1, 2
Let u(j) = -26*j**3 + 202*j**2 - 529*j + 469. Let w(h) = -5*h**3 + 40*h**2 - 106*h + 94. Let c(p) = 2*u(p) - 11*w(p). Factor c(l).
3*(l - 8)*(l - 2)**2
Let x(c) be the second derivative of 1/15*c**7 - 2/25*c**5 - 2/5*c**2 + 7/15*c**4 - 1/5*c**3 - 4/25*c**6 + 0 - 10*c. Determine q, given that x(q) = 0.
-1, -2/7, 1
Let p(u) = 34*u**2 + 244*u - 16. Let o(m) = -2*m**2 - 3*m + 1. Let c(r) = -16*o(r) - p(r). Let c(h) = 0. Calculate h.
-98, 0
Let m(w) = 6*w**2 + 494*w - 15856. Let r(g) = g**2 - g + 2. Let s(q) = -m(q) + 10*r(q). Let s(i) = 0. Calculate i.
63
Let o(t) = t**3 - 5*t**2 + 2*t - 1. Let b be o(5). Suppose -29 + b = -5*x. Factor m**2 - 8*m + m**2 + 0*m**2 - 6*m**2 - x.
-4*(m + 1)**2
Let w(s) be the second derivative of s**7/63 - s**6/45 - s**5/10 + 5*s**4/18 - 2*s**3/9 - 11*s + 5. Suppose w(y) = 0. What is y?
-2, 0, 1
Let f(w) = -6*w + 70. Let c be f(12). Let q be ((-33)/11 - c/2)/(-1). Factor -2/3*j**2 - q*j - 4/3.
-2*(j + 1)*(j + 2)/3
Let u(r) = -r**3 - r**2 - r. Let h be u(0). Let n be h - 5/(5/(-3)). Factor -2*m + 0*m**3 - 2*m**3 - 6*m**2 + 2*m**2 + 0*m**n.
-2*m*(m + 1)**2
Let y(k) be the first derivative of 3*k + 1/16*k**4 + 15 + 7/12*k**3 + 2*k**2. Factor y(g).
(g + 2)**2*(g + 3)/4
Suppose 2*d = z - 2*d - 9, 5*d + 5 = 0. Let r be z/(0 - (1 + -2)). Find y such that 7*y**2 - y**4 - y**r - 1 - 3*y**2 - y + 2*y**3 + y**2 - 3*y**2 = 0.
-1, 1
Let y(k) = 17*k**2 + 110*k + 601. Let m(i) = 275*i**2 + 1760*i + 9615. Let q(p) = 4*m(p) - 65*y(p). Factor q(u).
-5*(u + 11)**2
Factor 58*v**3 + 30 - 55*v**3 + 41*v**2 + 24*v**2 - 20*v**2 - 3*v**4 + 69*v.
-3*(v - 5)*(v + 1)**2*(v + 2)
Let u(z) be the third derivative of z**5/120 - 5*z**4/3 - 27*z**3/4 + 409*z**2 + 2*z. Factor u(i).
(i - 81)*(i + 1)/2
Let n(f) be the first derivative of -2*f**3/15 + 82*f**2/5 - 3362*f/5 - 131. Factor n(t).
-2*(t - 41)**2/5
Let u be -2*(-10)/8*6. Suppose 0 = -2*v - u + 57. Let -v*h**3 - 60*h + 54*h**2 - 8 + 2 + 12 + 18 + 3*h**4 = 0. Calculate h.
1, 2
Let 120/7*n**3 + 2700/7*n**2 + 27000/7*n + 2/7*n**4 + 101250/7 = 0. What is n?
-15
Determine c, given that -2/5*c**2 + 8/5 + 0*c = 0.
-2, 2
Let k(y) = y**3 + 15*y**2 + 44*y + 234. Let v be k(-13). Factor 1/3*g**2 - g + v.
g*(g - 3)/3
Let m(s) = -4*s. Let t be m(-9). Let c be (-2)/(-8) - 3*(-3)/t. Suppose c*f**4 - 1/10*f**2 - 7/10*f**3 + 0 + 3/10*f = 0. Calculate f.
-3/5, 0, 1
Let m be (-5 + 4)/(4/(-12)). Let p(d) be the second derivative of -4*d - 2/15*d**4 + 0*d**2 - 1/5*d**m + 0 - 1/50*d**5. Factor p(o).
-2*o*(o + 1)*(o + 3)/5
Let u = 24812 + -124031/5. Factor 6/5*m - u*m**2 + 0 + 9/5*m**3.
m*(m - 3)*(9*m - 2)/5
Let l(m) be the first derivative of -m**6/20 + 3*m**5/8 - 3*m**4/4 - 43*m - 6. Let n(w) be the first derivative of l(w). Suppose n(t) = 0. What is t?
