*f**3 - 210*f**2 + 79*f.
3*(f - 2)*(7*f + 2)**2
Determine z, given that 0 - 11/3*z**2 + 6*z + 1/3*z**3 = 0.
0, 2, 9
Let p(x) be the second derivative of 0 - 1/4*x**4 + 1/20*x**5 + 0*x**2 + 5/18*x**3 + 1/90*x**6 - 18*x. Find t such that p(t) = 0.
-5, 0, 1
Let g be 602/(-77) - ((-18 - -2) + 8). Determine z so that 2592/11*z + 72*z**2 + g*z**4 - 3456/11 + 70/11*z**3 = 0.
-12, 1
Let d = 2404963/3 + -801653. Let a be (-317)/(-3) + (-1)/(-1). Factor -256/3 - 68/3*x**2 - a*x - d*x**3.
-4*(x + 1)*(x + 8)**2/3
Determine b so that -10*b**3 - 1036*b**2 - 1090*b - 5*b**3 - 3*b**4 - b**4 - 101*b**3 - 2426*b - 4032 = 0.
-16, -7, -3
Suppose 2/3*z**4 - 182*z - 94/3*z**3 + 0 + 638/3*z**2 = 0. What is z?
0, 1, 7, 39
Let x(j) = 90*j - 6548. Let m be x(73). Let s(n) be the second derivative of -25/2*n**2 - 5/3*n**4 - m*n + 0 + 35/2*n**3. Determine o so that s(o) = 0.
1/4, 5
Suppose 6 = 2*y, -4*y + 3*y + 18 = 5*m. Suppose -m*p = p - 12. What is t in 4*t + 4*t**2 - 4 - 3*t**2 + t**2 - p*t**2 = 0?
2
Let c(u) be the first derivative of -10*u**2 + 98 - 200*u - 1/6*u**3. Suppose c(h) = 0. Calculate h.
-20
Let r(m) be the second derivative of -m**4/18 - 95*m**3/9 - 94*m**2/3 + 33*m - 3. Factor r(n).
-2*(n + 1)*(n + 94)/3
Let f be (-20)/15*-9 + -5. Factor 23*i - 33*i - 1 + f + i**2 + 3.
(i - 9)*(i - 1)
Let g(b) be the third derivative of -b**6/120 + 17*b**5/60 + b**4/24 - 17*b**3/6 - 2*b**2 - 2109*b. What is n in g(n) = 0?
-1, 1, 17
Factor 0 + 0*g**2 + 4/3*g**4 + 144*g - 12*g**3.
4*g*(g - 6)**2*(g + 3)/3
Let j(i) be the first derivative of -3*i**5/8 + 27*i**4/16 + i**3 - 1986. Determine f so that j(f) = 0.
-2/5, 0, 4
Let h(r) = -1 + 35*r**2 + 22*r**2 + r + 15*r**2. Let k be h(-1). Solve -2*b**4 - k*b**5 - b**3 + 69*b**5 + 0*b**4 = 0.
-1, 0
What is r in 3/7*r**4 + 159/7*r**2 - 180/7*r + 44/7 - 46/7*r**3 = 0?
1/3, 2, 11
Factor -135/7*s**2 + 0 - 3/7*s**4 - 486/7*s + 48/7*s**3.
-3*s*(s - 9)**2*(s + 2)/7
Suppose 4*r - 7*r = -9. Let o be (1/(-4))/(((-116)/48)/29). Factor 15*h**o - 8*h**2 + h**5 - 15*h**4 + r*h**2 + 4*h**5.
5*h**2*(h - 1)**3
Determine z, given that -5320*z - 5328*z**2 + 337*z**3 - 1154 - 618 - 2070*z**3 - 51*z**3 - 4*z**4 = 0.
-443, -1
Suppose 0 = -3*s - 5*s + 112. Suppose -3*z + 1 = 5*l - s, 4*l = 3*z - 15. Factor -v - 1/4*v**3 + v**2 + l.
-v*(v - 2)**2/4
Let z(s) be the third derivative of -2*s**2 - 1/360*s**6 - 3/20*s**5 - 24*s**3 - 3*s**4 + 0 - 274*s. Factor z(i).
-(i + 3)*(i + 12)**2/3
Let z = 26 - 24. Suppose 0 = -2*v - 4*s + 44, -z*s = -3*v + 2*s + 76. What is h in -5*h**4 + 8 - v*h - 45*h**4 + 22*h**2 - 16 + 60*h**3 = 0?
-2/5, 1
Factor -536/9 - 2/9*h**2 - 142/9*h.
-2*(h + 4)*(h + 67)/9
Let m(t) be the first derivative of -89 + 3/10*t**2 + 0*t - 1/30*t**3. Determine d, given that m(d) = 0.
