+ 1. Let q(n) = 2*p(n) - 2*x(n). Factor q(g).
-2*(g - 1)**2*(g + 1)**2
Suppose -3*y = 3*t + 6, -2*y + y = -3*t - 6. What is v in -8*v - 15*v**3 + 12*v**2 + 11*v**3 + y*v**3 = 0?
0, 1, 2
Let i be (30/(-4) + 3)/(2*(-15)/10). Factor 15/8 - i*m - 3/8*m**2.
-3*(m - 1)*(m + 5)/8
Let w(t) be the second derivative of -t**6/30 - 11*t**5/20 - 31*t**4/12 - 7*t**3/2 - 8*t + 8. Factor w(l).
-l*(l + 1)*(l + 3)*(l + 7)
Let b(d) = -d**2 - 11*d + 2622. Let n be b(46). Determine o so that -1/2*o - 3/4*o**4 + 1/4*o**5 + n + 3/4*o**2 + 1/4*o**3 = 0.
-1, 0, 1, 2
Let n = -115 + 117. Let i(f) be the first derivative of 16/15*f**3 - 13/10*f**4 - 4/5*f - 4 + 7/5*f**n - 24/25*f**5. Find o, given that i(o) = 0.
-1, 1/4, 2/3
Let v = 17003 + -119017/7. Factor 6/7*i**2 - 2/7 - 8/7*i**3 - 8/7*i**4 + v*i.
-2*(i + 1)**2*(2*i - 1)**2/7
Let n(k) be the first derivative of 2*k**5/25 - 2*k**4/5 - 8*k**3/15 + 16*k**2/5 - 108. Factor n(z).
2*z*(z - 4)*(z - 2)*(z + 2)/5
Let n(t) = 46*t + 3406. Let x be n(-74). Suppose 24 + 2/3*y**x + 8*y = 0. What is y?
-6
Let y(o) be the third derivative of 0*o - 1/60*o**5 + 0*o**3 + 26*o**2 + 0 + 1/3*o**4. Solve y(v) = 0.
0, 8
Let n(k) = -k**2 + 5*k + 17. Let x(t) = -t**3 - 9*t**2 + 10*t + 7. Let b be x(-10). Let f be n(b). Factor 0*v + 2/3*v**4 - 2/3*v**5 - 2/3*v**2 + 2/3*v**f + 0.
-2*v**2*(v - 1)**2*(v + 1)/3
Suppose 4*c = -4 + 16. Factor 3*d**c - 106*d**5 + 109*d**5 - 3*d**3.
3*d**5
Let n(j) be the third derivative of 0 + 0*j**4 + 1/392*j**8 + 0*j - 2/35*j**5 + 0*j**6 - 5*j**2 + 3/245*j**7 + 0*j**3. Find k such that n(k) = 0.
-2, 0, 1
Let z = -14087/4 + 98705/28. Factor -2/7*l**4 - 8/7 - 12/7*l**3 - 26/7*l**2 - z*l.
-2*(l + 1)**2*(l + 2)**2/7
Let g(h) be the first derivative of h**8/2520 + h**7/1260 - h**6/135 - h**5/45 - 2*h**3 - 22. Let a(v) be the third derivative of g(v). Solve a(r) = 0 for r.
-2, -1, 0, 2
Suppose -1613*k = -1600*k. Factor k*t**2 + 3/5*t**5 + 0 - 9/5*t**4 + 6/5*t**3 + 0*t.
3*t**3*(t - 2)*(t - 1)/5
Let w = 2983 + -8944/3. What is h in -5/3*h**2 + 10/3*h - w = 0?
1
Suppose 0 = 3*p + 2*b - 177 - 9, -4*p = b - 253. Factor -4*l**4 - 5*l**3 + 32*l**2 + 3*l**4 - 9*l**4 - 3*l**3 + 32 + p*l - 2*l**5.
-2*(l - 2)*(l + 1)*(l + 2)**3
Suppose 60*y = -2*p + 64*y - 8, 5 = -2*p + 3*y. What is h in 3/10*h - 9/10*h**p + 1/5 = 0?
-1/3, 2/3
Let i(y) be the second derivative of 0*y**2 - 1/18*y**4 + 31*y + 1/3*y**3 + 0. Find u, given that i(u) = 0.
0, 3
Let f(z) be the first derivative of -14*z**3/11 + 2*z**2 - 2*z/11 - 48. Find v, given that f(v) = 0.
1/21, 1
Let t(b) = -b + 3. Let p be t(1). Factor 26*i - 21*i - 5*i**p + 0*i**2 + 10*i.
-5*i*(i - 3)
Let b(r) be the first derivative of r**5 - 15*r**4/4 - 10*r**3/3 + 30*r**2 - 40*r - 127. Factor b(m).