0, 2, 3
Let w(h) be the first derivative of -h**5/110 + h**4/11 - 23*h - 17. Let c(p) be the first derivative of w(p). Factor c(k).
-2*k**2*(k - 6)/11
Let w be 1/((-12)/(-57)) + (-4)/(-16). Suppose -w + 7 + 6*r + 2*r + 4*r**2 + 2 = 0. What is r?
-1
Factor g**3 - 15*g - 18 + 26*g + 5*g**2 - g**2 + 0*g**2 - 14*g.
(g - 2)*(g + 3)**2
Suppose -5 = -5*t - 5*m, 4*t = m - 16 - 5. Let v be t/10 + 24/10. Solve -3*z**2 - 2*z**3 + z**v + 4*z**2 = 0 for z.
0, 1
Let u be (-44)/(-10) - (-4)/(-70)*7. Let n = -164 + 339. Find t such that -8*t - 372*t**2 - n*t**5 + 14 + 1456*t**u + 2 + 226*t**3 + 1057*t**5 = 0.
-1, -2/9, 2/7
Solve 2/15*i**5 + 16/15*i**4 + 0 + 32/15*i**3 + 0*i + 0*i**2 = 0 for i.
-4, 0
Let k = 10 + -2. Suppose -5*h = -k*h. Factor 1 + 3*z**4 + h + 3*z**5 - 1.
3*z**4*(z + 1)
Let z(l) be the third derivative of -l**9/15120 + l**8/8400 - 3*l**3/2 - 8*l**2. Let v(y) be the first derivative of z(y). Factor v(t).
-t**4*(t - 1)/5
Let o(f) = f**3 + 37*f**2 - 26*f + 456. Let k be o(-38). Determine x, given that k + 0*x + 6/7*x**3 + 6/7*x**5 - 16/7*x**4 + 4/7*x**2 = 0.
-1/3, 0, 1, 2
Let u = -1263 - -1275. Let i(l) be the first derivative of u + 3/2*l**2 - 1/3*l**3 - 2*l. Factor i(m).
-(m - 2)*(m - 1)
Let f(l) = -11*l**3 - 413*l**2 - 545*l - 143. Let y(q) = 35*q**3 + 1240*q**2 + 1636*q + 431. Let o(t) = 13*f(t) + 4*y(t). Factor o(a).
-(a + 1)*(a + 135)*(3*a + 1)
Let w be 2*1 + 16 + -15. Let 13*c**3 + 10 + 20*c**2 - 10*c**w - 25*c - 8*c**3 = 0. Calculate c.
1, 2
Let u(h) be the second derivative of h**4/18 + 2*h**3 - 19*h**2/3 - 57*h. Factor u(q).
2*(q - 1)*(q + 19)/3
Let m(y) be the third derivative of -1/1080*y**6 + 0*y + 1/270*y**5 + 8*y**2 + 1/216*y**4 + 0 - 1/27*y**3. Find q, given that m(q) = 0.
-1, 1, 2
Factor -1 - 144193*m**2 - 129*m**3 + 1 - 3*m**4 + 144463*m**2.
-3*m**2*(m - 2)*(m + 45)
Let o(g) be the third derivative of -g**5/90 - 77*g**4/18 - 5929*g**3/9 + 394*g**2. Factor o(j).
-2*(j + 77)**2/3
Let l be (-1)/(-4) + (-14)/16*-2. Factor -4*z**3 + 8*z**2 - l*z**2 - 2*z**3 + 3*z**3.
-3*z**2*(z - 2)
Suppose -331 = -57*z - 103. Factor 2/3*f**z + 0*f**3 + 2/3 + 0*f - 4/3*f**2.
2*(f - 1)**2*(f + 1)**2/3
Let i(p) be the third derivative of -p**7/105 + 7*p**5/30 - p**4/2 + 42*p**2 + 9*p. Solve i(x) = 0.
-3, 0, 1, 2
Let v be (2 + -1)/2 - -51*(-60)/(-504). Suppose -6*r**3 + 4/7*r**2 + 0 + 0*r - v*r**4 = 0. What is r?
-1, 0, 2/23
Factor 13 - 12*m**3 + 57*m - 33*m**2 - 48 + 23.
-3*(m - 1)*(m + 4)*(4*m - 1)
Let z = 182 - 179. Let h(b) be the second derivative of 0*b**z + 0*b**2 + 0 - 1/4*b**4 - 3/20*b**5 + 3*b. Factor h(m).
-3*m**2*(m + 1)
Let 10/9*g**3 - 8/9 + 2/9*g**4 - 10/9*g + 2/3*g**2 = 0. Calculate g.
-4, -1, 1
Suppose -6*b + 7*b = 2*b. Let h(y) be the second derivative of -y + 1/4*y**4 + 3/2*y**2 - y**3 + b. Factor h(r).
