- 363*t**4 + 249*t**5 + 20 = 0.
-2, 1/6, 1/2, 2
Let r be (-1 - (-30)/2)*18/21. Let f be 7/4 + 1 + r/(-16). Factor 14*i**3 - 6*i**3 + 4*i**5 - 7*i**3 - 5*i**3 + 4*i**f - 4*i**4.
4*i**2*(i - 1)**2*(i + 1)
Let y = -193 - -195. Let -3*m**2 + 2*m**3 + 2*m**2 + 4*m + 4*m**y - 9*m**2 = 0. What is m?
0, 1, 2
Let a = 34/1715 - -652/1715. Factor 20 - a*g**3 - 16/5*g**2 - 2*g.
-2*(g - 2)*(g + 5)**2/5
Suppose 3*j - 5*v + 2036 = 0, -3*v + v + 2024 = -3*j. Let w = j + 674. Factor 9/2*l + 0 + 3/2*l**w.
3*l*(l + 3)/2
Let m(l) be the first derivative of l**8/2856 - l**7/420 + 2*l**6/765 + l**5/85 - l**3/3 - 42*l + 80. Let q(a) be the third derivative of m(a). Factor q(i).
2*i*(i - 2)**2*(5*i + 3)/17
Let j(f) be the third derivative of 7/9*f**3 - 1/360*f**6 + 69*f**2 + 1/8*f**4 - f + 0 - 1/30*f**5. Let j(b) = 0. Calculate b.
-7, -1, 2
Factor -82369/5 - 1/5*o**2 - 574/5*o.
-(o + 287)**2/5
Let v(l) be the first derivative of -l**5/100 + l**4/30 - l**3/30 - 33*l - 44. Let i(a) be the first derivative of v(a). Factor i(h).
-h*(h - 1)**2/5
Let q be -1*((-70)/(-3))/((-13)/39). Let x be -3*14/(-24)*60/q. Factor x*f + 1/2*f**5 - f**2 - 2*f**3 + 0*f**4 + 1.
(f - 2)*(f - 1)*(f + 1)**3/2
Suppose g - 76 = -71. Suppose -3*j - g*w + 14 = -j, 2*j = -3*w + 10. Factor -27*k**j - 7 + 19 + 8*k + 37*k + 3*k.
-3*(k - 2)*(9*k + 2)
Let q(p) be the first derivative of p**5/40 - 7*p**4/32 - 53*p**3/24 - 81*p**2/16 - 9*p/2 + 2962. Factor q(w).
(w - 12)*(w + 1)**2*(w + 3)/8
Let w(p) be the third derivative of 0*p**3 + 0*p**5 - 1/180*p**6 + 1/630*p**7 + 0 + 0*p + 0*p**4 + 1/1008*p**8 - 133*p**2. Let w(u) = 0. What is u?
-2, 0, 1
Let u(l) be the second derivative of 15/8*l**3 + 9/16*l**4 + 21/8*l**2 - 14 + 2*l + 3/80*l**5. Find h, given that u(h) = 0.
-7, -1
Let k(d) be the third derivative of 3*d**7/70 + d**6/10 - d**5/30 - d**4/6 + d**3/6 - 237*d**2 - 2. Factor k(b).
(b + 1)**2*(3*b - 1)**2
Suppose -53*r = 26*r + 57*r. Let z(h) be the third derivative of r + 31*h**2 - 4/75*h**6 - 4/15*h**5 + 0*h + 49/15*h**3 + 7/60*h**4. Let z(p) = 0. What is p?
-7/4, 1
Factor -o**2 - 38*o + 0*o**2 - 25*o - 41*o.
-o*(o + 104)
Let c be 17*4/238*(-70)/(-6). Let c + 26/3*u + 92/15*u**2 - 14/15*u**4 + 2/15*u**5 - 4/15*u**3 = 0. Calculate u.
-1, 5
Factor 979/3 + 980/3*o + 1/3*o**2.
(o + 1)*(o + 979)/3
Let l(p) be the third derivative of -p**5/120 - 67*p**4/24 - 4489*p**3/12 - 2686*p**2. Factor l(a).
-(a + 67)**2/2
Let r = 6542421 - 6542419. Let j(d) = -4*d - 3. Let v be j(-2). Suppose -1/4*a**v + 1 + 5/4*a**3 - 5/4*a**r - a + 1/4*a**4 = 0. Calculate a.
-2, -1, 1, 2
Let h = 21061/27 + -780. Let c(w) be the second derivative of 0 - 1/54*w**4 - 5*w + 2/9*w**2 + h*w**3. Suppose c(a) = 0. Calculate a.
-1, 2
Suppose -12*z + 241 = -236 + 453. Factor -1/2*j**3 + 0 + 4*j - j**z.