5*(m - 2)**2*(m - 1)*(m + 2)
Factor 0 + 0*b - 3/2*b**4 + 1/2*b**3 + b**2.
-b**2*(b - 1)*(3*b + 2)/2
Let n(c) be the first derivative of c**7/3780 - c**6/1620 - c**5/270 - 7*c**3 + 14. Let y(o) be the third derivative of n(o). Solve y(x) = 0 for x.
-1, 0, 2
Determine n, given that -2*n - 4/3 + 2*n**2 + 14/3*n**3 + 2*n**4 = 0.
-1, 2/3
Factor 816/7*i + 1496/7*i**3 - 1684/7*i**2 - 144/7 - 484/7*i**4.
-4*(i - 1)**2*(11*i - 6)**2/7
Let w(g) = -g**3 + 3*g - 2. Suppose -3*z - 1 = -4. Let l be w(z). What is r in l*r - 1/5*r**2 - 4/5*r**3 + 0 = 0?
-1/4, 0
Let n(s) be the third derivative of s**7/840 - s**6/80 - 3*s**5/80 + 7*s**4/48 - 84*s**2 + 2. Suppose n(w) = 0. What is w?
-2, 0, 1, 7
Let b(j) be the third derivative of -j**7/1470 - j**6/60 - 23*j**5/420 + j**4/12 + 4*j**3/7 - 172*j**2. What is y in b(y) = 0?
-12, -2, -1, 1
Let p = 3687 - 3685. Factor -2/5*o**2 - 2/5*o**3 + p*o - 6/5.
-2*(o - 1)**2*(o + 3)/5
Let q = 27/2 - 943/70. Let l(a) be the second derivative of 0*a**2 - q*a**5 - 1/105*a**6 + 0 + 4*a + 1/42*a**4 + 2/21*a**3. Suppose l(y) = 0. What is y?
-2, -1, 0, 1
Let t(d) = 14*d + 21. Let r(x) = -5*x - 7. Let y(k) = 11*r(k) + 4*t(k). Let g be y(-4). Factor -7*c**3 - 8*c**3 + 12*c**3 + 3*c**4 + 3*c**5 - g*c**2.
3*c**2*(c - 1)*(c + 1)**2
Let s(o) be the first derivative of 1/4*o**4 + 13 + 0*o**2 + 0*o + 0*o**3. Let s(t) = 0. Calculate t.
0
Suppose 5*i - 12*i = 13*i. Let q(t) be the second derivative of -1/16*t**4 + 0*t**3 + i + t + 0*t**2. Factor q(h).
-3*h**2/4
Let d be (-10)/(-35) - 38/(-14). Factor 24*u**3 - 21*u**d - 2*u**2 + 0*u**4 - u**4.
-u**2*(u - 2)*(u - 1)
Let y(d) be the first derivative of d**6/40 + 3*d**5/16 + d**4/2 + d**3/2 + 32*d + 11. Let k(q) be the first derivative of y(q). Factor k(j).
3*j*(j + 1)*(j + 2)**2/4
Let c = 1606 - 1603. Let s(b) be the first derivative of -4/3*b**c - 8*b**2 - 8 - 16*b. Suppose s(g) = 0. What is g?
-2
Suppose 20*n + 5 = 21*n. Suppose -k = -n*f + 2, 2*f - 3 = -1. Find s such that 0*s - 2/7*s**5 + 4/7*s**k + 0 - 2/7*s**4 + 0*s**2 = 0.
-2, 0, 1
Let g be (60/(-33))/(120/(-220)). What is a in -4 + 26/3*a - g*a**2 = 0?
3/5, 2
Let b(h) be the first derivative of 5*h**4/8 + 5*h**3/3 - 25*h**2/4 - 15*h - 422. Factor b(x).
5*(x - 2)*(x + 1)*(x + 3)/2
Suppose -23*t + 39 + 145 = 0. Let r(d) be the first derivative of 0*d - 3/10*d**4 - t - 2/3*d**3 - 2/5*d**2. Factor r(a).
-2*a*(a + 1)*(3*a + 2)/5
Determine j so that 2/3 + 2/15*j**2 + 4/5*j = 0.
-5, -1
Let u(i) be the second derivative of i**6/765 + i**5/255 + i**4/204 - 19*i**3/6 + 26*i. Let h(b) be the second derivative of u(b). Factor h(r).
2*(2*r + 1)**2/17
Determine h, given that 0*h + 2/5*h**5 + 18/5*h**3 - 12/5*h**4 - 8/5*h**2 + 0 = 0.
0, 1, 4
Let c(t) be the third derivative of -t**7/105 + t**6/24 + t**5/6 + 20*t**2. Let h(u) = -5*u**4 + 10*u**3 + 20*u**2. Let i(a) = 5*c(a) - 3*h(a). Solve i(o) = 0.
