1, 0, 2/7, 1
Suppose 55*y - 60*y + 3 = -3*s, 2*y + 3*s = -3. Let 0*t - 1/7*t**2 - 3/7*t**4 + y - 3/7*t**3 - 1/7*t**5 = 0. What is t?
-1, 0
Determine m so that 0 - 12/7*m**2 - 2/7*m**3 - 10/7*m = 0.
-5, -1, 0
Let y(c) = -c**3 - 6*c**2 - 14*c - 21. Let w be y(-4). Suppose -w*f + 12 = 3*f. Solve 12 - 6*g + 3/2*g**3 - 3*g**f = 0.
-2, 2
Suppose 6*c - 11*c = -160. Let y be 2/(-7) + c/14. Factor -2*u**2 - 4*u + 15 - 19 - y*u.
-2*(u + 1)*(u + 2)
Let y(b) be the third derivative of -b**5/90 - 79*b**4/18 - 6241*b**3/9 + 6*b**2 - 17. What is p in y(p) = 0?
-79
Factor -1/3*x**5 - 4/3*x**3 + 5/3*x**4 + 32/3*x - 16/3 - 16/3*x**2.
-(x - 2)**3*(x - 1)*(x + 2)/3
Let u(c) = 7*c**2 - 19*c + 25. Let f(t) = -t**2 + t - 1. Let x(h) = -5*f(h) - u(h). Factor x(m).
-2*(m - 5)*(m - 2)
Let o(s) be the first derivative of -s**6/10 + 36*s**5/25 - 42*s**4/5 + 126*s**3/5 - 81*s**2/2 + 162*s/5 + 69. What is m in o(m) = 0?
1, 2, 3
Let t be 21 + -20 + ((-6)/(-4) - 1). Factor -t*l + 3/2*l**3 + 0 + 3/2*l**4 - 3/2*l**2.
3*l*(l - 1)*(l + 1)**2/2
Let t(i) be the third derivative of -i**6/960 + i**4/48 - 113*i**2. Factor t(n).
-n*(n - 2)*(n + 2)/8
Let b(p) be the first derivative of -3*p**6 - 36*p**3 - 16*p + 2 + 24/5*p**5 + 36*p**2 + 23/2*p**4. Determine u, given that b(u) = 0.
-2, 2/3, 1
Suppose 0 = 4*m - 5*y + 36 - 114, 2*m - 40 = 3*y. Let f be -12 + m - (0 - -1). Factor -15/2*r**2 + 15*r**3 - 45/4*r**f + 3*r**5 + 0*r + 3/4.
3*(r - 1)**4*(4*r + 1)/4
Let o(x) be the third derivative of -x**8/840 - 4*x**7/525 - 5*x**2 - 9. Solve o(q) = 0.
-4, 0
Let i(l) be the third derivative of 7*l**6/300 + 139*l**5/75 + 136*l**4/3 - 160*l**3/3 + 39*l**2. Factor i(t).
2*(t + 20)**2*(7*t - 2)/5
Let u(s) = -15. Let a(l) = l**2 + l + 1. Suppose n + v = 5*v - 17, -37 = 5*n - 4*v. Let m(r) = n*a(r) - u(r). Factor m(f).
-5*(f - 1)*(f + 2)
Factor 10/3 + 2/3*q**2 - 4*q.
2*(q - 5)*(q - 1)/3
Factor -856/7*i + 4/7*i**2 + 45796/7.
4*(i - 107)**2/7
Suppose -3*a - 3 = -3*v - 33, -4*a + 32 = -2*v. Let t be a - ((-3 - -4) + 3). Factor -f**5 + 2*f**2 - 4*f**2 - 1 + f**3 + 3*f**4 + 5 - 5*f**t.
-(f - 2)**2*(f - 1)*(f + 1)**2
Suppose 3*p**4 - 128*p - 65*p**2 + 308 + 2*p**4 - 127*p + 15*p**3 - 488 = 0. Calculate p.
-3, -1, 4
Let r(a) be the first derivative of -4*a**5/5 - 13*a**4 - 160*a**3/3 - 72*a**2 + 57. Factor r(m).
-4*m*(m + 2)**2*(m + 9)
Let a(c) be the second derivative of c**6/6 - 2*c**5/5 - 199*c**4/12 - 73*c**3 - 72*c**2 - 15*c + 15. Solve a(q) = 0.
-3, -2/5, 8
Let l(r) = -9*r - 4. Let y be l(-4). Suppose 5*z = 4*o - y, 3*o = -o - 3*z. Factor 0*j**5 + 4*j**o + 0*j**5 - 2*j**3 - 2*j**5.
-2*j**3*(j - 1)*(j + 1)
Let s(i) be the second derivative of 0 + 3/7*i**2 - 11/14*i**3 + 2/49*i**7 - 13/70*i**6 + 3/20*i**5 + 11/28*i**4 - 17*i. Solve s(y) = 0 for y.
