- 9*w - 17. Let d be r(12). Suppose 20*z = d*z + 2. Determine s, given that 20*s + 8 - 2*s**z - 3*s**2 - 8 = 0.
0, 4
Suppose -2*v = 3*a + 191, 126 = -2*a + 3*v - 23. Let p = 73 + a. What is k in 3*k**5 + 10*k**4 - 16*k**3 + p*k**5 - 11*k**5 + 8*k**2 = 0?
0, 1, 2
Let v(f) = -8*f - 7. Let l be v(-2). Suppose -s - 9 = -13. Factor -278*d**5 + 16*d**3 - 16*d**2 + 286*d**5 + 19*d**s + l*d**4.
4*d**2*(d + 2)**2*(2*d - 1)
Let u(o) = -o**3 + 8*o**2 - 14*o + 10. Let y be u(5). Factor i**4 + 7*i**3 - 2*i - y*i + 11*i - 10*i + 8*i**2.
i*(i - 1)*(i + 4)**2
Let p = -4/645811 - -2583264/3229055. Suppose 9/5*i**2 - p*i - 12/5 - 1/5*i**4 + 0*i**3 = 0. What is i?
-3, -1, 2
Let n(z) be the second derivative of z**6/270 + z**5/60 - 4*z**4/27 - 8*z**3/9 + 573*z. Factor n(v).
v*(v - 4)*(v + 3)*(v + 4)/9
Let b be (1/5 + (-40)/(-50))*-606. Let o = b - -608. Factor 0*m**3 - 1/5*m**o + 1/10 + 0*m + 1/10*m**4.
(m - 1)**2*(m + 1)**2/10
Suppose 2248 = 15*p - 977. Suppose -3*t + 3*z = 0, p*t - 219*t + 12 = 2*z. Find k, given that 1/3*k + 2 - 1/3*k**t = 0.
-2, 3
Let r(f) be the first derivative of -2*f**4 + 532*f**3/3 - 392*f**2 + 260*f + 714. Factor r(x).
-4*(x - 65)*(x - 1)*(2*x - 1)
Let v = 1992717 - 1992716. Let y = -9 + 13. Factor -7/4*p + 1/2*p**2 - 1/4*p**5 + 1/2*p**y + 2*p**3 - v.
-(p - 4)*(p - 1)*(p + 1)**3/4
Let r(k) be the second derivative of -63/20*k**5 - 2 + 121/2*k**3 + 0*k**2 - 114*k - 99/4*k**4 - 1/10*k**6. Factor r(a).
-3*a*(a - 1)*(a + 11)**2
Let q = -26 - -30. Factor 0*v**q + 0*v - 12 + 6*v**3 + 0*v**4 - v + 9*v**2 + v**4 - 3*v.
(v - 1)*(v + 2)**2*(v + 3)
Let a(m) be the first derivative of -4*m**5/35 - 62*m**4/7 - 76*m**3/7 + 496*m**2/7 + 976*m/7 + 2652. Determine r so that a(r) = 0.
-61, -2, -1, 2
Let -2/7*i**2 + 4588/7*i - 2631218/7 = 0. What is i?
1147
Suppose -5*q - 5 = 0, -8*i + 11*i - 5 = 2*q. Suppose 2*p + 3*z + 5 = 0, 18 + i = 2*p - 5*z. Factor 0*w**p + 9/4*w**3 - 3/4*w**4 + 0 - 3*w.
-3*w*(w - 2)**2*(w + 1)/4
What is j in 1675*j**3 + 2*j + 5*j**2 + 40 + 2*j**5 - 1679*j**3 + 40*j**4 - 85*j**2 = 0?
-20, -1, 1
Let c be (-168)/168*(18/2 - 12). Determine v, given that 0*v**2 + 0 + 2/13*v**4 + 2/13*v**c + 0*v = 0.
-1, 0
Let t = 66156 + -463072/7. Factor -2/7*r**2 + 22/7 - t*r.
-2*(r - 1)*(r + 11)/7
Let q(l) = l**2 - l - 1. Let u(r) = -2*r**2 - 8*r + 23. Let f(g) = -g**2 - 32*g + 1. Let k be f(-32). Let i(w) = k*q(w) + u(w). Factor i(c).
-(c - 2)*(c + 11)
Let z(p) be the third derivative of 9*p**6/40 + 5*p**5/4 - 12*p**4 + 10*p**3 - 38*p**2 + 23. Factor z(b).
3*(b - 2)*(b + 5)*(9*b - 2)
Let s(v) be the third derivative of 0 - 1/600*v**6 + 0*v**4 - v**2 + 43*v + 1/75*v**5 + 0*v**3. Factor s(g).
-g**2*(g - 4)/5
Let j be (-4)/(-16)*-3 - (-45)/12. Factor 51*m**3 - 51*m**j - 2*m**4.