3*(r - 1)**2
Determine f so that -13*f - 899 + 2*f**2 + 899 + 45*f = 0.
-16, 0
Let s(h) = 65*h**2 - 8 + 15*h - 4 - 66*h**2. Let p be s(9). Factor -36*l**2 + 2*l**5 - 15*l**3 - 5*l**5 + p*l**2 + 12*l**4.
-3*l**2*(l - 2)*(l - 1)**2
Suppose -8/11*v**2 - 10/11*v**3 + 12/11 + 14/11*v = 0. What is v?
-1, 6/5
Let j be (12 + (-228)/20)/(2/30). Suppose 2/3 + j*w**3 + 14*w**2 + 17/3*w = 0. What is w?
-1, -1/3, -2/9
Factor -1/2*s**2 + 91*s - 8281/2.
-(s - 91)**2/2
Let m = 61 + -61. Let b be 52/18 - (4 - (11 - 9)). Determine o, given that m + 2/3*o**4 - 10/9*o**2 - b*o**3 + 4/9*o = 0.
-1, 0, 1/3, 2
Let p = -85 + 88. Let a be 4/p*((-39)/(-12) - 1). Factor 4/9*h**5 - 10/9*h**4 + 0 + 0*h + 8/9*h**a - 2/9*h**2.
2*h**2*(h - 1)**2*(2*h - 1)/9
Let d(h) be the first derivative of 2*h**5/105 - 13*h**4/42 + 46*h**3/63 - 11*h**2/21 - 58. Determine t so that d(t) = 0.
0, 1, 11
What is p in -10/3*p**2 + 4 - 2/3*p + 4/3*p**3 = 0?
-1, 3/2, 2
Let x = 25 - 16. Suppose -3*f + x + 0 = 0. Factor 5*b**2 - 4*b + 2*b**f - 3*b**2 - 4*b**2.
2*b*(b - 2)*(b + 1)
Suppose -2*k + 8 = -6*k. Let n be 1 - (k + -1 + 0). Determine w so that 3 - 6*w + n + 0*w - 4*w**2 - 9 = 0.
-1, -1/2
Let s(b) = -b**3 - 7*b**2 + b + 13. Let g be s(-8). Factor -249 + 63*i - 12*i - 5*i**2 + 9*i + g.
-5*(i - 6)**2
Factor 3*o + 7*o + 3*o**4 - 11*o**4 + 3*o**4 + 15*o**2.
-5*o*(o - 2)*(o + 1)**2
Suppose 35*g**2 + 4 + 26*g - 49/2*g**3 = 0. What is g?
-2/7, 2
Factor -2/11*n**2 - 128/11 - 32/11*n.
-2*(n + 8)**2/11
Suppose -4/7*c - 18/7*c**2 + 0 = 0. Calculate c.
-2/9, 0
Let f be ((-2)/5)/(4/20). Let n be (-5 - f)*(-3)/27. Determine u, given that 2/3*u**2 - n*u**5 - 8/3 - 11/3*u**3 + 4*u + 2*u**4 = 0.
-1, 1, 2
Let r(x) be the first derivative of x**6/72 - x**5/12 + 5*x**4/24 - 4*x**3 - 1. Let g(a) be the third derivative of r(a). Factor g(u).
5*(u - 1)**2
Let s(f) be the first derivative of -3*f**3 + 3/4*f**4 - 31 + 3/5*f**5 - 3/2*f**2 + 6*f. Factor s(n).
3*(n - 1)**2*(n + 1)*(n + 2)
Let n(c) = -3*c**4 - 39*c**3 - 33*c**2 + 48*c + 36. Let k(t) = -t**4 - 10*t**3 - 8*t**2 + 12*t + 9. Let m(j) = -9*k(j) + 2*n(j). Factor m(i).
3*(i - 1)*(i + 1)**2*(i + 3)
Let d(j) be the first derivative of -3/2*j**2 + 4*j**3 - 2*j - 33 - 7/4*j**4. What is p in d(p) = 0?
-2/7, 1
Let i = 3968 - 3968. Find z such that 0 + 1/2*z**5 + 0*z**4 + 1/2*z - z**3 + i*z**2 = 0.
-1, 0, 1
Let o(r) be the third derivative of 4/63*r**7 - 1/45*r**6 - 1/5*r**5 + 0 + 13/36*r**4 - 1/56*r**8 + 0*r - 2/9*r**3 + 28*r**2. Solve o(u) = 0 for u.
-1, 2/9, 1
Let u(m) be the first derivative of m**4/10 - 12*m**3/5 - 27*m**2 - 432*m/5 - 60. Determine q so that u(q) = 0.
-3, 24
Suppose -2*u = 3*b + 9, 0*b - b - 5*u = 3. Let n = 5 + b. Factor 2*j + 6*j**n + 7*j - 11*j - 4 + 