/6 - 539*j + 2. Suppose c(y) = 0. Calculate y.
-2, -1, 0, 5
Let i(d) be the first derivative of -2*d**5/35 + d**4/7 + 80*d**3/21 + 64*d**2/7 - 3546. Let i(b) = 0. Calculate b.
-4, -2, 0, 8
Factor -438 + 2/3*w**2 - 1312/3*w.
2*(w - 657)*(w + 1)/3
Let c(v) be the second derivative of -v**6/180 + v**5/40 + v**4/12 - 2*v**3/9 + 667*v. Find s such that c(s) = 0.
-2, 0, 1, 4
Let d(x) be the first derivative of -3*x**5/40 - x**4/4 + 5*x**3/4 + 9*x**2/2 - 54*x - 2. Let i(q) be the first derivative of d(q). Factor i(z).
-3*(z - 2)*(z + 1)*(z + 3)/2
Factor 0 + 34/5*k**3 + 38/5*k**4 + 0*k - 4/5*k**2.
2*k**2*(k + 1)*(19*k - 2)/5
Let d = -2/5931 - -53399/59310. Let a(y) be the second derivative of 1/5*y**3 - d*y**2 + 0 - 1/60*y**4 - 3*y. Find s such that a(s) = 0.
3
Suppose 5*u = -h - 1, -111 = -3*h - 2*h + 4*u. Suppose 4*i - 3 = 7*i, -2*x = 3*i - h. Factor 9*b**2 + 3*b**5 - 15*b**3 + b + 14*b**4 - 12*b**4 - 11*b**4 + x*b.
3*b*(b - 4)*(b - 1)*(b + 1)**2
Factor -140*w**2 - 35*w**3 + 27*w**2 - 106*w**2 - w**2 + 5*w**4.
5*w**2*(w - 11)*(w + 4)
Factor -2*t**4 + 0*t**4 - 8*t**3 - 12*t + 3428*t**2 + 0*t**4 - 3406*t**2.
-2*t*(t - 1)**2*(t + 6)
Let a be 1/1 - (-10 - -9). Let c(q) = 2*q - 56. Let u be c(29). Factor -295*o**3 + o + 0*o**a + 294*o**3 - o**u + 3*o**4 - 2*o**4.
o*(o - 1)**2*(o + 1)
Suppose 230*k = 246*k - 160. Let a be 11 + (-310)/30 + k/(-24). Factor -1/2 + a*f + 1/4*f**2.
(f - 1)*(f + 2)/4
Let x(c) be the first derivative of -3/14*c**2 + 3/28*c**4 + 56 - 2/7*c + 1/21*c**3 + 1/35*c**5. Suppose x(n) = 0. What is n?
-2, -1, 1
Suppose -p - 493 = -5*l - 135, 3*l + 5*p = 226. Let z be 6/(-27)*-1 + 38/l. Determine b, given that 3*b + 15/4 - z*b**2 = 0.
-1, 5
Let p = 1660 - -7000. Factor -270*r - 1440 - 306*r + p + 196*r + 5*r**2.
5*(r - 38)**2
Suppose x - 16 = 3*i, 12 = 5*x - 82*i + 84*i. Let y = -12/5 + x. Suppose 2*v**3 + 4*v**2 - 2/5*v**5 - y*v - 16/5 - 4/5*v**4 = 0. What is v?
-2, -1, 1, 2
Solve -15*x**5 - 76*x**3 + 29*x**5 + 51*x**4 - 11*x**4 + 2*x**4 - 16*x**5 = 0.
0, 2, 19
Suppose 25*h - 176*h = 291*h - 8398. Determine z so that -3/2*z**3 + h*z**2 - 66*z + 36 = 0.
2/3, 6
Let s(p) be the third derivative of 5*p**8/1008 - p**7/10 + 221*p**6/360 - 7*p**5/12 - 113*p**4/36 + 28*p**3/3 + 2*p**2 + 3903*p. What is g in s(g) = 0?
-1, 1, 28/5, 6
Let p(j) = -23*j**3 - 65*j**2 - 229*j - 121. Let q(o) = 3*o**3 - o - 9. Let l(d) = p(d) + 6*q(d).