
-1, 0, 1
Let m(t) = 2*t**4 + 7*t**3 - 36*t**2 + 7. Let r(x) = x**4 + 5*x**3 - 24*x**2 + 5. Let k(n) = 5*m(n) - 7*r(n). Factor k(z).
3*z**2*(z - 2)*(z + 2)
Let u(o) = 66*o**3 - 90*o**2 + 117*o - 66. Let k(p) = -5*p**3 + 7*p**2 - 9*p + 5. Let v be 6*(9/2 + 0). Let m(q) = v*k(q) + 2*u(q). Find g such that m(g) = 0.
1
Let c = -2/19 - -136/209. Factor -c*r - 2/11 - 4/11*r**2.
-2*(r + 1)*(2*r + 1)/11
Let l(i) be the third derivative of 0*i**3 + 1/240*i**6 + 1/60*i**5 + 1/48*i**4 + 0 + 0*i + 3*i**2. Factor l(s).
s*(s + 1)**2/2
Let a = 24/11 + -194/99. Factor 2/9 - 2/9*t**3 + a*t - 2/9*t**2.
-2*(t - 1)*(t + 1)**2/9
Let n = -1283 - -3724/3. Let j = -41 - n. What is k in 7/3*k - k**2 - j = 0?
1/3, 2
Let f(i) = i**3 - 4*i**2 - 3*i. Let b(x) = -3*x**3 + 13*x**2 + 9*x. Let t(n) = -6*b(n) - 21*f(n). Solve t(a) = 0 for a.
-1, 0, 3
Suppose -2*n + 35 = 3. Let u be (-6)/(-4) + 8/n. Find a such that -2/3*a**u - 10*a**3 - 14/3*a**5 + 0 + 4/3*a - 38/3*a**4 = 0.
-1, 0, 2/7
Let r(m) = -m**3 - 4*m**2 - 2*m - 3. Suppose -3*l - 2*l - 20 = 0. Let s be r(l). Solve 0*t + 2/7*t**2 + 6/7*t**4 + 6/7*t**3 + 0 + 2/7*t**s = 0 for t.
-1, 0
Suppose 0 = -k - 3. Let r = k - -7. Factor 6/5*b**r + 2/5 - 4*b**3 - 12/5*b + 24/5*b**2.
2*(b - 1)**3*(3*b - 1)/5
Let x(t) be the first derivative of -t**4 - 4*t**3/3 + 21. Find l such that x(l) = 0.
-1, 0
Suppose j - 5 + 5 = 0. Factor 3*d**2 + 0*d + 21/4*d**4 + j + 12*d**3.
3*d**2*(d + 2)*(7*d + 2)/4
Suppose -4*d - 11 = -4*b + 1, -4*b = 4*d - 28. Suppose i - d = -0. Factor 2/5*c**i + 2/5 + 4/5*c.
2*(c + 1)**2/5
Let r be (-5)/(20 + -5) + 20/56. Let g(n) be the second derivative of 0*n**3 - 4*n - 1/105*n**6 + 0*n**2 + 0*n**5 + 0 + r*n**4. Factor g(j).
-2*j**2*(j - 1)*(j + 1)/7
Let r(c) be the second derivative of 1/42*c**7 + 0 + 0*c**2 + 1/6*c**3 - c + 0*c**6 - 1/10*c**5 + 0*c**4. Solve r(x) = 0.
-1, 0, 1
Let d = 1/83 - -79/332. Factor d*h**2 + 1/2*h + 1/4.
(h + 1)**2/4
Let s(k) be the first derivative of -k**4/4 - 5*k**3/6 + 3*k**2/4 + 7. Factor s(p).
-p*(p + 3)*(2*p - 1)/2
Let g = 127 - 379/3. Factor 2/3*l**4 - 2/9*l**5 - 2/9 - 4/9*l**2 - 4/9*l**3 + g*l.
-2*(l - 1)**4*(l + 1)/9
Let i(c) be the third derivative of 1/525*c**7 + 0*c**5 + 1/30*c**4 + 0 + 0*c - 4*c**2 - 1/15*c**3 - 1/150*c**6. Factor i(u).
2*(u - 1)**3*(u + 1)/5
Let t(h) be the first derivative of 5/3*h**3 - h**2 + 1/6*h**6 - 1/5*h**5 + 0*h - 3/4*h**4 + 5. Determine q so that t(q) = 0.
-2, 0, 1
Determine r so that 32*r**3 + 3*r**2 - 13*r**3 + 5*r**2 - 15*r**3 + 4*r = 0.
-1, 0
Factor -48/5*k**3 - 27/5*k + 3/5 + 72/5*k**2.
-3*(k - 1)*(4*k - 1)**2/5
Let a(w) = w. Let t be a(-1). Let m be t/((-3)/24) - 0. Factor 5*d + 10*d**2 + 4 - 11*d - m*d.
