q**2 + 5*q + 6. Let r(t) = t + 1. Let u(p) = g(p) - 6*r(p). Factor u(n).
-n*(n + 1)
Find h, given that -32/5*h - 2/5*h**2 - 126/5 = 0.
-9, -7
Factor -8 - 24 + 8*d**2 - 172*d + 116.
4*(d - 21)*(2*d - 1)
Let t be 3/(-18) - 646/12. Let j be (-12)/t - (-2)/(-9). Factor -a**2 + 1 + 0 - 5*a + a**3 + j*a**2 + 4*a.
(a - 1)**2*(a + 1)
Solve -53/3*k + 28/3*k**2 + 26/3 - 1/3*k**3 = 0.
1, 26
Let n(d) = -2*d**4 - 129*d**3 - 200*d**2 - 51*d + 17. Let s(y) = -4*y**4 - 129*y**3 - 199*y**2 - 51*y + 19. Let o(p) = 4*n(p) - 5*s(p). Factor o(a).
3*(a + 1)**2*(a + 9)*(4*a - 1)
Factor -4/5*t**4 - 23/10*t - 1/10*t**5 - 17/5*t**2 - 12/5*t**3 - 3/5.
-(t + 1)**3*(t + 2)*(t + 3)/10
Let g be 1/(-2) + (-143)/(-26). Suppose -36*y**2 - 4*y**4 + 20*y**3 + 2 - 5 - g + 28*y = 0. What is y?
1, 2
Let u = -4619 - -23097/5. What is t in -u*t**4 + 0*t - 8/5*t**3 + 0 - 8/5*t**2 = 0?
-2, 0
Factor -136/21*z**3 - 2/3*z**4 + 0*z + 40/21*z**2 + 0.
-2*z**2*(z + 10)*(7*z - 2)/21
Let w = 2/6429 + 424276/122151. Let a = w + -1084/323. Factor a*j**3 + 0*j + 0 + 6/17*j**2.
2*j**2*(j + 3)/17
Let f(u) = -2*u**3 - 2*u**2 + 2*u - 1. Let k(v) = -9*v**5 - 12*v**4 + 18*v**3 + 24*v**2 - 9*v + 6. Let b(t) = -6*f(t) - k(t). What is y in b(y) = 0?
-1, -1/3, 0, 1
Let s(r) be the third derivative of r**7/1050 - r**6/300 - r**5/100 - 58*r**2 - 1. Factor s(l).
l**2*(l - 3)*(l + 1)/5
Suppose -g + 3*g - 5*k - 26 = 0, -g - 3*k = 9. Suppose -22*x - 2*x**g - 20*x + 60*x - 16*x = 0. What is x?
-1, 0, 1
Let w(g) be the second derivative of 2*g**6/15 - g**5/5 - g**4/3 + 2*g**3/3 + 73*g. Factor w(u).
4*u*(u - 1)**2*(u + 1)
Let m(q) be the first derivative of 3*q**5/5 + 27*q**4/4 - 36*q**3 + 6*q**2 + 144*q + 483. Solve m(n) = 0 for n.
-12, -1, 2
Let m = -45 + 47. Determine i, given that -8*i**2 - i**2 + 12*i + 5*i**2 - 10*i - m*i**3 + 4 = 0.
-2, -1, 1
Let k(i) be the second derivative of 3/4*i**4 - 45/2*i**3 - 1/100*i**5 + 0 - 15*i + 675/2*i**2. Factor k(y).
-(y - 15)**3/5
What is q in 7*q**2 + 18*q**2 - 102*q + 3*q**2 + 72 + 3*q**3 - 9*q**2 + 8*q**2 = 0?
-12, 1, 2
Let t(h) = 10*h**3 + 43*h**2 + 103*h - 3. Let m(y) = -32*y**3 - 130*y**2 - 310*y + 10. Let x(o) = 3*m(o) + 10*t(o). Solve x(f) = 0.
-5, 0
Suppose 10*z - 6*z = -16. Let d(g) = 8*g**2 + 32*g - 28. Let t(j) = -j**2 + j - 1. Let w(s) = z*t(s) + d(s). Solve w(k) = 0 for k.
-3, 2/3
Let o(b) = -11*b + 23. Let a be o(5). Let i be -7*(a/18)/((-3)/(-9)). Find p, given that 268/3*p**2 - i*p + 16/3 + 148/3*p**4 - 292/3*p**3 - 28/3*p**5 = 0.
2/7, 1, 2
Let w(y) be the third derivative of 0*y**4 + 2/15*y**5 - 1/6*y**6 - 23*y**2 - 1/84*y**8 + 0*y + 0 + 0*y**3 + 8/105*y**7. Find v such that w(v) = 0.
