 2*r**x + 14/3*r**4.
2*r*(r + 1)**3*(3*r - 2)/3
Let i(v) = v + 18. Let f be i(-15). Determine h, given that -4*h**3 + 7 - f*h**4 - 3*h**2 - 2*h**3 - 7 = 0.
-1, 0
Factor -1/3*c**2 + 0 + 11/3*c.
-c*(c - 11)/3
Let z be (-6)/(42/35) - -5. Let o(n) be the second derivative of -1/40*n**5 + 0 + z*n**2 - 3/4*n**3 - 2*n + 1/4*n**4. Determine s so that o(s) = 0.
0, 3
Let y(x) be the third derivative of -x**6/24 - 17*x**5/12 - 105*x**4/8 + 135*x**3/2 - 5*x**2 - x. Factor y(w).
-5*(w - 1)*(w + 9)**2
Suppose 9/2*j + 15/4*j**2 + 0 - 3/4*j**3 = 0. Calculate j.
-1, 0, 6
Let x be (-7)/30*45/(-280). Let m(y) be the second derivative of -1/16*y**4 + 0*y**2 + 9*y + 0 + 1/40*y**6 + x*y**5 - 1/8*y**3. Determine q so that m(q) = 0.
-1, 0, 1
Let r(v) be the second derivative of v**5/30 - v**4/4 + 2*v**3/3 + v**2/2 - v. Let n(f) be the first derivative of r(f). Factor n(o).
2*(o - 2)*(o - 1)
Factor 32/9 - 38/9*c**2 + 2/3*c**3 - 28/3*c.
2*(c - 8)*(c + 2)*(3*c - 1)/9
Suppose -177*l + 945 = 12*l. Find h, given that 9/5*h**4 + 4/5*h**l + 1/5*h + 6/5 - 3*h**2 - h**3 = 0.
-2, -1, 3/4, 1
Suppose -5*m + n + 3 = 5*n, 3 = -3*m - 4*n. Factor i**3 - 3 + 0*i**m + 7*i + 0 - 5*i**2.
(i - 3)*(i - 1)**2
Let q(z) be the third derivative of z**8/504 - 2*z**7/63 + 17*z**6/90 - 2*z**5/5 - 3*z**4/4 + 6*z**3 + 2*z**2 + 4. Factor q(k).
2*(k - 3)**3*(k - 2)*(k + 1)/3
Factor -12/7*u - 2/7*u**2 + 110/7.
-2*(u - 5)*(u + 11)/7
Suppose -109 - 251 = -4*c. Let q be ((-4)/c)/(2238/320 - 7). Solve -16/9*j**4 + 32/9*j - q*j**2 + 0 + 2/9*j**5 + 16/3*j**3 = 0 for j.
0, 2
Let s be -1 + 3752/20 - 2*2. Let l = s + -182. Factor -3/5*z**2 - l*z + 6/5.
-3*(z - 1)*(z + 2)/5
Let j = -72749/150 - -485. Let b = j + 13/50. Factor -b*l**2 - 2/15*l**3 + 0 + 2/5*l.
-2*l*(l - 1)*(l + 3)/15
Let y(f) = -f**3 + 8*f**2 + f + 2. Let p be y(8). Let m = 14 - p. Factor m*k**3 - 13*k + 4*k - 6*k**2 - k**3.
3*k*(k - 3)*(k + 1)
Let k(t) be the third derivative of -t**5/600 + 13*t**4/240 + 7*t**3/30 - 6*t**2. Factor k(v).
-(v - 14)*(v + 1)/10
Let y = -527/24 - -65/3. Let g = -1/24 - y. Factor g*s**2 + 0 + 1/4*s**3 - 1/4*s**4 - 1/4*s.
-s*(s - 1)**2*(s + 1)/4
Factor 18/11 + 12/11*t - 6/11*t**2.
-6*(t - 3)*(t + 1)/11
Let g(x) be the first derivative of 19*x**3 - 69*x**2/2 + 12*x - 375. What is l in g(l) = 0?
4/19, 1
Suppose -2*j + j = 2, 5*g = -5*j + 315. Suppose -g*h - 24 = -77*h. Factor 14/5*o**3 - 8/5 + 38/5*o**h + 16/5*o.
2*(o + 1)*(o + 2)*(7*o - 2)/5
Let v(i) = -100*i**3 - 520*i**2 + 444*i + 160. Let c(a) = -66*a**3 - 347*a**2 + 296*a + 107. Let m(u) = 8*c(u) - 5*v(u). Solve m(d) = 0.
-7, -2/7, 1
Let t(r) be the second derivative of 0 - 1/2*r**3 + 0*r**2 - 1/8*r**4 + 14*r. Suppose t(j) = 0. What is j?
-2, 0
Let t(c) = c**3 - 3*c**2 - 2*c - 8. Let i be t(4). Let p(u) be the first derivative of i*u - u**3 + 0*u**2 + 4 + 3/4*u**4. Factor p(m).