-1, 1/4, 1, 2
Factor -30 + 1/3*o**2 - 43/3*o.
(o - 45)*(o + 2)/3
Let j be (8/(-10))/(1/(-5)). Suppose 0*r**4 + 0*r**4 + 35*r**2 + 5*r - 20*r**2 + 15*r**3 + 5*r**j = 0. What is r?
-1, 0
Let y(o) = -49*o - 635. Let i be y(-13). Solve -p**4 + p**i + 0 - 1/2*p**3 + 1/2*p**5 + 0*p = 0.
-1, 0, 1, 2
Let j(w) be the first derivative of w**5/4 - 5*w**4/4 + 25*w**3/12 - 5*w**2/4 + 136. Solve j(v) = 0.
0, 1, 2
Let b(l) be the second derivative of 3/2*l**2 - 1/210*l**5 - 1/28*l**4 + 0 - 9*l - 2/21*l**3. Let z(i) be the first derivative of b(i). Factor z(k).
-2*(k + 1)*(k + 2)/7
Let s be -1*16/40 + 84/10. Factor 8*q**2 + 10*q - s*q - 4*q**4 + 4*q**3 - 2*q.
-4*q**2*(q - 2)*(q + 1)
Let o be (-15)/(-20) + (2565/60 - 8). Determine n so that -3/2 - 12*n**4 + 8*n**5 - 9/2*n**2 + 19/2*n - o*n**3 = 0.
-1, 1/4, 3
Factor -2/11*b**5 + 0*b - 2/11*b**4 + 2/11*b**2 + 0 + 2/11*b**3.
-2*b**2*(b - 1)*(b + 1)**2/11
Let b(y) = 3*y**3 + 9*y**2 + 2. Let j(u) = 2*u**4 + 11*u**3 + 37*u**2 + u + 9. Let x(g) = -9*b(g) + 2*j(g). Factor x(c).
c*(c - 2)*(c + 1)*(4*c - 1)
Let i = 11 - 3. Factor 0*s**2 + 4*s**2 - 4*s - i*s**2.
-4*s*(s + 1)
Let k(g) be the second derivative of -g**6/90 + g**5/3 + 11*g**4/6 + 34*g**3/9 + 23*g**2/6 - g - 234. Suppose k(f) = 0. Calculate f.
-1, 23
Let t(n) be the second derivative of -n**5/10 - 9*n**4/2 - 81*n**3 - 729*n**2 + 3*n. Determine s, given that t(s) = 0.
-9
Let o = -3313/11280 + 14/47. Let v(p) be the third derivative of o*p**5 - 9*p**2 + 1/16*p**4 + 0*p + 0 + 3/8*p**3. Factor v(g).
(g + 3)**2/4
Let p(x) be the first derivative of x**4/10 - 86*x**3/15 + 88*x**2 + 968*x/5 - 14. Find s such that p(s) = 0.
-1, 22
Let p(j) be the first derivative of 4*j**2 + 2/3*j**3 + 0*j - 12. Factor p(o).
2*o*(o + 4)
Let f(b) be the second derivative of -5*b + 10*b**2 + 2 - 35/6*b**3 - 1/3*b**6 - 5/6*b**4 + 2*b**5 - 5/42*b**7. Factor f(z).
-5*(z - 1)**3*(z + 1)*(z + 4)
Let p(v) be the second derivative of -v**4/48 - v**3/4 + 55*v**2/8 + 329*v. Determine d so that p(d) = 0.
-11, 5
Let d(w) be the third derivative of -1/3*w**3 - w**2 + 0 - 1/180*w**6 + 0*w**4 + 0*w + 1/60*w**5. Let m(o) be the first derivative of d(o). Factor m(k).
-2*k*(k - 1)
Let i(r) be the first derivative of 60*r**2 - 5/3*r**3 + 13 - 720*r. Factor i(v).
-5*(v - 12)**2
Suppose 3*o = -l + 44, -o + 4*o - 4*l - 49 = 0. Let m be (-4 - 1)*(-6)/o. Factor -4*w**2 - 2 + 5*w**m + w**2.
2*(w - 1)*(w + 1)
Let m be -1*(-1)/5*1. Let u be 3/45 + 9/243*9. Determine h so that -1/5*h - m*h**3 - u*h**2 + 0 = 0.
-1, 0
Find v, given that -342/5*v + 27/5*v**2 + 1083/5 = 0.
19/3
Let t(w) be the second derivative of 0 - 15*w**2 - 1/6*w**6 + 5/4*w**4 + 3/4*w**5 + 4*w - 35/6*w**3. Factor t(l).
-5*(l - 3)*(l - 2)*(l + 1)**2
Let q(x) = -x**3 + 46*x**2 - 167*x - 2. Let j be q(4). Factor 0*h**j + 1/2*h + 0 - 1/2*h**3.