0, 1, 2
Let i = 3681 + -3678. Factor -8/5*v**i + 4/5 + 2/5*v**5 + 0*v**4 + 6/5*v - 4/5*v**2.
2*(v - 2)*(v - 1)*(v + 1)**3/5
Let w(i) = -i**2 - 2*i + 4. Let a be w(-3). Let 5*o**2 - 2*o**3 + o - a + o**3 - 4*o**2 = 0. What is o?
-1, 1
Let n(z) = 7*z**2 + 699*z + 30267. Let t(g) = -g**2 - g + 3. Let r(d) = -n(d) - 3*t(d). Factor r(f).
-4*(f + 87)**2
Let s(c) be the first derivative of 4489*c**3/18 + 67*c**2/2 + 3*c/2 - 517. Solve s(k) = 0.
-3/67
Let s be (-42)/56 + (0 - (3 - 2) - -3). Factor s*k + 15/2 - 5/4*k**2.
-5*(k - 3)*(k + 2)/4
Let j(x) be the first derivative of -49 + 0*x**3 + 0*x**2 - x**4 - 1/10*x**5 + 0*x. Solve j(z) = 0.
-8, 0
Suppose -23*a = -28*a. Let k(w) be the third derivative of -1/50*w**5 + 0*w + 1/150*w**6 + 0 - w**2 - 1/30*w**4 + a*w**3. Factor k(t).
2*t*(t - 2)*(2*t + 1)/5
Let d(c) be the third derivative of c**8/1176 - 3*c**6/140 - 12*c**2 - c. Let d(j) = 0. Calculate j.
-3, 0, 3
Let q be -2 - 2376/(-30)*(-4)/(-156). Let v(b) be the first derivative of -q*b**5 + 1/26*b**4 + 0*b + 1 - 1/13*b**2 + 2/39*b**3. Determine i so that v(i) = 0.
-1, 0, 1
Suppose 49*j + 51 - 51 = 0. Let p(s) be the first derivative of -5/3*s**6 + j*s**2 + 5/4*s**4 - 11 - s**5 + 0*s**3 + 0*s. Solve p(l) = 0 for l.
-1, 0, 1/2
Let x be (-72)/75*(115/30 - 3)*-4. Factor 4/5*t**2 - x + 0*t.
4*(t - 2)*(t + 2)/5
Let p(z) be the first derivative of -z**5/120 - z**4/16 + z**3/3 + 12*z**2 + 2. Let i(n) be the second derivative of p(n). What is u in i(u) = 0?
-4, 1
Suppose -w + 11 = -3*v - 0*v, -12 = 4*v. Suppose 4 = w*n - 3*g, 2*n + g - 5 + 1 = 0. Let -1/2*a**n + 3/2 + a = 0. Calculate a.
-1, 3
Let k(w) be the second derivative of 0 + 9*w**2 + 1/24*w**4 + 24*w + w**3. Factor k(b).
(b + 6)**2/2
Let i = -202 - 4. Let l = -204 - i. Factor 0*w + 0*w**l + 1/3*w**3 + 0.
w**3/3
Let o = 281 - 279. Find y such that -3/5*y + 3/5*y**o - 6/5 = 0.
-1, 2
Suppose 2408*w = 2415*w - 21. Factor 9/4*g**5 + 0 + 0*g + 3/4*g**3 + 0*g**2 + w*g**4.
3*g**3*(g + 1)*(3*g + 1)/4
Let q(c) = -12*c + 9. Let t be q(-8). Let l = t - 71. Factor -3*r**3 + l*r**2 - 36*r**2 + 4*r + r**3.
-2*r*(r - 1)*(r + 2)
Let h(c) be the third derivative of c**8/504 + 4*c**7/315 - c**6/90 - 4*c**5/45 + c**4/36 + 4*c**3/9 - 7*c**2 - 1. Find z, given that h(z) = 0.
-4, -1, 1
Let d(p) = -p**2 + 31*p + 950. Let r be d(-19). Factor 9/7*x**2 + r - 3/7*x**3 + 12/7*x.
-3*x*(x - 4)*(x + 1)/7
Let l be 9 - (14345/84)/19. Let t(h) be the third derivative of 0*h**3 + 9*h**2 + 0*h + 1/70*h**6 - l*h**4 + 0 + 1/84*h**5. Factor t(u).
u*(3*u + 2)*(4*u - 1)/7
Solve 2/3*h**5 + 188356/9 - 2612/9*h**4 - 95914/9*h + 286004/9*h**3 - 41760*h**2 = 0 for h.
-2/3, 1, 217
Let f(k) be the first derivative of k**5/15 - k**4/2 + 4*k**3/3 + 7*k**2 - 6. Let v(y) be the second derivative of f(y). What is h in v(h) = 0?
1, 2
Let o(s) be the third derivative of -7*s**5/270 - s**4/108 + 2*s**3/9 + 2*s**2 - 4*s. What is t in o(t) = 0?