3*m**2*(m - 1)
Suppose 10*i - 4/3*i**2 - 14/3 = 0. Calculate i.
1/2, 7
Let a = 4043 - 4041. Find x, given that 0*x + 5/2*x**a - 5/2 = 0.
-1, 1
Determine w so that 988/5*w**2 - 896/5*w + 48/5 - 28*w**3 = 0.
2/35, 1, 6
Let c(y) be the first derivative of y**5 + 10*y**4 + 30*y**3 + 40*y**2 + 25*y - 55. Determine m so that c(m) = 0.
-5, -1
Let x(b) = b**3 - 13*b**2 + 22*b + 2. Let y be x(11). Let g(v) be the first derivative of 2*v**3 + v**y + 9/8*v**4 - 6 + 0*v. Find p, given that g(p) = 0.
-2/3, 0
Suppose 168 = -3*j - j. Let h be (-1)/6*-11 - (-14)/j. Factor -3/2*u + h*u**2 + 0.
3*u*(u - 1)/2
Let u(n) be the second derivative of -7/6*n**3 - 1/60*n**5 + 2/9*n**4 + 3*n**2 - 2*n + 9. What is x in u(x) = 0?
2, 3
Solve 1/4*j**3 + 9/4*j + 1 + 3/2*j**2 = 0 for j.
-4, -1
Let 0 + 0*c**2 + 0*c + 1/7*c**4 - 1/7*c**3 = 0. What is c?
0, 1
Factor -1/2*t**4 + 4 + 0*t**3 + 9*t + 11/2*t**2.
-(t - 4)*(t + 1)**2*(t + 2)/2
Suppose -65*q**2 - 4225/2*q - 1/2*q**3 + 0 = 0. What is q?
-65, 0
Let s(p) = -p**3 - p**2 + 5*p + 5. Let g be s(-3). Suppose -x**3 - 11*x**2 + g*x**2 - 2*x**3 + 2*x**3 = 0. Calculate x.
-3, 0
Let l(j) = j**2 + 18*j + 84. Let h be l(-9). Let m(i) = -i**2 - i + 4. Let v be m(0). Factor -3/4*d + 1/2*d**h + 1/4 + 1/4*d**5 - 3/4*d**v + 1/2*d**2.
(d - 1)**4*(d + 1)/4
Let i be 3 - (440/25 - 3). Let d = -396/35 - i. Solve -d*a**4 - 2/7*a**2 + 0 - 4/7*a**3 + 0*a = 0.
-1, 0
Let p = 22 + -20. Factor -2*m**3 + 5*m + m**3 - 15*m**2 + 24*m**p - 6*m**2 - m**4 + 2.
-(m - 2)*(m + 1)**3
Suppose 5*g = 10 + 10, 2*g - 80 = 2*a. Let v be 4/a*(-3)/1. Determine j, given that v - 1/3*j**2 + 1/3*j**3 - 1/3*j = 0.
-1, 1
Suppose -3*o - 22 = 2*b + 24, -4*b - 60 = -2*o. Let n = b - -19. Factor n*m + m**3 + 2*m**2 + 2*m - 6*m**2 - 5*m**3 + 4.
-4*(m - 1)*(m + 1)**2
Let l(i) = i**3 + 20*i**2 + 37*i + 22. Let j(d) = -d**2 + 29*d + 44. Let t be j(31). Let m be l(t). Factor 3*r**2 - 3*r**m + 3/2*r**5 - 3/2*r + 0 + 0*r**3.
3*r*(r - 1)**3*(r + 1)/2
Let t(y) be the third derivative of y**6/180 + 19*y**5/90 - 5*y**4/9 - 11*y**2 - 5*y. Factor t(i).
2*i*(i - 1)*(i + 20)/3
Let l(t) be the third derivative of t**8/224 + 3*t**7/70 - 3*t**6/80 - 2*t**5/5 + 3*t**4/4 - 4*t**2 + 21*t. Determine w so that l(w) = 0.
-6, -2, 0, 1
Suppose -6*t + 59 = 35. Let x(k) be the second derivative of 0 - 2/21*k**7 + 2/3*k**t + 2*k**3 - 2/5*k**5 - 4*k + 2*k**2 - 2/5*k**6. Factor x(f).
-4*(f - 1)*(f + 1)**4
Suppose 2*c = 5*t + 9, -4*c - 1 + 4 = 5*t. Solve -11*b**3 + 40*b + 5*b**4 + 9*b**3 + 32*b**3 + 60*b**c = 0 for b.
-2, 0
Let a(q) be the first derivative of -20*q**3/21 - 6*q**2 + 353. Factor a(u).
-4*u*(5*u + 21)/7
Let p be ((-78)/14)/(160/(-280)). Factor p*u**2 + 9/4*u**3 + 3 + 12*u.