0, 6
Let l be (-6)/(-27) + 125350/(-3150) + 40. Determine h so that 0 - 6/7*h + 6/7*h**3 - l*h**2 + 3/7*h**4 = 0.
-2, -1, 0, 1
Factor -1329 - 12*i**3 + i**5 - 15*i**3 - 6*i**4 + 2*i**5 + 1329 + 54*i**2.
3*i**2*(i - 3)*(i - 2)*(i + 3)
Let i(s) be the first derivative of -s**5 + 5*s**4 + 70*s**3/3 - 90*s**2 - 225*s - 358. Solve i(h) = 0.
-3, -1, 3, 5
Let k(g) be the first derivative of -9/2*g**2 - g**3 + 0*g - 182. Find p, given that k(p) = 0.
-3, 0
Suppose -24*s + 25*s - 5*n = -28, 2*n = 3*s + 6. Let m(i) = i**2 + 10*i + 12. Let f be m(-9). Factor 1/3*c**f - c + 0*c**s + 2/3.
(c - 1)**2*(c + 2)/3
Let f(o) be the third derivative of 0*o - 13/180*o**5 - 1/12*o**4 - 1/45*o**6 + 0 + 71*o**2 - 1/630*o**7 + 0*o**3. Factor f(t).
-t*(t + 1)**2*(t + 6)/3
Let v(w) be the third derivative of -11*w**5/60 + w**4/4 + 100*w**3/3 - 636*w**2. Factor v(f).
-(f + 4)*(11*f - 50)
Let x(b) be the second derivative of b**5/15 - 8*b**3/3 - 45*b**2 + 69*b. Let h(p) be the first derivative of x(p). Factor h(m).
4*(m - 2)*(m + 2)
What is t in -1/3*t**2 - 305/6 - 611/6*t = 0?
-305, -1/2
Suppose 8 = 4*g, 6*s + 690 = 5*s + 2*g. Let w be -7 - s/90 - 2/9. Suppose 0*o - w*o**2 + 0 + 2/5*o**3 = 0. Calculate o.
0, 1
Factor 18068*w**2 - 375689*w**2 - w**4 + 142210*w**2 - 7573350625 - 102689500*w - 1180*w**3 - 306739*w**2.
-(w + 295)**4
Let c(t) be the first derivative of -t**6/2 - 69*t**5/5 - 297*t**4/4 - 169*t**3 - 192*t**2 - 108*t + 94. Suppose c(f) = 0. What is f?
-18, -2, -1
Suppose 9*k + 1412 - 134 = 435*k. Factor -k*u + 0 + 13/4*u**2 - 1/4*u**3.
-u*(u - 12)*(u - 1)/4
Find n, given that -167*n**5 - 110*n**4 - 698*n**3 + 38*n**2 - 3338*n**2 - 4500*n - 207*n**3 + 162*n**5 = 0.
-6, -5, 0
Let -5*q**3 - 824*q**4 + 9*q**3 - 23*q**2 - 9*q - 7*q + 828*q**4 + 7*q**2 = 0. What is q?
-2, -1, 0, 2
Let n(m) be the second derivative of 3*m**5/20 + 199*m**4/4 - 201*m**3 + 58*m - 6. Factor n(a).
3*a*(a - 2)*(a + 201)
Let j(x) be the second derivative of -x**7/126 + x**6/15 - x**5/12 - x**4/3 + 94*x. Solve j(m) = 0.
-1, 0, 3, 4
Determine d, given that 32*d + 54*d**3 - 16*d**2 + 4*d**5 - 78*d**3 + 552*d**4 - 548*d**4 = 0.
-2, 0, 1, 2
Let i = 5131714/5 - 1026342. Let -i*j**2 + 14/5*j - 6/5 = 0. What is j?
1/2, 3
Let w(c) be the third derivative of -c**8/2016 - c**7/180 - c**6/144 + 7*c**5/360 + c**4/24 + 208*c**2. What is n in w(n) = 0?
-6, -1, 0, 1
Let m(k) = 3*k**2 + 39*k + 5. Let u be m(-13). Suppose 4*r - 3*r = -4, -4*b + u*r = -32. Suppose -1/6*p**b + 0*p + 1/2*p**2 - 2/3 = 0. What is p?
-1, 2
Solve -1/3*u**2 + 19/3*u + 92/3 = 0 for u.
-4, 23
Let v be (-1566)/144 + 10 - (-31)/8. Let p(g) = -g + 8. Let f be p(7). Factor 1/4*d**v - 5/4*d**2 + 2*d - f.
(d - 2)**2*(d - 1)/4
Let n(m) = -68*m**2 + 10*m + 18. Let i(w) = 171*w**2 - 18*w - 35. Let b(p) = 2*i(p) + 5*n(p). Factor b(j).
