- p*g**2 = 0.
0
Determine r so that 1/6 - 2/3*r + 1/2*r**2 = 0.
1/3, 1
Let y(v) = 3*v + 3*v**3 + v**3 - 2*v**2 - 3*v**3 - 1. Let o be y(2). Factor -9*p**4 + 12*p**5 - 2*p**3 - 3*p**2 - 7*p**3 - 15*p**o.
-3*p**2*(p + 1)**3
Factor -20/3*j - 4/3*j**3 - 8/3 - 16/3*j**2.
-4*(j + 1)**2*(j + 2)/3
Let h(o) be the first derivative of o**4/28 + o**3/21 - 17. Factor h(s).
s**2*(s + 1)/7
Let w(v) be the first derivative of v**5/240 + v**4/48 + v**3/24 + v**2 - 2. Let x(b) be the second derivative of w(b). Factor x(h).
(h + 1)**2/4
Let v(i) = -i**2 + 6*i + 6. Let j be v(6). Factor 1 - t**3 - 2*t**3 - j*t**2 - 1.
-3*t**2*(t + 2)
Let f = -1027 - -5137/5. What is q in -2/5 - 6/5*q**2 - f*q**3 - 6/5*q = 0?
-1
Suppose 0*j + 4 = j. Factor 0*p**4 + 6*p**4 + 6*p**3 - 3*p**j + 3*p**2.
3*p**2*(p + 1)**2
Let y(b) be the first derivative of b**3/24 + b**2/8 + b/8 + 5. Determine d, given that y(d) = 0.
-1
Suppose 2*z**4 + 9*z**3 + 9*z**2 + 2*z**4 + 2*z + 4*z**3 + 2*z**2 = 0. What is z?
-2, -1, -1/4, 0
Suppose i = -2*i + 6. Let o(w) = w**2 - 20*w + 25. Let n(l) = -l**2 + 41*l - 49. Let m(p) = i*n(p) + 5*o(p). Factor m(z).
3*(z - 3)**2
Factor 4*f**2 + 5*f - 27*f**3 + 9*f**3 + 7*f - 4*f**4 + 6*f**3.
-4*f*(f - 1)*(f + 1)*(f + 3)
Let d(w) be the first derivative of -8/3*w - 2 + 4/3*w**2 + 2/3*w**3 + 2/15*w**5 - 2/3*w**4. Factor d(j).
2*(j - 2)**2*(j - 1)*(j + 1)/3
Let u(z) be the first derivative of -2*z**6/15 + 8*z**5/25 - z**4/5 + 1. Let u(v) = 0. What is v?
0, 1
Determine j, given that 3/8*j**4 + 0*j + 3/4*j**3 + 3/8*j**2 + 0 = 0.
-1, 0
Let v(l) be the third derivative of -l**7/980 + l**6/1260 + l**5/210 + l**3/3 + 3*l**2. Let b(s) be the first derivative of v(s). Factor b(y).
-2*y*(y - 1)*(3*y + 2)/7
Factor 219*m - 108 - 39 - 3*m**2 - 261*m.
-3*(m + 7)**2
Solve 5*l**3 + 6*l**2 + 10*l**5 - 3*l**5 - 12*l**3 - 6*l**5 = 0.
-3, 0, 1, 2
Let a(b) be the first derivative of -10*b**3 + 2*b**2 - 1. Suppose a(f) = 0. Calculate f.
0, 2/15
Let u be 24/(-108) + 4871/495. Let g = 49/5 - u. Factor g*p - 2/11*p**4 + 2/11*p**2 - 2/11*p**3 + 0.
-2*p*(p - 1)*(p + 1)**2/11
Let t(a) = -a**2 + 12*a - 10. Let w be t(11). Suppose -b = -4*j + w, -2*j + 11 = 4*b - b. Suppose -6 + 2 + 3 - k**b + k + k**2 = 0. Calculate k.
-1, 1
Suppose -3*r = r - 12. Let x(d) = 2*d - 4. Let j be x(r). Factor 2/5*y**j + 18/5*y**4 + 12/5*y**3 + 0 + 0*y + 8/5*y**5.
2*y**2*(y + 1)**2*(4*y + 1)/5
Factor -27*k + 1 + 25*k**2 - 5*k**3 + k + 14 - 9*k.
-5*(k - 3)*(k - 1)**2
Let z(g) be the first derivative of 8*g**5/5 + 9*g**4 + 12*g**3 - 16*g**2 - 48*g + 42. Solve z(o) = 0.
-2, -3/2, 1
Suppose -21 = 5*v + 4*a, 0 = -3*a + a - 8. Let w = v - -3. Factor -2*u**3 - u**4 - 4*u**w + u**2 - u**3 - u.
-u*(u + 1)**3
Suppose 5*h + 3 = -4*b, -b + 12 = b - 2*h. Factor -2 + 3 + 2*k**2 - 6 + b.
