i - 1)*(i + 1)
Factor -7/3*x**2 - 6 - 65/3*x.
-(x + 9)*(7*x + 2)/3
Let f be (4758/36)/13 - 2/12. Solve 1 + 25*v + 20*v**2 - f - 1 + 15*v**2 = 0 for v.
-1, 2/7
Let k = -20684 - -20787418/1005. Let v = 4006/7035 - k. Factor 0 - 8/7*c**2 + 0*c - 12/7*c**5 + v*c**3 + 16/7*c**4.
-4*c**2*(c - 1)**2*(3*c + 2)/7
Let a = -51 + 57. Factor 2*z**2 + z**2 + 26*z + 19*z**2 - 44 - a*z**3 + 42*z**2.
-2*(z - 11)*(z + 1)*(3*z - 2)
Let q(s) be the third derivative of -2/105*s**5 - 6*s**2 + 0 - 5/84*s**4 + 0*s - 1/21*s**3. What is i in q(i) = 0?
-1, -1/4
Factor 0 + 0*r**2 - 1/4*r**3 + 25/4*r.
-r*(r - 5)*(r + 5)/4
Let h = -112553/9 - -12507. Suppose 26/9*k + 4/3 - h*k**2 = 0. What is k?
-2/5, 3
Let n(w) = 5*w**2 - 12*w + 9. Let j = 35 - 33. Let l(s) = 6*s**2 - 12*s + 9. Let u(t) = j*l(t) - 3*n(t). Factor u(k).
-3*(k - 3)*(k - 1)
Suppose 2*p - 14 = -0*p + 4*x, 0 = -3*p + 2*x + 9. Suppose 3*s = 2*l - l + 8, 0 = -l + p. Suppose 0*i + 2*i**3 + s*i - 3*i**3 - 7 + 5 = 0. What is i?
-2, 1
Let b(y) = 10*y**4 - 168*y**3 + 152*y**2 - 3*y + 12. Let c(z) = 2*z**2 + z - 4. Let q(o) = b(o) + 3*c(o). Factor q(a).
2*a**2*(a - 1)*(5*a - 79)
Let s = -226 + 228. Let v(u) be the first derivative of 1/3*u**3 + 0*u + u**s - 11. Determine c so that v(c) = 0.
-2, 0
Let b(x) be the third derivative of x**7/420 + x**6/48 + 7*x**5/120 + x**4/16 + 13*x**2 - 2. What is t in b(t) = 0?
-3, -1, 0
Let v(c) be the third derivative of -c**5/510 - 13*c**4/204 + 14*c**3/51 - 44*c**2 - 4*c. Factor v(q).
-2*(q - 1)*(q + 14)/17
Solve -2/13*l**2 + 32/13*l + 0 = 0.
0, 16
Let k(h) be the first derivative of -h**6/270 - h**5/90 + h**4/9 - 5*h**3 + 5. Let u(z) be the third derivative of k(z). Determine y, given that u(y) = 0.
-2, 1
Let p be (-256)/224 - (-44)/14. Let x(o) be the first derivative of 2/9*o**3 - 8 + 0*o - 1/12*o**4 - 1/6*o**p. Determine j so that x(j) = 0.
0, 1
Let j = 69 - 18. Let z(i) = -i**2 + 15*i - 23. Let f be z(9). Find s such that -f*s**4 + 12*s**2 - 5*s**5 - 2*s**2 - 25*s**3 + j*s**4 = 0.
0, 1, 2
Let d(v) = 81*v**4 - 354*v**3 + 609*v**2 - 114*v - 21. Let i(w) = 16*w**4 - 71*w**3 + 122*w**2 - 23*w - 4. Let j(c) = 4*d(c) - 21*i(c). Factor j(r).
-3*r*(r - 3)**2*(4*r - 1)
Solve 45*o**2 - 25 - 3*o**3 - 144*o - 119 + 45 - 93 = 0 for o.
-1, 8
Let b = 2/35 + 1324/105. Let j = -12 + b. Solve -j - 5/3*k**3 + 3*k**2 - 7/3*k**4 + 5/3*k = 0 for k.
-1, 2/7, 1
Let r(q) be the first derivative of q**2 + 0*q**4 + 1/2*q**3 - 1/20*q**5 - 6 - 8*q. Let h(x) be the first derivative of r(x). Solve h(g) = 0 for g.
-1, 2
Let x(f) be the second derivative of -f**6/30 - f**5/20 + f**4/3 + 2*f**3/3 - 433*f. Suppose x(k) = 0. Calculate k.
-2, -1, 0, 2
Suppose 9*a**2 + 3*a**4 + 2*a**4 - 20*a - 10*a**4 + 5*a**3 + 11*a**2 = 0. Calculate a.
-2, 0, 1, 2
Let l(p) be the third derivative of -2*p**5/75 - 3*p**4/20 + 3*p**3/5 + 31*p**2. Factor l(h).
