 Factor i(t).
5*t**2*(t + 2)
Suppose -914 = -285*s + 8*s - 180*s. Suppose -1/7 - 3/7*z**s + 4/7*z = 0. Calculate z.
1/3, 1
Let k(o) = -o**2 - 1. Let v(b) = -5*b**4 + 27*b**3 - 35*b**2 + 12*b + 5. Let q(a) = -10*k(a) - 2*v(a). Solve q(t) = 0.
0, 2/5, 2, 3
Let d(u) be the second derivative of -u**6/45 - u**5/10 - u**4/6 - u**3/9 + 12*u - 2. Factor d(g).
-2*g*(g + 1)**3/3
Let d = 65 - 60. Suppose -4*x = -d*x + 11*x. What is n in 1/2*n - 1/2*n**2 + x = 0?
0, 1
Let l(x) be the first derivative of -2*x**3/9 - 2*x**2/3 + 204. Factor l(p).
-2*p*(p + 2)/3
Factor 7/2 - 5/2*z**2 - z.
-(z - 1)*(5*z + 7)/2
Let b(j) be the first derivative of 24 + 2/27*j**3 - 5/9*j**2 + 0*j. Factor b(s).
2*s*(s - 5)/9
Let j(o) = o - 1. Let s(g) be the second derivative of -g**4/6 - g**3/2 - 11*g**2/2 - 36*g. Let n(i) = 5*j(i) - s(i). Find m, given that n(m) = 0.
-3, -1
Let h = -148/3 + 50. Let y be (24/(-54))/(32/(-24)). Factor -h + 0*f**2 + f - y*f**3.
-(f - 1)**2*(f + 2)/3
Let x(g) be the second derivative of g**5/20 - g**4 - g**3/6 + 6*g**2 + 7*g + 5. Factor x(q).
(q - 12)*(q - 1)*(q + 1)
Let z(n) be the first derivative of -n**6/10 - 9*n**5/20 - 3*n**4/4 - n**3/2 + 8*n + 15. Let b(p) be the first derivative of z(p). Factor b(y).
-3*y*(y + 1)**3
Let f = 642 + -639. Let i(d) be the second derivative of -3*d + 0 + 1/3*d**f - 3/2*d**2 + 1/12*d**4. Determine p so that i(p) = 0.
-3, 1
Let u(s) = -s**4 + s**3 + s**2 - s + 1. Let b(d) = 18*d**4 - 3*d**3 - 54*d**2 - 105*d + 129. Let o(q) = -b(q) - 15*u(q). Suppose o(h) = 0. What is h?
-4, 1, 3
Factor 56/13*q - 58/13 + 2/13*q**2.
2*(q - 1)*(q + 29)/13
Let p(v) = 2*v - 11. Let h = -29 - -36. Let k be p(h). Factor 4/9 + 2/9*n**k - 2/9*n - 4/9*n**2.
2*(n - 2)*(n - 1)*(n + 1)/9
Let t be (-42)/(-65) - (-84)/546. Factor -6/5*s**2 + 0 + t*s.
-2*s*(3*s - 2)/5
Suppose -3*r - 10*w = -8*w - 19, 2*r + 2*w - 14 = 0. Factor 14*s - 17*s + r*s**2 - 13*s**3 - s**4 + 12*s**3.
-s*(s - 1)**2*(s + 3)
Suppose 19*p - 237 - 258 = -438. Solve 32/11 + 18/11*n**p + 48/11*n**2 - 8*n = 0.
-4, 2/3
Suppose 38 = 11*d + 5. Let i(f) be the first derivative of 1/22*f**4 + d + 54/11*f + 27/11*f**2 + 6/11*f**3. Let i(l) = 0. Calculate l.
-3
Find q such that -4*q**2 - 14/3*q**3 + 1 + 4/3*q**5 + 3*q**4 + 10/3*q = 0.
-3, -1, -1/4, 1
Factor -11*u**3 - 2*u**4 - 6*u + 18*u - u**3 + 10*u**2 - 8*u**2.
-2*u*(u - 1)*(u + 1)*(u + 6)
Let x(j) be the third derivative of -j**6/280 - j**5/70 + j**4/56 + j**3/7 - 31*j**2. Factor x(t).
-3*(t - 1)*(t + 1)*(t + 2)/7
Let b(g) be the first derivative of g**2/2 + 18*g + 2. Let c be b(-14). Let -5*t**4 + t**2 - t + 0*t**2 - 2*t**3 + 3*t + c*t**4 = 0. What is t?
-2, -1, 0, 1
Let c be 58*6/(-90) - -4. Let r(a) be the second derivative of 0 + 2/3*a**3 + 1/3*a**4 + 0*a**2 + 5*a - 1/5*a**5 - c*a**6. Determine d, given that r(d) = 0.