2*(k - 1)*(k + 1)
Factor -4/9*g - 2/9*g**2 + 2/3.
-2*(g - 1)*(g + 3)/9
Let g = -9029/70 - -129. Let n(q) be the second derivative of -1/21*q**4 - g*q**5 - 2*q + 0 + 0*q**2 + 0*q**3. Solve n(w) = 0.
-2, 0
Find a, given that -8/3 - 1/3*a**2 + 3*a = 0.
1, 8
Let w be (968/(-100) - -10)/(4/10). Solve 6/5*b**4 - 6/5*b**2 + 0 + 2/5*b**3 - w*b + 2/5*b**5 = 0 for b.
-2, -1, 0, 1
Let v = -28 - -33. Suppose 5*s = 2*h - 6*h - 5, v*s = 4*h - 45. Determine o, given that 2/5*o + 0*o**3 + 0 - 4/5*o**2 + 4/5*o**4 - 2/5*o**h = 0.
-1, 0, 1
Let s = 2 - 0. Solve -2*n**3 + 4*n**2 + 7*n**5 + n - 4*n**s - 6*n**5 = 0 for n.
-1, 0, 1
Let g(n) be the first derivative of -n**6/9 + 4*n**5/15 + n**4/2 - 8*n**3/9 - 4*n**2/3 - 54. Factor g(t).
-2*t*(t - 2)**2*(t + 1)**2/3
Let p = -59 - -297/5. Let -1/5*m + 4/5*m**2 - 2/5 - p*m**4 - 1/5*m**5 + 2/5*m**3 = 0. Calculate m.
-2, -1, 1
Solve 2/13*c**2 + 2/13 - 4/13*c = 0 for c.
1
Suppose -6 = 36*l - 38*l. Let g(p) be the second derivative of 0*p**l - 1/36*p**4 + 0 + 0*p**2 + 1/60*p**5 + p. Factor g(o).
o**2*(o - 1)/3
Suppose 0*w = 4*w + 4. Let z(r) = r**2 - r - 1. Let q be z(w). Let -d**2 + 0*d + q + 0*d = 0. Calculate d.
-1, 1
Factor 0 - 1/4*m**2 + 1/2*m.
-m*(m - 2)/4
Let r(j) be the second derivative of 13*j**4/9 + 56*j**3/9 + 8*j**2/3 + 25*j. Factor r(c).
4*(c + 2)*(13*c + 2)/3
Let o(y) be the third derivative of y**8/6720 - y**7/3360 + y**3/6 + y**2. Let t(c) be the first derivative of o(c). Solve t(n) = 0 for n.
0, 1
Solve -2*x**3 + 34 + 5*x**3 - 44 + 10*x**2 - 5*x + 2*x**3 = 0.
-2, -1, 1
Let z(f) be the third derivative of -25*f**8/168 - f**7/3 + 13*f**6/20 + 19*f**5/30 + f**4/6 + 69*f**2. Let z(u) = 0. What is u?
-2, -1/5, 0, 1
Let p be (-3)/105 + (-6)/(-14). Let i(k) be the first derivative of -2*k**3 + p*k**5 + 4*k - 3 - 1/2*k**4 + k**2. Determine f, given that i(f) = 0.
-1, 1, 2
Let q(n) be the second derivative of 0*n**3 + 1/120*n**5 + 1/180*n**6 + 0*n**2 + 0 + 0*n**4 + 4*n. Factor q(z).
z**3*(z + 1)/6
Factor -2/5 - 2/5*j**4 + 0*j**3 + 4/5*j**2 + 0*j.
-2*(j - 1)**2*(j + 1)**2/5
Let q(d) = -16*d**2 - 20*d - 8. Let t(g) = g**4 + g**3 + g**2. Let r(v) = -q(v) - 4*t(v). Factor r(i).
-4*(i - 2)*(i + 1)**3
Let l(z) = 3*z**2 - 20*z + 16. Let j be l(6). Factor -3/4*p - 3/4*p**5 + 3/4 + 3/4*p**j - 3/2*p**2 + 3/2*p**3.
-3*(p - 1)**3*(p + 1)**2/4
Let i(v) = v. Let g be i(2). Let 1/2*a**5 - 3/2*a + a**3 - a**g + 3/2*a**4 - 1/2 = 0. Calculate a.
-1, 1
Let v(a) be the first derivative of 1/6*a**4 + 2/15*a**5 + 0*a**2 + 0*a + 2/27*a**3 + 1/27*a**6 - 1. Let v(x) = 0. Calculate x.
-1, 0
Let q = 238 + -1662/7. Solve -2/7*m**2 - 2/7 - q*m = 0.
-1
Let c(k) be the second derivative of 1/18*k**4 - 1/3*k**3 + 1/45*k**6 - 2/3*k**2 + 2*k + 1/10*k**5 + 0. Solve c(j) = 0 for j.