-2*(h + 3)*(4*h - 3)/5
Let n = -16232/3 - -5411. Determine z, given that -4/3*z**2 - n - 5/3*z = 0.
-1, -1/4
Let s = -135 - -151. Let o be 6*(36/s - 3 - -1). Suppose 27/4*l**2 + o + 21/4*l + 15/4*l**3 + 3/4*l**4 = 0. Calculate l.
-2, -1
Suppose 106*a = 112*a. Suppose -5*q + 9*q = 8. Factor 0*c**4 + a*c - 1/5*c**3 + 0 + 0*c**q + 1/5*c**5.
c**3*(c - 1)*(c + 1)/5
Let m(l) = -l**3 - 3*l**2 + 71*l + 271. Let d be m(-4). Solve 3*a**2 + 0 + 9/2*a - 3/2*a**d = 0.
-1, 0, 3
What is j in 67/9 - 68/9*j + 1/9*j**2 = 0?
1, 67
Suppose 13 - 97 = -21*d. Let q(v) be the third derivative of 0*v**5 + 0*v**3 - 1/120*v**6 + 0 - 5*v**2 + 0*v + 1/24*v**d. Factor q(x).
-x*(x - 1)*(x + 1)
Let l(c) = c**5 + 7*c**4 + 20*c**3 + 16*c**2 + 2*c. Let v(t) = -3*t**5 - 20*t**4 - 58*t**3 - 48*t**2 - 7*t. Let h(f) = -7*l(f) - 2*v(f). Factor h(k).
-k**2*(k + 1)*(k + 4)**2
Let x = -32683/5 + 6537. Determine t, given that 12/5 - 14/5*t + x*t**2 = 0.
1, 6
Let c(o) = o**3 - 39*o**2 + 379*o + 21. Let l be c(19). Solve -9*y - 15/4*y**4 + 1/4*y**3 + l + 21/2*y**2 = 0 for y.
-2, 2/5, 2/3, 1
Find t, given that 0 - 2/3*t**4 - 8/3*t**3 + 14/3*t**2 + 20/3*t = 0.
-5, -1, 0, 2
Let w(n) be the second derivative of 7*n**6/30 - n**5/10 - 7*n**4/4 + 10*n**3/3 - 2*n**2 - 267*n. What is b in w(b) = 0?
-2, 2/7, 1
Let i(u) = -u**2 + 6*u - 5. Let z be i(4). Suppose -5*a + 75 = 2*r, 2*a + z*r = -2*a + 67. Suppose -a*c + 13*c + 0*c**2 + c**2 - c**4 = 0. What is c?
-1, 0, 1
Let k(y) be the first derivative of -y**6/30 + 2*y**5/5 - 11*y**4/6 + 4*y**3 - 9*y**2/2 - 6*y - 1. Let l(w) be the first derivative of k(w). Factor l(x).
-(x - 3)**2*(x - 1)**2
Let n(l) = 8*l**3 + 27*l**2 - 18*l - 17. Let p(y) = 3*y**3 + 9*y**2 - 6*y - 6. Suppose -2*j + 6 = -3*j. Let q(v) = j*n(v) + 17*p(v). Solve q(d) = 0 for d.
0, 1, 2
Let y be ((-1050)/49)/(2/(-14)). Let w be 3/y*-4*-5. Factor 2/5*q**4 + w*q**3 - 2/5*q + 0 - 2/5*q**2.
2*q*(q - 1)*(q + 1)**2/5
Determine a, given that 6/5*a**2 - 6/5*a**4 + 1/5*a**5 + 0 + 8/5*a**3 - 9/5*a = 0.
-1, 0, 1, 3
Let w(k) be the first derivative of -2*k**6/105 + 2*k**5/35 - 4*k**3/21 + 2*k**2/7 + 25*k - 18. Let h(y) be the first derivative of w(y). Factor h(z).
-4*(z - 1)**3*(z + 1)/7
Factor 0 + 1/7*c**2 + 9/7*c.
c*(c + 9)/7
Let l(z) = 4*z**3 + 276*z**2 - 4*z - 8. Let w(s) = -4*s**3 - 277*s**2 + 3*s + 6. Let f(o) = 3*l(o) + 4*w(o). What is t in f(t) = 0?
-70, 0
Let b be (7/14)/((-2)/(-6)). Let z(f) be the first derivative of b*f**2 + f**3 - 3 + 0*f. Factor z(k).
3*k*(k + 1)
Let u(g) be the third derivative of g**6/30 - g**5/15 - 5*g**4/3 - 16*g**3/3 - 77*g**2. Suppose u(b) = 0. What is b?
-2, -1, 4
Let u(d) = 8*d**2 - d - 7. Let m be u(-2). Let 148*a - 6 - 6 + 184*a**2 - 340*a**3 - 7 + m = 0. Calculate a.