-h*(h - 1)*(h + 1)/2
Let m(j) = 31*j**3 - 218*j**2 + 340*j - 82. Let s(h) = 525*h**3 - 3705*h**2 + 5780*h - 1395. Let x(c) = -35*m(c) + 2*s(c). Let x(k) = 0. What is k?
2/7, 2, 4
Suppose 3 = -g, 0 = c - 33*g + 32*g - 3. Factor 2/7*x**3 + c*x - 6/7*x**2 + 0.
2*x**2*(x - 3)/7
Factor 7/4*z - 1/4*z**2 + 15/2.
-(z - 10)*(z + 3)/4
Let s be (-6 + -98*1/(-16))/((-3)/(-12)). Solve 5/2 - s*w**2 - 2*w = 0 for w.
-5, 1
Suppose -14*k + 17*k = -21. Let t(p) = -3*p**3 + 4*p**2 + 7*p + 6. Let o(v) = -10*v**3 + 13*v**2 + 21*v + 19. Let a(g) = k*t(g) + 2*o(g). What is c in a(c) = 0?
-1, 4
Let o be ((-7)/(-56)*-2)/(762/8). Let z = o - -297/254. Find y such that z*y**2 + 1/6*y**5 + 5/6*y**4 + 0 + 3/2*y**3 + 1/3*y = 0.
-2, -1, 0
Let y(n) be the first derivative of 2*n**3 + 64*n**2 + 42*n + 109. Solve y(x) = 0.
-21, -1/3
Let m(f) be the second derivative of -13*f + 3/100*f**5 - 4/15*f**4 + 1/10*f**3 + f**2 + 0. Find k, given that m(k) = 0.
-2/3, 1, 5
Suppose -5*h - 3 = -13. Factor -25*v**4 + 2*v**3 + 23*v**4 - h*v**5 + 2*v**3.
-2*v**3*(v - 1)*(v + 2)
Let g(w) = 7*w - 5*w**4 - 4*w**2 - w**3 + 4*w**4 + 5*w**2 - 6*w**3. Let b(r) = -r**3 + r. Let x(s) = 5*b(s) - g(s). Factor x(j).
j*(j - 1)*(j + 1)*(j + 2)
Factor -3 + 9/7*p**2 + 60/7*p.
3*(p + 7)*(3*p - 1)/7
Let s be (-2)/((7 - 10)*1) + 0. Suppose 0*m - s*m**4 + 4/3*m**3 + 0 + 2*m**2 = 0. What is m?
-1, 0, 3
Suppose -4/11*q**3 + 1/11*q**4 + 48/11 - 13/11*q**2 + 40/11*q = 0. What is q?
-3, -1, 4
Let r(d) be the first derivative of d**3/3 - 38*d**2 + 1444*d + 229. What is q in r(q) = 0?
38
Suppose l + 5*b = 2*l + 10, 5*b = -5*l + 10. Let g(n) be the first derivative of 3/4*n**4 - n**3 + 0*n**2 + l*n - 13. Suppose g(a) = 0. What is a?
0, 1
Let r(g) = -g**4 + g**3 - g + 1. Let b(m) = -14*m**4 + 33*m**3 + 5*m**2 - 10*m + 4. Let p(y) = -b(y) + 4*r(y). Factor p(c).
c*(c - 3)*(2*c + 1)*(5*c - 2)
Let b = 37 + -33. Suppose -2*w + 6 = 3*i, -2*i + b = w - 2*w. Factor 18 - i + 17*j**2 - 16*j**2 - 8*j.
(j - 4)**2
Let n(p) be the first derivative of p**2/2 + 9*p + 1. Let o be n(-7). Factor -26 + 20 - u**2 - o*u**2 - 9*u.
-3*(u + 1)*(u + 2)
Let h be 4/8*22 + 4. Suppose -6 + 5*i**3 + 28*i + 0*i**3 - h*i - 4*i**3 - 8*i**2 = 0. Calculate i.
1, 6
Suppose 16/7*t**3 - 2/7*t**4 + 8*t - 24/7 - 46/7*t**2 = 0. What is t?
1, 2, 3
Find w, given that -51*w - 181*w**2 - 845*w**4 - 9*w - 3245*w**3 - 619*w**2 + 450*w**3 = 0.
-3, -2/13, 0
Let k(g) be the first derivative of -2*g**3/21 - 52*g**2/7 - 200*g/7 - 96. Factor k(y).
-2*(y + 2)*(y + 50)/7
Let d(k) be the first derivative of 3*k**5 - 325*k**4/4 - 110*k**3/3 + 55. Factor d(p).
5*p**2*(p - 22)*(3*p + 1)
Let z = -478 - -8128/17. Factor 32/17 + 16/17*f + z*f**2.
2*(f + 4)**2/17