-2*m**4
Let 5/4 + 53/8*d**3 - 49/8*d - 1/2*d**5 + 25/8*d**2 - 35/8*d**4 = 0. What is d?
-10, -1, 1/4, 1
Suppose 3*f = -5*g + 2631, 3*f + 584 - 3215 = -4*g. Let d = f - 6133/7. Factor -3/7*r**2 + 6/7*r + 3/7*r**4 + 0 - d*r**3.
3*r*(r - 2)*(r - 1)*(r + 1)/7
Let j = -13338 - -13338. Let p(f) be the second derivative of -1/8*f**4 - 3/4*f**2 + 1/2*f**3 - f + j. Factor p(u).
-3*(u - 1)**2/2
Determine k so that -1/10*k**4 + 1/2*k**3 - 1/2*k - 3/10*k**2 + 2/5 = 0.
-1, 1, 4
Let r = 1063 + -726. Let q = r - 3705/11. Factor 6/11*l**2 - 4/11*l + 0 - q*l**3.
-2*l*(l - 2)*(l - 1)/11
Find v such that -18/5*v**2 - 32/5*v + 2/5*v**3 + 24 = 0.
-3, 2, 10
Let g(w) = 3*w**3 - 17*w**2 - 44*w - 2. Let l(b) = b**3 + b**2 - b - 1. Let o(f) = -4*g(f) + 8*l(f). Determine k, given that o(k) = 0.
-2, 0, 21
Solve 146*o**2 - 293*o + 440/3 + 1/3*o**3 = 0 for o.
-440, 1
Let f = 29322/13 + -448189/195. Let m = f - -216/5. Factor -m*z**2 - 1/6*z + 0 - 1/6*z**3.
-z*(z + 1)**2/6
Let z(s) be the first derivative of s**6/6 - 113*s**5/5 - 229*s**4/4 - 115*s**3/3 + 1168. Find y such that z(y) = 0.
-1, 0, 115
Let i = -24 - -15. Let a = 14 + i. Factor -2*x**3 - 2*x**3 - 3*x**a + 2*x + 5*x**5.
2*x*(x - 1)**2*(x + 1)**2
Let m(d) be the second derivative of d**5/60 - 68*d**4/9 + 30*d**3 - 3236*d. Factor m(z).
z*(z - 270)*(z - 2)/3
Suppose -3*m + 18 = -o, 5 = -476*o + 480*o - m. Let x(v) be the first derivative of -32 + 2/21*v**o + 0*v**2 - 2/7*v. Suppose x(f) = 0. Calculate f.
-1, 1
Let c be ((-19)/(-4 - (-5 - 0)))/(-1). Suppose 5*q - s = c, q + 5*s = -0*q - 17. Find a, given that 150*a**q - 43*a - 5*a**2 - 100*a**3 - 15*a**4 + 13*a = 0.
-2/3, 0, 1, 3
Let q(g) be the first derivative of g**4/4 - g**3 - 12*g**2 + 18*g - 103. Let r(h) be the first derivative of q(h). What is u in r(u) = 0?
-2, 4
Let t = 11807 - 106255/9. Let d(z) be the first derivative of -8/9*z + 9 + t*z**2 - 10/27*z**3 + 1/18*z**4. Suppose d(c) = 0. Calculate c.
1, 2
Let d(g) = -20*g**5 + 208*g**4 - 692*g**3 + 480*g**2. Let q(b) = 12*b**5 - 125*b**4 + 415*b**3 - 288*b**2. Let s(i) = -7*d(i) - 12*q(i). Solve s(u) = 0.
0, 1, 4, 6
Let o(g) = 3*g**3 + 4. Let h be o(-3). Let c = -73 - h. Suppose 3*j**c + 80*j**3 - 86*j**3 + 6*j + 0*j - 3 = 0. What is j?
-1, 1
Let h(l) = -10*l**3 - 123*l**2 - 343*l + 483. Let g = 56 + -60. Let r(q) = 5*q**3 + 61*q**2 + 171*q - 241. Let z(d) = g*h(d) - 7*r(d). Factor z(o).
5*(o - 1)*(o + 7)**2
Let p be (29 - 35)*20/(-48). Factor 35/2*f + 15 + p*f**2.
5*(f + 1)*(f + 6)/2
Let m be (-70)/(-30) + (-2 - 10/(-6)). Let n be m/4 + 6/4. Factor 18*r**n - 13*r**2 + 15*r + 0*r.
5*r*(r + 3)
Let m(u) be the third derivative of -7/60*u**6 + 0*u - 1/10*u**5 + 0*u**4 - 2/105*u**7 - 114*u**2 + 0 + 0*u**3. Factor m(s).