-j*(j - 2)*(j + 4)/2
Let d(o) be the first derivative of -64/3*o**2 + 2/15*o**5 - 11/6*o**4 - 42 + 28/3*o**3 + 64/3*o. Determine c so that d(c) = 0.
1, 2, 4
Factor 1/2*u**4 + 0*u + 0 - 66*u**2 - 32*u**3.
u**2*(u - 66)*(u + 2)/2
Let u be 20/(-80) + (2/8 - 0). Let v(n) = n**3 + n + 3. Let t be v(u). Solve 124*w**4 + t*w**5 + 33*w**3 + 6*w**5 + 3*w**2 - 91*w**4 - 6*w = 0 for w.
-2, -1, 0, 1/3
Let 396/7*h**2 - 60/7*h**4 + 4/7*h**5 + 4*h**3 - 32/7*h - 48 = 0. What is h?
-2, -1, 1, 3, 14
Let z(y) = -23*y**2 + 5102*y - 2152217. Let a(d) = 16*d**2 - 3402*d + 1434811. Let b(c) = -10*a(c) - 7*z(c). Find v such that b(v) = 0.
847
Suppose f - 4*k - 10 = 0, -2*f - 2*k + 3*k + 20 = 0. Factor -45*a**2 - f*a - 53076 + 53076.
-5*a*(9*a + 2)
Let d(s) be the second derivative of 0*s**2 - 1/3*s**3 - 2/9*s**4 + 0 - 100*s - 1/30*s**5. Factor d(t).
-2*t*(t + 1)*(t + 3)/3
Suppose f - 52 + 7 = -2*v, -4*v + 3*f + 75 = 0. Suppose 85*t = 78*t + v. Factor -1/3*r**4 + 2/3*r**t - 2/3*r + 0 + 1/3*r**2.
-r*(r - 2)*(r - 1)*(r + 1)/3
Let y(d) = 13*d**4 - 28*d**3 - 173*d**2 - 17*d. Let k(m) = -6*m**4 + 15*m**3 + 75*m**2 + 8*m. Let n(z) = -10*k(z) - 4*y(z). Solve n(t) = 0.
-1, -1/4, 0, 6
Let r(o) be the first derivative of 2*o**3/15 - 130*o**2 + 42250*o + 1093. Factor r(k).
2*(k - 325)**2/5
Solve 144*v + 27/2*v**4 + 1/2*v**5 + 0 + 240*v**2 + 109*v**3 = 0.
-12, -2, -1, 0
Suppose 21*z - 16*z - 5 = 0, 4*a + z = 9. Suppose -5 + 13 = a*o + t, 5*o - 5*t - 20 = 0. Factor -4/3*d**5 + 4/3*d**2 + 4*d**4 + 0 - o*d**3 + 0*d.
-4*d**2*(d - 1)**3/3
Let -64*j - 48977*j**2 + 16324*j**2 + 16322*j**2 + 16333*j**2 + 16*j - 104 = 0. Calculate j.
-2, 26
Let c(x) = -4*x**4 + 32*x**3 + 42*x**2 + 44*x - 2. Let t(f) = -5*f**4 + 48*f**3 + 42*f**2 + 46*f - 3. Let p(u) = -3*c(u) + 2*t(u). Factor p(q).
2*q*(q - 5)*(q + 1)*(q + 4)
What is w in 136*w**4 - 720 - 300*w - 131*w**4 + 11*w**3 - 30*w**3 - 56*w**3 + 340*w**2 = 0?
-1, 4, 6
Let t(a) be the first derivative of a**7/168 + a**6/72 + 4*a**3/3 - 2*a**2 + 47. Let i(q) be the third derivative of t(q). Factor i(p).
5*p**2*(p + 1)
Let b(r) be the third derivative of 7/40*r**6 - 41*r**2 - 7/8*r**4 - 1/70*r**7 + 1/20*r**5 + 0*r**3 + 0*r + 0. Factor b(g).
-3*g*(g - 7)*(g - 1)*(g + 1)
Let n be (1/(-8))/((-21)/(-28) - 10/8). Let l(u) be the first derivative of -1 - n*u**4 - 4*u + u**3 + 0*u**2. Factor l(v).
-(v - 2)**2*(v + 1)
Let x(u) be the first derivative of 3*u**4/4 - 5*u**3 - 132*u**2 - 624*u + 874. Factor x(v).
3*(v - 13)*(v + 4)**2
Let y(t) be the first derivative of t**4/10 + 88*t**3 - 1323*t**2/5 + 1324*t/5 - 3694. Factor y(q).
2*(q - 1)**2*(q + 662)/5
Let h(p) = 3*p**4 - 2*p**3 - p**2 - 2*p + 2. Let f = -22 + 27. Let a(s) = -8 - 3*s**4 + f + 0*s**4 + 3*s**3 + 3*s. Let g(t) = -2*a(t) - 3*h(t). Factor g(y).