2*(d - 1)*(5*d - 2)
Suppose -9 = -2*w + 1, d + 2*w - 25 = 0. Let m be (20/d)/(4/6). Factor 2*c - 5 + 2 - 2*c**m + 3.
-2*c*(c - 1)
Let a(w) be the third derivative of w**7/630 + w**6/120 + w**5/180 - w**4/24 - w**3/9 - w**2. Find i, given that a(i) = 0.
-2, -1, 1
Let t = 22 + -305/14. Let w(g) be the first derivative of 2/35*g**5 - t*g**4 + 2/7*g**3 - 1/7*g**2 - 3 + 0*g. Suppose w(b) = 0. Calculate b.
0, 1
Let s(x) = -9*x**5 + 7*x**4 + 7*x**3 + 8*x**2 - 9*x - 15. Let t(n) = 5*n**5 - 4*n**4 - 4*n**3 - 4*n**2 + 5*n + 8. Let p(g) = 6*s(g) + 11*t(g). Factor p(j).
(j - 2)*(j - 1)**2*(j + 1)**2
Let -3*k - 6*k**2 - 595*k**3 - 2 + 593*k**3 - 3*k = 0. What is k?
-1
Let w be ((1 - 8) + -8)*2/(-9). What is g in -w*g + 2*g**2 + 4/3 = 0?
2/3, 1
Let i = 11 + -9. Let l be (i/(-2)*1)/(-3). Factor 0 - l*z**2 - z**4 - 1/3*z**5 + 0*z - z**3.
-z**2*(z + 1)**3/3
Let m(v) = 4*v**3 + 18*v**2 - 60*v + 54. Let f(j) = j**3 - j. Let g(i) = -12*f(i) + 2*m(i). Factor g(k).
-4*(k - 3)**3
Suppose 2*k + 6 = -k. Let j(z) = 12*z**3 - z. Let a be j(1). Let c(x) = -2*x - 2. Let r(u) = -u**2 - 11*u - 10. Let o(f) = a*c(f) + k*r(f). Factor o(s).
2*(s - 1)*(s + 1)
Let b(y) be the third derivative of y**7/280 - 3*y**6/160 + y**5/80 + 3*y**4/32 - y**3/4 + 16*y**2 + y. Factor b(j).
3*(j - 2)*(j - 1)**2*(j + 1)/4
Let t(q) be the first derivative of 7*q**5/15 + 5*q**4/12 - 10*q**3/3 - 10*q**2/3 + 8*q/3 + 5. Determine b, given that t(b) = 0.
-2, -1, 2/7, 2
What is u in -1/6*u**2 + 1/3*u - 1/6 = 0?
1
Let f(d) = -6 + 2 + 3 + d. Let z be f(1). Find j, given that 2/3*j**2 + z*j - 2/3 = 0.
-1, 1
Let d(y) be the third derivative of y**6/180 - y**5/90 - y**4/18 - 15*y**2. Factor d(i).
2*i*(i - 2)*(i + 1)/3
Let r be (-3 + 1)*(-14)/(-2). Let y be (-240)/(-84) + 4/r. Suppose -12/7*c**2 + 2/7*c + 0 + y*c**3 = 0. Calculate c.
0, 1/3
Let b(l) = 3*l**3 + 9*l**2 + 17*l + 7. Let f(m) = m**3 + m. Let g(d) = -b(d) + 2*f(d). Factor g(n).
-(n + 1)**2*(n + 7)
Suppose 12*u**4 - 12*u**2 - 8*u + 12*u**5 + 34*u**3 - 8*u**5 - 30*u**3 = 0. Calculate u.
-2, -1, 0, 1
Let w(q) be the third derivative of q**8/1680 - q**7/350 - q**6/600 + 7*q**5/300 - 2*q**3/15 - 7*q**2. Determine c so that w(c) = 0.
-1, 1, 2
Let j(g) be the third derivative of -g**6/120 - g**5/60 + 19*g**3/2 + g**2. Let q be j(0). Factor -57*i - i**5 + q*i - 3*i**3 + 3*i**4 + i**2.
-i**2*(i - 1)**3
Let o be -3 + (-246)/(-78) - (-92)/78. What is c in 2/3*c**3 - 2/3*c - 4/3*c**2 + o = 0?
-1, 1, 2
Let s(q) = q + 13. Let d be s(-7). Suppose 15*m - 18*m = -d. Solve -2/3*k - 1/3*k**m - 1/3 = 0.
-1
Let h(c) be the third derivative of c**8/1680 + c**7/210 + 3*c**6/200 + 7*c**5/300 + c**4/60 - 11*c**2. Factor h(g).
g*(g + 1)**3*(g + 2)/5
Let p = 90 + -179/2. Determine c, given that p + 5/2*c**2 - c**3 - 2*c = 0.