-2, -1, 1
Let h(y) be the third derivative of -y**6/40 + y**5/5 - 3*y**4/8 - 44*y**2. Suppose h(p) = 0. Calculate p.
0, 1, 3
Let f(q) be the second derivative of -q**8/26880 - q**7/10080 + q**4/2 + 7*q. Let k(x) be the third derivative of f(x). Find g, given that k(g) = 0.
-1, 0
Let c(y) be the third derivative of y**5/20 - y**3/3 + 4*y**2. Let d(k) = -6*k**2 + 5. Let p(x) = -5*c(x) - 2*d(x). Factor p(m).
-3*m**2
Let k(p) be the first derivative of 2/55*p**5 + 2/33*p**3 + 0*p + 0*p**2 - 2 - 1/11*p**4. Factor k(h).
2*h**2*(h - 1)**2/11
Let y be (-2)/(-1) - (-25)/(-15). Factor -4/3 - 5/3*h**2 - 8/3*h - y*h**3.
-(h + 1)*(h + 2)**2/3
Factor -40/3*d**3 + 100*d**2 - 1000/3*d + 2/3*d**4 + 1250/3.
2*(d - 5)**4/3
Let l = -2/11281 + -22168/2222357. Let z = l - -2567/591. Let 2/3*i - z*i**2 + 7/3*i**5 - 23/3*i**4 + 9*i**3 + 0 = 0. What is i?
0, 2/7, 1
Let l = -14/11 - -148/99. Factor -4/9 + 2/3*v - l*v**2.
-2*(v - 2)*(v - 1)/9
Let k(w) = -4*w + 4. Let c be k(-2). Factor -5*n**2 + c*n**2 - 7*n**2 + n**3.
n**3
Let y(v) be the second derivative of -v**6/10 + 3*v**5/20 + v**4/4 - v**3/2 - 7*v. What is d in y(d) = 0?
-1, 0, 1
Let n(j) be the second derivative of j**4/2 + 8*j**3/3 + 4*j**2 + 2*j. Factor n(h).
2*(h + 2)*(3*h + 2)
Factor 0*l**2 - 3*l**5 - 4*l**4 - 6*l**3 + 2*l + 7*l + 6*l**2 - 5*l**4 + 3.
-3*(l - 1)*(l + 1)**4
Let r = -27/5 - -59/10. Factor r*l - 1 - 1/2*l**3 + l**2.
-(l - 2)*(l - 1)*(l + 1)/2
Let l(w) be the first derivative of -3 - 1/15*w**6 + 0*w**3 + 1/5*w**4 + 0*w**5 - 1/5*w**2 + 0*w. Factor l(c).
-2*c*(c - 1)**2*(c + 1)**2/5
Let g be 55/20 + 3/(-4). Let l(w) be the second derivative of -1/36*w**4 - 1/6*w**3 + g*w + 0 - 1/3*w**2. What is y in l(y) = 0?
-2, -1
Let u = 13 - 17. Let m be (2*1)/(4 - u). Factor 1/4*p**2 + 0*p**3 - m*p**4 + 0*p + 0.
-p**2*(p - 1)*(p + 1)/4
Let r = 39 + -24. Let l be -1 + -3 + 66/r. Determine k so that l*k**2 - 2/5 + 0*k = 0.
-1, 1
Let o = 416 - 180. Let y be -2 - (o/(-28) + 1). Factor -y*n**4 - 2*n**5 - 30/7*n**3 - 2/7*n**2 + 4/7*n + 0.
-2*n*(n + 1)**3*(7*n - 2)/7
Let b(q) = q**3 - 11*q**2 + 7*q + 33. Let p be b(10). Solve -9/4*s + 3/4 + 3/4*s**2 + 9/4*s**p - 3/2*s**4 = 0.
-1, 1/2, 1
Let f(h) be the second derivative of -h**4/12 - h**3/3 + 3*h**2/2 + 21*h. Factor f(l).
-(l - 1)*(l + 3)
Let a(c) be the third derivative of -3*c**8/560 + c**7/175 + 29*c**6/600 + c**5/150 - c**4/6 - 4*c**3/15 - 3*c**2. Find q such that a(q) = 0.
-1, -2/3, 1, 2
Suppose y + m + 37 = -4*m, 3*y - 3*m = -129. Let b be y/(-15) + 3/15. Factor -7*o**b - 7*o**3 - o**2 + 8*o - 4 + 5*o**2 + 6*o.
-2*(o - 1)*(o + 1)*(7*o - 2)
Suppose 4*z = -7*p + 2*p + 20, -4*z - 12 = -3*p. Suppose 2 = p*j + k, -j + 2*k = 2*j - 7. Determine n, given that -1 + 2 + 4*n + 2*n**2 + j = 0.
-1
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