-3*y**2*(y - 1)*(y + 1)
Let a(j) = -j + 9. Let o(c) = 3*c - 12. Let b be o(6). Let y be a(b). Factor -3 - 16*i**2 + 4*i**3 - 5 + 0*i**y + 9*i + 11*i.
4*(i - 2)*(i - 1)**2
Suppose 781 = 391*n + 141 - 142. Factor -2/3*y - 1/3 - 1/3*y**n.
-(y + 1)**2/3
Suppose -2*h - 147*w + 6 = -145*w, -5*h + 15 = -2*w. Factor 4/5 - 4/5*r**2 + 2*r - 2*r**h.
-2*(r - 1)*(r + 1)*(5*r + 2)/5
Factor 3*w**2 - 938*w - 149 - 5*w**2 + 66*w + 464 + 559.
-2*(w - 1)*(w + 437)
Let p(t) = 3*t**3 - 52*t**2 - 680*t - 624. Let c(d) = d**2 + 2*d. Let k(o) = c(o) + p(o). What is l in k(l) = 0?
-8, -1, 26
Solve -186*g - 2*g**4 + g**4 - 2*g**4 - 2388*g**2 + 216 + 36*g**3 + 2325*g**2 = 0 for g.
-2, 1, 4, 9
Let d(o) be the second derivative of 0 + 2/3*o**3 - 9/4*o**2 - 114*o + 1/24*o**4. Factor d(q).
(q - 1)*(q + 9)/2
Suppose -1945 = -584*t + 391. Let -4*n**2 + 1/2*n**5 + 3*n**3 - 7/2*n + 0 + t*n**4 = 0. Calculate n.
-7, -1, 0, 1
Let a = 2353/6 + -392. Let g(t) be the second derivative of 0 - 26*t - 1/48*t**4 + a*t**3 + 0*t**2. What is s in g(s) = 0?
0, 4
Let r(b) be the second derivative of b**6/120 + b**5/120 - b**4/12 - b**3/4 + 85*b**2 - 62*b. Let f(y) be the first derivative of r(y). Factor f(h).
(h + 1)**2*(2*h - 3)/2
Let j be (1014/26 + -39)/(2 + -4). Factor 4/7*i - 1/7*i**2 + j.
-i*(i - 4)/7
Let a(o) = -406*o + 5690. Let l be a(14). Let m(s) be the first derivative of 2/5*s**5 + 0*s**4 + 0*s**3 + 1/3*s**l + 0*s + 12 + 0*s**2. Factor m(b).
2*b**4*(b + 1)
Let h(c) be the first derivative of c**7/1680 - c**6/240 + c**5/120 - 41*c**3 - 141. Let g(l) be the third derivative of h(l). Factor g(f).
f*(f - 2)*(f - 1)/2
Let o(p) be the second derivative of 0*p**2 + 4*p - 2/5*p**5 - 1/6*p**4 - 1/15*p**6 + 2*p**3 - 4. Determine h, given that o(h) = 0.
-3, -2, 0, 1
Let l(g) = -20*g - 7. Let p be l(-2). Let j = p - 29. Factor 0*u**5 + 2*u**5 - 8*u**j + 7*u**4 - 7*u**4 + 10*u**3 - 4*u**2.
2*u**2*(u - 2)*(u - 1)**2
Let i = 313 - 144. Let g be -22*(-3)/18 + 6/(-9). Factor -61*k + 3*k**5 + k**2 + i*k - 19*k**2 - 24 - 219*k**g - 30*k**5 - 144*k**4.
-3*(k + 2)**3*(3*k - 1)**2
Find c such that 15465*c**2 - 71389*c + 595*c**3 + 146997 + 13544 - 41471 - 63746*c + 5*c**4 = 0.
-63, 1, 6
Suppose 5*s - 40 = -3*p, 10*s - 20 = 6*s. Let g(x) be the third derivative of 0 + 2/3*x**4 - 8/3*x**3 - 1/15*x**p - 9*x**2 + 0*x. Factor g(a).
-4*(a - 2)**2
Suppose 82*h = 53*h - 62*h + 219 + 54. Find l such that 1/3*l**5 + 100/3*l - 60*l**2 + 6*l**4 + 61/3*l**h + 0 = 0.
-10, 0, 1
Let d(m) be the first derivative of m**4/108 + m**3/54 - m**2/3 - 56*m + 96. Let v(l) be the first derivative of d(l). Determine y so that v(y) = 0.
-3, 2
Let j(h) be the first derivative of -52 + 2*h**2 - 1/27*h**3 - 36*h. Factor j(u).
-(u - 18)**2