-1, 0, 2
Let y(p) be the first derivative of 3*p**6/10 - 102*p**5/25 + 63*p**4/5 + 72*p**3/5 - 202. Suppose y(q) = 0. What is q?
-2/3, 0, 6
Let h(b) be the third derivative of 11*b**6/480 + 9*b**5/20 - 5*b**4/24 + 12*b**2. Factor h(u).
u*(u + 10)*(11*u - 2)/4
Suppose -4*i = -0*i. Suppose -3*r - 3*f + 6 = 0, -19 = -2*r + f - 12. Factor -1/2*b**2 + 0*b + i - 1/4*b**r.
-b**2*(b + 2)/4
Suppose 2*a - 5*a = -5*t - 1, 0 = -a + 2*t. Find n, given that 19*n**3 + 7*n**2 - 3*n**a - 15*n**3 = 0.
-1, 0
Factor 2*m**2 + 0 + m - 5/4*m**3.
-m*(m - 2)*(5*m + 2)/4
Let k(p) be the third derivative of -p**7/560 + p**6/320 + p**5/40 - p**4/16 - 14*p**2. Factor k(d).
-3*d*(d - 2)*(d - 1)*(d + 2)/8
Solve 3*p**3 - 140*p + 16 - p**3 + 6*p**4 + 132*p + 0*p**3 - 28*p**2 = 0 for p.
-2, -1, 2/3, 2
Suppose -37*x - 28*x = -130. Determine t so that 6/11*t**x + 6/11*t + 2/11*t**3 + 2/11 = 0.
-1
Suppose 0 = -3*s + 19 + 38. Suppose 31 = 5*g - s. Factor -g*w**3 + 8*w + 13*w**3 + 3 + 9*w**2 + w.
3*(w + 1)**3
Solve -40/9 + 2/9*c**2 + 2/9*c = 0.
-5, 4
Let f(d) = 34*d**3 + 100*d**2 + 154*d + 60. Let k(v) = -509*v - 11 - 1 + 478*v - 7*v**3 - 20*v**2. Let g(a) = -3*f(a) - 14*k(a). Factor g(w).
-4*(w + 1)**2*(w + 3)
Let k(f) be the first derivative of 0*f - 2/3*f**3 + 13 + 1/4*f**4 + 1/2*f**2. Factor k(x).
x*(x - 1)**2
Let q(k) be the second derivative of 0 + 1/8*k**2 + 1/12*k**3 + 1/48*k**4 + k. Let q(v) = 0. Calculate v.
-1
Let y(c) = -4*c + 12. Let b be y(3). Let j(v) be the third derivative of 0 + 0*v + b*v**4 + 1/90*v**5 + 5*v**2 + 0*v**3. Factor j(s).
2*s**2/3
Let a(z) = -13*z**3 - 20*z**2 + 1073*z - 210. Let f(h) = -41*h**3 - 60*h**2 + 3216*h - 630. Let t(p) = -17*a(p) + 6*f(p). Factor t(j).
-5*(j - 6)*(j + 7)*(5*j - 1)
Let v = 7 + -4. Let g = 97/7 + -284/21. Factor 2/3*u**2 + 0*u + 0 + g*u**v.
u**2*(u + 2)/3
Factor 0 + 0*q + 0*q**2 - 8/9*q**4 + 4/3*q**3 - 4/9*q**5.
-4*q**3*(q - 1)*(q + 3)/9
Let i = -130062/11 + 11824. Factor 18/11*c**3 + i*c + 0 - 12/11*c**2.
2*c*(3*c - 1)**2/11
Suppose 5*k - 5*l = 500, 2*l - 145 = -k - 48. Suppose 5*z - 513 + 3 = 0. Determine u so that -z + k - 3*u + u + u**2 = 0.
-1, 3
Let i(t) be the first derivative of 9*t**4/4 - 11*t**3/3 - 8*t**2 + 4*t - 7. Factor i(m).
(m - 2)*(m + 1)*(9*m - 2)
Let k(f) be the second derivative of f**6/6 - 9*f**5/2 - 205*f**4/3 - 225*f**3 - 625*f**2/2 + 189*f. Find o, given that k(o) = 0.
-5, -1, 25
Let v be (-68)/(-20) + 132/(-330). Solve 2/5*s + 2/5*s**4 - 2/5*s**2 + 0 - 2/5*s**v = 0.
-1, 0, 1
Let r be 188/2303*(8 - 1). Let u(m) be the first derivative of 4/7*m - 1 + 4/21*m**3 + r*m**2. Find v such that u(v) = 0.
-1
Let k(b) be the second derivative of 3*b**5/20 + b**4/3 - 14*b**3/3 + 8