1/2, 1
Factor 3/2*s**2 + 0 + s + 1/2*s**3.
s*(s + 1)*(s + 2)/2
Let q(z) = -14*z**3 - 4*z**2 - 14*z. Let s(v) = 5*v**3 - 213 + v**2 + 5*v + 213. Let k(a) = -3*q(a) - 8*s(a). Factor k(j).
2*j*(j + 1)**2
Let x be (2/(-3))/((-2)/15). Let -7*v**2 + 3*v + x*v**3 + 4*v**2 - 4*v**3 - 1 = 0. What is v?
1
Let x(j) be the second derivative of -j**7/84 - j**6/30 - j**5/40 - 7*j. Factor x(u).
-u**3*(u + 1)**2/2
Let x(g) be the second derivative of -g**6/45 - g**5/10 - g**4/6 - g**3/9 - 8*g. Solve x(p) = 0.
-1, 0
Let d(w) = -w**5 + 2*w**4 + 5*w**3 + 5*w**2 - w + 2. Let x(l) = -l**5 + 3*l**4 + 6*l**3 + 6*l**2 - l + 3. Let s(a) = -4*d(a) + 3*x(a). Factor s(t).
(t - 1)**2*(t + 1)**3
Suppose 4*a + 3*g = a + 21, -g = -a - 3. Let -9/4*i**4 + 9/4*i**a + 0 + 15*i**5 + 3/2*i - 33/2*i**3 = 0. Calculate i.
-1, -1/4, 0, 2/5, 1
Let i be 4/8 - 7/(-2). Let k be (10/(-8))/((-1)/i). Factor -2*d**3 + d**5 - 2*d**5 + 2*d**k + d.
d*(d - 1)**2*(d + 1)**2
Let b(x) be the second derivative of -x**6/105 - 3*x**5/70 + 2*x**4/21 - 30*x. Let b(p) = 0. Calculate p.
-4, 0, 1
Let i(y) = y**3 + y**2 + 6. Let v be i(0). Let j(c) be the third derivative of 2*c**2 + 1/27*c**3 + 1/108*c**4 - 1/270*c**5 - 1/540*c**v + 0*c + 0. Factor j(g).
-2*(g - 1)*(g + 1)**2/9
Let w(x) be the third derivative of x**5/140 + x**4/14 + 2*x**3/7 - 6*x**2. Suppose w(v) = 0. Calculate v.
-2
Suppose 1 + 2 = s. Let u(h) = -h**4 - 3*h**3 + h**2 - 3*h + 3. Let r(o) = -o**4 - 2*o**3 + o**2 - 2*o + 2. Let m(c) = s*r(c) - 2*u(c). Factor m(i).
-i**2*(i - 1)*(i + 1)
Suppose 3*i - 5 = -x, 4*x + 0*i = -i + 9. Let d be 8/6*(-3)/(-2). Factor 18*c + 8 - 18*c**3 - x - d - 4*c**2.
-2*(c - 1)*(c + 1)*(9*c + 2)
Let x(y) be the first derivative of -y**5/30 - 19*y**4/24 - 7*y**3 - 27*y**2 - 36*y + 30. Factor x(f).
-(f + 1)*(f + 6)**3/6
Let b = 242/3 - 80. Let k(t) = -t**2 - 7*t - 4. Let s be k(-6). Factor -2/9 - b*a**s - 8/9*a.
-2*(a + 1)*(3*a + 1)/9
Let a(x) be the first derivative of 3/8*x**2 - 3/16*x**4 + 3 - 1/4*x + 1/12*x**3. Solve a(d) = 0.
-1, 1/3, 1
Let h be -1 + 1 + 0/((-30)/6). Let d(l) be the third derivative of 0*l + 0*l**4 + 0 + 1/420*l**7 + 1/120*l**5 - 1/120*l**6 - 2*l**2 + h*l**3. Factor d(k).
k**2*(k - 1)**2/2
Determine r so that 5*r**2 - 21*r**3 - 6*r**2 + 3*r**2 + 19*r**3 = 0.
0, 1
Solve -4*z**2 + 12*z**2 - 4*z**2 + 0*z**2 - 4 = 0.
-1, 1
Let b(q) be the third derivative of q**7/15 - 4*q**6/15 + 2*q**5/15 - 9*q**2. Factor b(s).
2*s**2*(s - 2)*(7*s - 2)
Determine l, given that -4*l**2 - 4/3*l**3 + 16/3 + 0*l = 0.
-2, 1
Let y(g) = -5 - 2 + 26*g + 26*g**2 - 78*g**2 - 19*g**2. Let n(m) = -m**2 + m + 1. Let u(r) = -4*n(r) - y(r). Factor u(d).
3*(5*d - 1)**2
Suppose -5*t - 3*a - 70 = -5*a, -5*a = 4*t + 23. Let p be (-3)/6 + (-6)/t. Factor -1/2*w**2 - 1/4*w + p - 1/4*w**3.
-w*(w + 1)**2/4
Let h = 3 - -2. Determine n, given tha