-2/5, -1/17, 1
Let o = 7317 - 36567/5. Solve 81/5*x**2 + 1/5 + o*x = 0.
-1/9
Let c be (-264)/(-36) + (-8)/6. Factor c*v - 3*v**2 + 46 - 46.
-3*v*(v - 2)
Let a(i) = 8*i**4 + 4*i**3 - 16*i**2 + 12 + 0*i**3 + 8*i**2 + 8*i**5. Let l(m) = -m**5 - m**4 + m**2 - 1. Let b(r) = a(r) + 12*l(r). What is o in b(o) = 0?
-1, 0, 1
Let w = 41199 + -41194. Factor 1/3*b**w - 2/3*b**2 + 2/3*b**4 + 0 - 1/3*b + 0*b**3.
b*(b - 1)*(b + 1)**3/3
Let g(h) be the first derivative of -h**5/10 + h**4/2 + 2*h**3 - 8*h**2 - 32*h - 912. Factor g(r).
-(r - 4)**2*(r + 2)**2/2
Let r be 1813/343 - (-5)/((-35)/2). Let -190/9*f**2 + 100/9*f + 2/9*f**r + 38/3*f**3 - 26/9*f**4 + 0 = 0. Calculate f.
0, 1, 2, 5
Let c(m) be the first derivative of -m**5 - 15*m**4/4 + 5*m**3/3 + 15*m**2/2 + 170. Let c(v) = 0. What is v?
-3, -1, 0, 1
Determine t, given that -15/2*t**2 + 3 + 9/2*t = 0.
-2/5, 1
Let m(j) = -5*j**2. Let x(b) = -31*b**2 + 1. Let y be (-92)/(-20) + 2/5. Let i(u) = y*x(u) - 30*m(u). Factor i(z).
-5*(z - 1)*(z + 1)
Let n(a) = a**2 - 11*a + 7. Let y be 66/(-55) + (-2)/(-10). Let t(m) = m**2 + m - 1. Let h(i) = y*n(i) - 3*t(i). Factor h(c).
-4*(c - 1)**2
Let t be (-3)/(-10)*(9 + -7)*4. Determine o so that -12/5*o**2 + t*o**4 - 9/5*o**3 - 3/5*o**5 + 0 + 12/5*o = 0.
-1, 0, 1, 2
Let g(p) = -2*p**2 + 13*p - 15. Let q be g(2). Let l(w) be the first derivative of w + 1/2*w**4 + 2 + 0*w**q - w**2 - 1/5*w**5. Factor l(a).
-(a - 1)**3*(a + 1)
Factor -368*a - 65*a**2 + 46*a**3 - 41*a**3 + 17*a**2 + 3*a**2 - 132 - 48*a**2.
(a - 22)*(a + 3)*(5*a + 2)
Let s(c) be the first derivative of 0*c - 16/7*c**2 + 36 - 4/21*c**3. What is t in s(t) = 0?
-8, 0
Let -12*k**2 - 2*k**4 + k**3 + 4*k**2 - 5*k**3 + 12*k**2 + 12*k**2 = 0. Calculate k.
-4, 0, 2
Let s(l) be the first derivative of -40*l**3 - 128/5*l**5 + 104*l**2 - 32*l + 42*l**6 - 185*l**4 + 22. Suppose s(o) = 0. What is o?
-1, 2/9, 2/7, 2
Let o(y) be the first derivative of 11 + 5*y**2 + 5/12*y**4 + 11*y + 5/2*y**3. Let b(z) be the first derivative of o(z). Factor b(s).
5*(s + 1)*(s + 2)
Let o be -4 + (-182)/(-52) - 23/(-6). Factor -25/6*v - 5/6*v**3 - 5/3 - o*v**2.
-5*(v + 1)**2*(v + 2)/6
Let c = -4474 - -22376/5. Factor 0*k**4 + 3/5*k**5 - 12/5*k**3 + c + 9/5*k - 6/5*k**2.
3*(k - 2)*(k - 1)*(k + 1)**3/5
Let w = -34049/17 - -2003. Suppose 4/17 - 6/17*a + w*a**2 = 0. Calculate a.
1, 2
Let v = 448561/420 - 1068. Let k(t) be the third derivative of 0*t + 0 - 2/21*t**3 - 2*t**2 + v*t**6 - 2/105*t**5 + 5/84*t**4. What is i in k(i) = 0?
1, 2
Suppose -6*z = -63 - 15. Factor z*x**2 - 2*x**2 - 9*x**2 - 8*x + 8.
2*(x - 2)**2
Let p = 129 - 113. Suppose 2*h - 5*m + p = -m, -5*h + 3*m - 12 = 0. Solve 1/3*r**3 - 4/3*r**2 + h + 0*r = 0.
0,