-2*s**2*(s + 3)*(2*s + 1)
Let l(c) be the first derivative of 24*c + 44 + 34 - 45*c**2 - c**4 + 59*c**2. Factor l(f).
-4*(f - 3)*(f + 1)*(f + 2)
Let j(y) = 2*y**2 + 11*y + 14. Suppose 20*a + 28 = -72. Let p(i) = 69 - 31*i + 0 + 9*i**2 + 85*i. Let v(r) = a*p(r) + 24*j(r). Factor v(c).
3*(c - 3)*(c + 1)
Let c = -156/17 + 675/68. Let l(m) be the second derivative of -13/2*m**3 - 11/4*m**4 + 9/2*m**2 + 0 - 17*m + c*m**5. Find t such that l(t) = 0.
-1, 1/5, 3
Let n(x) be the first derivative of 7/180*x**5 - 2/9*x**3 + 0*x + 8*x**2 + 5 + 1/24*x**4. Let i(o) be the second derivative of n(o). Solve i(d) = 0 for d.
-1, 4/7
Let w = -98 - -98. Suppose -3*b = -w - 12. Find v, given that -v**5 - 5*v + 4*v**3 + 5*v - v**4 - 4*v**2 + 2*v**b = 0.
-2, 0, 1, 2
Let s be -3 + 456/(-258) - -5. Let z = 82/387 + s. Factor 2/9*v**3 + 0*v**2 - 2/3*v + z.
2*(v - 1)**2*(v + 2)/9
Let w = 3119/49 + -5993/98. Factor 1/5*g + 0 + w*g**2.
g*(25*g + 2)/10
Let w = 291799/5 - 58359. Solve 0 + 0*j**2 + 0*j + w*j**5 + 0*j**3 + 4/5*j**4 = 0.
-1, 0
Suppose -31*c + 440 = 189*c. Factor 1/5*b**c + 14/5*b + 13/5.
(b + 1)*(b + 13)/5
Let v(y) be the third derivative of -y**7/1050 + 211*y**6/600 - 337*y**5/10 - 5555*y**4/6 + 12100*y**3/3 - 13*y**2 - 2*y - 68. Find t, given that v(t) = 0.
-10, 1, 110
Suppose 28 = -146*z + 153*z. Factor 2*i**4 + 0*i**z - 3*i**4 - 11*i**3 + 9*i**3 + i**5.
i**3*(i - 2)*(i + 1)
Let n be -50 - -47 - (2 - 7 - 0). Factor -8 + 8*t + 9*t**2 - 10*t**2 - n*t**3 + 3*t**2.
-2*(t - 2)*(t - 1)*(t + 2)
Let y(l) be the first derivative of l**6/33 - 126*l**5/55 + 540*l**4/11 - 5392*l**3/33 - 240*l**2/11 + 7200*l/11 - 1556. Solve y(f) = 0.
-1, 2, 30
Let m(f) be the first derivative of -2/5*f**5 - 5/2*f**4 + 0*f + 28 + 0*f**2 - 4*f**3. Factor m(v).
-2*v**2*(v + 2)*(v + 3)
Solve -14*x**2 - 4*x**5 + 21*x**4 - 8*x**2 - 12*x**3 - x**4 - 16*x**2 + 2*x**2 = 0.
-1, 0, 3
Let q(m) be the third derivative of m**5/180 - 1189*m**4/36 + 1413721*m**3/18 - 194*m**2 - 2*m - 7. Factor q(y).
(y - 1189)**2/3
Let t be (-3)/(-3) - 1 - -2. Let a = 8345 + -8341. Determine w, given that 8/7*w**3 + 2/7*w**a + 0 + 4/7*w + 10/7*w**t = 0.
-2, -1, 0
Let b(y) = -y**3 + 34*y**2 - 32*y - 31. Let v be b(33). Factor 55 - 46 + 0*o**v - o**2 - 8*o.
-(o - 1)*(o + 9)
Let i = -1209 + 13309/11. Let w = 6355/35013 + 1/3183. Factor -i*h + w*h**2 + 12/11.
2*(h - 3)*(h - 2)/11
Let z(b) = 13*b**2 - 1. Let a be z(1). Factor 4 - w**2 + 29*w**2 + 5352*w**5 - 22*w**3 + 8*w**4 - a*w - 5*w - 5353*w**5.
-(w - 4)*(w - 1)**4
Let u = 16093/24198 - -13/8066. Determine r, given that 2/9 + 8/9*r - u*r**4 - 8/9*r**3 + 4/9*r**2 = 0.
-1, -1/3, 1
Factor 400/3 + 202/3*l + 1/3*l**2.
(l + 2)*(l + 200)/3
Let n = -3/1835 - -95/13212. Let z(p) be the third derivative of 3*p**2 - n*p**6 + 1/30*p**5 + 0*p**3 + 0*p**4 + 0*p + 0. Fa