3*(u + 2)**2*(3*u + 1)/4
Let r(t) be the second derivative of -t**5/15 + t**4/2 - 4*t**3/3 - 7*t**2/2 - 5*t. Let n(z) be the first derivative of r(z). Let n(a) = 0. What is a?
1, 2
Find c such that 2/15*c**5 + 28/15*c**3 - 4/15*c**2 + 6/5*c**4 - 14/15 - 2*c = 0.
-7, -1, 1
Suppose -3*t = 28 + 62. Let i be 4/t*(-81)/(-36)*-4. Solve -i*k - 2/5*k**2 - 4/5 = 0.
-2, -1
Suppose 0 = 15*s - 69 - 51. Suppose 0 = s*k - 17*k + 18. Solve 0 + 2/7*i**k + 4/7*i = 0.
-2, 0
Let g(l) be the second derivative of l**7/168 + 23*l**6/120 + 59*l**5/40 - 4*l**4 - 12*l**3 - 115*l + 1. Solve g(o) = 0.
-12, -1, 0, 2
Factor 635*b + 5*b**3 + 654*b + 260 - 1009*b + 85*b**2.
5*(b + 2)**2*(b + 13)
Solve 1/3*y**2 + 22/3*y + 19 = 0 for y.
-19, -3
Suppose -3*c + 73 = 5*b - 57, 0 = 5*b - 10. Let k be (-9)/4*c/(-15). Factor 3*d**2 + 0*d**2 + k*d - d**2 - 5*d**2.
-3*d*(d - 2)
Let -5*a**2 + a - 7/4*a**4 + 23/4*a**3 + 0 = 0. What is a?
0, 2/7, 1, 2
Solve 30*r**3 - 28*r**5 + 24*r**4 + 16*r**2 + 10*r**5 + 6*r**3 + 22*r**5 = 0 for r.
-4, -1, 0
Let f be 4*-1 + (-1)/42*-186. Factor -9/7*u**3 - 3/7*u**2 + 9/7*u + 0 + f*u**4.
3*u*(u - 3)*(u - 1)*(u + 1)/7
Let j be 0 + -5 - (-3 + 0). Let b be (j/15)/((-128)/160). What is k in -13/6*k**2 - 2/3 - 2*k - b*k**4 - k**3 = 0?
-2, -1
Factor 52/3*r + 40/3 + 8/3*r**2 - 4/3*r**3.
-4*(r - 5)*(r + 1)*(r + 2)/3
Factor 5*x**2 + 3/2*x**3 + 3/2 - 1/4*x**5 - 1/2*x**4 + 19/4*x.
-(x - 3)*(x + 1)**3*(x + 2)/4
Let c = 3958 - 27694/7. Let -16/7*k**2 + 2/7*k**3 - c + 26/7*k = 0. What is k?
1, 6
Let y be (-15)/((-3)/2*-1). Let g be y/(-4)*(-4)/(-5). Factor 5*j**2 - 7*j**g + 5*j + 2 - 2*j**3 - 3*j.
-2*(j - 1)*(j + 1)**2
Solve 16*f**4 - 1932*f**2 + 940*f**3 + 648 + 1982*f**2 + 4728*f**2 + 34*f**4 + 3384*f = 0 for f.
-9, -2/5
Let x be -3*(-1)/((-9)/(-6)). Suppose 0 = -f + 4*g - 2*g + 1, -4*g = -4*f + 20. What is j in -6*j**3 - 9 + 3*j - 6*j**4 - f*j**x + 3*j**5 + 3 + 21*j**2 = 0?
-1, 1, 2
Let u(l) be the third derivative of -l**7/1050 + l**6/600 + l**5/60 + l**4/40 - 125*l**2. Factor u(r).
-r*(r - 3)*(r + 1)**2/5
Suppose t + 24 = 5*t + i, 2*i = -3*t + 23. Let v be -4 + 5/(5/4). What is x in -2*x**4 + t*x**4 + v - 6*x**2 + 0*x**4 + 3 = 0?
-1, 1
Factor -1/3*j**3 + 4/3*j**2 + 0 - 4/3*j.
-j*(j - 2)**2/3
Suppose 0 = -4*x + 8 + 8. Let y(j) = j**3 + 9*j**2 - 12*j - 15. Let k be y(-10). Factor 6*l**3 + k*l**4 + 0*l**4 - 8*l**x + 4*l - 10*l + 3*l**2.
-3*l*(l - 2)*(l - 1)*(l + 1)
Let s(c) be the third derivative of -c**5/60 + c**3/6 + 59*c**2. Let l(u) = u**3 - 14*u**2 - u + 14. Let x(h) = l(h) - 6*s(h). Factor x(p).
(p - 8)*(p - 1)*(p + 1)
Suppose 0 = j + 5*p, -2*j - 5*p = -0*p. Let q(x) be the third derivative of j*x + 0*x**3 + 5*x**2 + 0*x**4 - 1/180*x**6 - 1/45*x**5 + 0. Factor q(m).
-2*m**2*(m + 2)/3