2*(j + 2)*(j + 5)
Let s(n) = 4*n**3 - n**2 - n - 2. Let f(r) = 141*r**3 - 3783*r**2 - 4506*r - 744. Let x(m) = -f(m) + 27*s(m). Let x(y) = 0. Calculate y.
-1, -2/11, 115
Let x = -46969/39849 + 145/359. Let p = -4/37 - x. Let 0*u + p*u**4 + 20/3*u**3 + 6*u**2 + 0 = 0. Calculate u.
-9, -1, 0
Let m(k) be the second derivative of -k**4/12 - 19*k**3/6 - 42*k**2 - 185*k - 17. Factor m(p).
-(p + 7)*(p + 12)
Let t(q) be the second derivative of 0 - 7/18*q**4 - 49/9*q**3 + 17*q - 9/2*q**2 - 1/90*q**5. Let o(l) be the first derivative of t(l). Factor o(c).
-2*(c + 7)**2/3
Suppose -22*o - 135 = -25*o. Suppose -17 = 2*w - o. Let 48*s**2 - w*s - 51*s**2 - 4*s = 0. Calculate s.
-6, 0
Suppose 0 = 23*k - 152 + 83. Let c(x) be the third derivative of 0 + 5*x**2 + 3*x - 1/96*x**6 + 5/12*x**4 + 5/2*x**k - 1/48*x**5. Find h, given that c(h) = 0.
-2, 3
Let j(r) be the first derivative of -1/3*r**4 + 8*r**2 - 7 - 2*r**3 + 22*r. Let c(d) be the first derivative of j(d). Determine h so that c(h) = 0.
-4, 1
Let f(y) = 2*y**2 + 18*y + 10. Let u(i) = 8 + 13 + 9 + 55*i + 5*i**2. Let k(p) = -10*f(p) + 3*u(p). Find w such that k(w) = 0.
-2, -1
Suppose x - 3*h + 282 = -5*h, 5*x = -2*h - 1378. Let c = 279 + x. Factor -20*j - 1/2*j**4 - c*j**3 - 8 - 33/2*j**2.
-(j + 1)**2*(j + 4)**2/2
Let k(s) = -2*s**2 - 800*s - 66549. Let z be k(-118). Find l, given that -4*l**2 + 15/2 - 13/4*l - 1/4*l**z = 0.
-15, -2, 1
Let c(m) = -4*m**4 - 16*m**3 + 36*m**2 + 134*m. Let t(h) = h. Let b(u) = c(u) + 10*t(u). Find p such that b(p) = 0.
-4, -3, 0, 3
Factor -10 - 23/2*l + 5/4*l**2.
(l - 10)*(5*l + 4)/4
Let y(z) be the first derivative of 40/39*z**3 - 1/13*z**4 - 24/13*z**2 - 2/65*z**5 + 139 + 0*z. Factor y(d).
-2*d*(d - 2)**2*(d + 6)/13
Suppose -r = -0*v + v - 4, -2*v + 2*r = 4. Let a be ((-5 - -7) + 0)/v. Let 774 + 64*h - 9*h**4 + 12*h**a - 64*h**3 - 758 - 19*h**4 = 0. Calculate h.
-2, -1, -2/7, 1
Let v = -169 + 654. Let -v + 3*c**3 + 229 - 192*c - 7*c**3 - 48*c**2 = 0. Calculate c.
-4
Let b(m) = 15*m**3 - 26*m**2 - 555*m - 525. Let o(l) = -5*l**3 + 9*l**2 + 185*l + 175. Let p(z) = -4*b(z) - 11*o(z). Suppose p(x) = 0. What is x?
-5, -1, 7
Factor -2440*i + 5*i**4 - 1753*i - 318*i**3 - 341*i**3 + 508*i**3 + 1395*i**2 + 784.
(i - 16)*(i - 7)**2*(5*i - 1)
Suppose -11*i = 7*i - 36. Let h(d) = -26*d**2 - 124*d + 22. Let l(y) = -5*y**2 - 25*y + 4. Let u(p) = i*h(p) - 11*l(p). Factor u(k).
3*k*(k + 9)
Let f = 746726/11 - 67884. Suppose 2/11*g**4 - 6/11*g**3 - 2/11*g**2 + f*g**5 + 0 + 4/11*g = 0. What is g?
-2, -1, 0, 1
Let c(t) = 21*t**2 + 19*t + 68. Let l be c(-6). Let j be (6/10)/(284/l). Factor 1/2*y**4 - j*y**2 - 1/2*y + 1/2*y**3 + 1.
(y - 1)**2*(y + 1)*(y + 2)/2
Let w(r) be the first deriva