-1, 6/7
Let c(w) be the first derivative of -w**4/4 - 130*w**3/3 - 257*w**2/2 - 128*w - 72. Factor c(v).
-(v + 1)**2*(v + 128)
Factor -10*u**4 - 2*u**2 + 16*u**4 - 4*u**4 - 4*u**4 + 4*u**3.
-2*u**2*(u - 1)**2
Let x(i) = -24 - 41*i**2 + 10*i + 61*i**2 - i**3 - 31*i**2. Let a be x(-12). Let 0*o**4 + a*o + 0 - 3/7*o**3 + 0*o**2 + 3/7*o**5 = 0. What is o?
-1, 0, 1
Let t(y) be the first derivative of 2*y**3/21 - 158*y**2/7 + 12482*y/7 - 115. Suppose t(d) = 0. What is d?
79
Find o such that 162/13*o**2 - 2/13*o**5 + 0 + 216/13*o + 18/13*o**3 - 10/13*o**4 = 0.
-3, 0, 4
Factor 0*a**2 + 0 - 6/7*a**3 - 3*a**4 + 0*a.
-3*a**3*(7*a + 2)/7
Let z(r) = 2*r**2 - 12*r + 7. Let x(q) = -3*q**2 + 23*q - 14. Let l(t) = 4*x(t) + 7*z(t). Let y(j) = -j**2 - j + 1. Let v(m) = l(m) + 3*y(m). Factor v(h).
-(h - 4)*(h - 1)
Let d = 84 - 84. Let q(v) be the first derivative of 0*v**3 + 1/20*v**4 + d*v**2 + 0*v + 8. Find z, given that q(z) = 0.
0
Factor 0 - 6/13*u**3 + 0*u + 4/13*u**2 + 2/13*u**4.
2*u**2*(u - 2)*(u - 1)/13
Let j(h) be the second derivative of 0*h**4 + 0*h**3 - 2/105*h**6 + 0*h**2 - 1/70*h**5 - 6*h - 1/147*h**7 + 0. Factor j(d).
-2*d**3*(d + 1)**2/7
Let r(v) be the third derivative of v**7/105 - v**6/60 - v**5/15 + 314*v**2. Factor r(s).
2*s**2*(s - 2)*(s + 1)
Let u = 40 - 17. Suppose -4*y - 5*p = -u, 5*p = y - 3*y + 19. Find f such that 8*f**3 + 0*f**4 - 4*f**3 + 4*f - 8*f**3 + 2*f**2 - y*f**4 = 0.
-2, -1, 0, 1
Let w(d) be the second derivative of d**4/6 + 10*d**3 + 225*d**2 + d - 5. Factor w(p).
2*(p + 15)**2
Let h = -3 - -14. Suppose 2*j - h = -4*a - 5, 2 = -2*a - 2*j. Find r such that -8/7*r + 6/7*r**2 + 8/7*r**3 - 8/7 + 2/7*r**a = 0.
-2, -1, 1
Factor 147/2*a + 3/4*a**2 - 150.
3*(a - 2)*(a + 100)/4
Let i(j) = 4*j**2 - j + 2. Let a be i(1). Factor 3*k**5 - 4*k**4 + k**4 + a*k + k + 12 + 18*k - 15*k**3 + 3*k**2.
3*(k - 2)**2*(k + 1)**3
Let x(a) be the third derivative of -a**8/13440 + a**7/5040 + a**6/720 + a**4/8 + 10*a**2. Let f(v) be the second derivative of x(v). Let f(g) = 0. Calculate g.
-1, 0, 2
Let -1/4*s**4 - 25/4 - 15*s - 3*s**3 - 23/2*s**2 = 0. What is s?
-5, -1
Let g(u) = -6*u**4 + 55*u**3 + 123*u**2 + 65*u - 2. Let v(n) = -n**4 - 2*n**2 - 2. Let k(r) = -g(r) + v(r). Factor k(f).
5*f*(f - 13)*(f + 1)**2
Let i(o) be the first derivative of 25/6*o**2 - 25/12*o**4 - 11 - 10/9*o**3 + 10/3*o. Let i(g) = 0. Calculate g.
-1, -2/5, 1
Let a = 23 - 21. Suppose 6*g**a + 2*g - 8*g - 5 - 14*g**2 + 7*g**2 = 0. What is g?
-5, -1
Let f be (70/55)/((-375)/(-275)). Let i(s) be the first derivative of -10 + s**2 + f*s**3 - 4/5*s. Let i(x) = 0. Calculate x.
-1, 2/7
Solve 32 - 16*u - 2*u + 125*u**2 - 124*u**2 = 0 for u.
2, 16
Let w be (0*(-18)/(-216))/5. Factor -3*r**3 +