-1, 0, 1
Determine s so that 28*s**2 + 29*s**2 + 24*s**3 + 2*s**2 + 3*s**4 - 11*s**2 = 0.
-4, 0
Let s(c) be the third derivative of c**7/420 - c**6/120 + c**5/120 - 3*c**2 + 11*c. Let s(h) = 0. What is h?
0, 1
Let o(k) = k**3 + 2*k**2 + k - 2. Let p be o(1). Let w be (-15)/(135/(-24))*p/4. Determine q, given that -2*q**3 - 2/3*q**4 + 2*q - 2/3*q**2 + w = 0.
-2, -1, 1
Let t = 131/70 - 278/35. Let z = t + 46/7. Factor z*x**2 + 9/2 + 3*x.
(x + 3)**2/2
Let v = -2/5989 + 11984/17967. Factor v*d + 0 - d**2 + 1/3*d**3.
d*(d - 2)*(d - 1)/3
Let b(u) be the second derivative of 5*u**7/56 - 23*u**6/40 - 9*u**5/16 + 83*u**4/16 + 47*u**3/4 + 9*u**2 - 117*u + 2. Determine m, given that b(m) = 0.
-1, -2/5, 3, 4
Let w(j) be the second derivative of -j**7/21 - j**6/15 + 3*j**5/10 + 5*j**4/6 + 2*j**3/3 + 2*j - 2. Suppose w(r) = 0. Calculate r.
-1, 0, 2
Let c(v) = 16*v**4 - 12*v**3 + 0*v**4 + 16*v - 8 - 12*v**4 + 4*v**2. Let t(y) = -y**3 + y**2 - 1. Let k(l) = -c(l) - 4*t(l). Solve k(s) = 0 for s.
-1, 1, 3
Let j = -22 - -36. Suppose 4*t + g - j = 3, -5 = -g. Suppose -2*m - 6*m + 2*m**2 + 4*m + 2*m**t = 0. What is m?
-2, 0, 1
Let i = 244 + -2195/9. Let m(z) be the second derivative of -i*z**3 + z + 1/18*z**4 - 1/3*z**2 + 0 + 1/30*z**5. Determine k so that m(k) = 0.
-1, 1
Let f(b) = 11*b**4 + b**2 + 6*b - 12. Let y(q) = 2*q**4 + q - 2. Let c(a) = -f(a) + 6*y(a). Factor c(d).
d**2*(d - 1)*(d + 1)
Let b(z) be the third derivative of -z**6/90 + z**5/30 + z**4/3 - 7*z**3/3 - 11*z**2. Let m(r) be the first derivative of b(r). Solve m(d) = 0 for d.
-1, 2
Let u = -2/79 - -91/474. Let m(b) be the first derivative of -2 + u*b**3 + b**2 + 2*b. Find i such that m(i) = 0.
-2
Let q be -1 - -6 - ((14 - -2) + -16). Let 15/4*w + 15/4*w**5 + 5/2*w**4 - 15/2*w**3 + 5/2 - q*w**2 = 0. Calculate w.
-1, -2/3, 1
Let p(r) be the third derivative of 1/195*r**6 + 0*r**4 + 1/273*r**7 + 0*r**5 + 0 + 0*r + 0*r**3 + 1/2184*r**8 - 20*r**2. Let p(f) = 0. What is f?
-4, -1, 0
Let m(d) be the third derivative of 0 + 5*d**2 + 0*d**3 + 0*d + 0*d**4 + 1/60*d**6 + 1/15*d**5. What is g in m(g) = 0?
-2, 0
Let n(x) be the third derivative of x**8/672 + x**7/420 - x**6/80 - x**5/24 - x**4/24 - 4*x**2 + 67*x. Let n(j) = 0. What is j?
-1, 0, 2
Let w(j) be the second derivative of -j**5/5 - j**4 + 8*j**3/3 + 24*j**2 + 2*j + 15. Suppose w(r) = 0. Calculate r.
-3, -2, 2
Let j(v) be the second derivative of v**4/16 + 195*v**3/8 - 147*v**2/2 - 11*v - 8. Factor j(q).
3*(q - 1)*(q + 196)/4
Let d(b) be the second derivative of -b**4/18 - b**3/27 + 2*b**2/9 + 65*b. Factor d(p).
-2*(p + 1)*(3*p - 2)/9
Suppose 0 = -48*f + 50*f - 20. Suppose 17*c = f*c. Factor -2/5*z + 0*z**2 + 2/5*z**3 + c.
2*z*(z - 1)*(z + 1)/5
Let x = 79 - 79. Let b(j) be the second derivative of j - 1/3*j**3 + 1/6*j**4 + 0 + x*j**2. Suppose b(i) = 0. Calculate i.
0, 1
Solve -4*t**4 + 12*t**3 + 3*t**2 + 144*t - 2*t**5 + 12 - 106*t - t**2 + 38*t**2 = 0 for t.
-2, -1, 3
Let c = 5 - 7. Let j = c + 4. Factor -64 + 16*o**j - 61*o - 4*o**4 + 61*o + 16*o**2.
-4*(o - 2)**2*(o + 2)**2
Let a(o) be the first derivative of -1/15*o**5 - 25 + 1/9*o**3 + 0*o**2 + 0*o**4 + 0*o. Solve a(l) = 0.
-1, 0, 1
Let m(r) be the second derivative of -r**5/105 - 2*r**4/21 - 8*r**3/21 - 4*r**2 - 12*r. Let b(g) be the first derivative of m(g). Factor b(p).
-4*(p + 2)**2/7
Let u(g) = g**2 + 7*g - 4. Let o be u(-8). Let t(f) be the first derivative of o + 0*f**2 - 4/9*f**3 + 3/2*f**4 - 8/5*f**5 + 5/9*f**6 + 0*f. Factor t(b).
2*b**2*(b - 1)**2*(5*b - 2)/3
Let t = -62 + 67. Solve -41*b**4 - 8*b**t + 48*b**4 - 12*b**3 - 16 + 45*b**4 + 20*b - 80*b**3 + 44*b**2 = 0 for b.
-1/2, 1, 4
Let d(s) be the first derivative of 2*s**5/75 - 14*s**4/15 - 11. Find q, given that d(q) = 0.
0, 28
Let z(f) be the second derivative of 2*f**7/21 - 4*f**6/15 - f**5/5 + 2*f**4/3 + 3*f - 22. Find v, given that z(v) = 0.
-1, 0, 1, 2
Let g(n) be the third derivative of -n**5/160 + 3*n**4/64 - n**3/8 + n**2 + 31*n. Factor g(d).
-3*(d - 2)*(d - 1)/8
Let m = 99 + -96. Let -8*x - m*x**2 + 4 + x**2 + 2*x**2 + 4*x**2 = 0. Calculate x.
1
Let x(i) be the third derivative of 2*i**7/105 - 3*i**6/10 + 28*i**5/15 - 6*i**4 + 32*i**3/3 + 91*i**2 - 3*i. Factor x(q).
4*(q - 4)*(q - 2)**2*(q - 1)
Suppose 14*y - 17*y + 12 = 0. Let d be y/8 - ((-140)/24)/7. Factor -d*u**3 - 1/3*u + 5/3*u**2 + 0.
-u*(u - 1)*(4*u - 1)/3
Let h(m) be the second derivative of 3*m**3/2 + 5*m**2/2 - 14*m. Let c be h(3). Factor 10*d**3 - 2*d**4 + c*d**2 + 14*d**4 - 26*d**4 + 8*d.
-2*d*(d - 2)*(d + 1)*(7*d + 2)
Suppose -5*n - 5*b = -85, 2*n + 2 - 39 = -b. Let k be ((80/25)/4)/(8/n). Determine h, given that 1/4*h**k + 0 + 0*h = 0.
0
Suppose 12 = 7*w - w. Let x = 2258/7 - 322. Suppose -w*t + 2*t**2 + x - 4/7*t**3 = 0. Calculate t.
1/2, 1, 2
Let y = 32 - 27. Factor -2*r**4 + r - 69*r**2 + y*r**3 - 69*r**2 + 134*r**2.
-r*(r - 1)**2*(2*r - 1)
Let u(z) = 15*z**3 - 7*z**2 - 16*z. Let t(b) = 2*b**3 - 2*b**2 - b. Let a(n) = -24*t(n) + 3*u(n). Suppose a(x) = 0. Calculate x.
0, 1, 8
Factor 1 + 5/3*n**3 - 5/3*n - n**2.
(n - 1)*(n + 1)*(5*n - 3)/3
Suppose 65 = -6*o + 245. Find v such that -3*v**2 - 3*v**5 + 33*v**3 - v**4 + 6*v**2 - 2*v**4 - o*v**3 = 0.
-1, 0, 1
Let c(m) = 2*m**5 - 2*m**4 - 2*m**3 - m**2 - m. Let h(k) = 2*k**5 - 246*k**4 - 4054*k**3 - 13443*k**2 - 12547*k. Let z(l) = 3*c(l) - h(l). Factor z(r).
4*r*(r + 2)**2*(r + 28)**2
Determine z so that 4666*z + 8*z**2 + 3*z**3 - 4666*z - 7*z**3 = 0.
0, 2
Factor -1/3*m**2 + 8/3 