2*p - 1. Let f be (-2)/(j - -2) + 4. Factor 0*u**2 + 8*u**f + 7*u**4 + 8*u**3 - 5*u**4.
2*u**2*(u + 2)**2
Determine z, given that -2/3*z**4 + 2/3*z + 2/3*z**2 + 0 - 2/3*z**3 = 0.
-1, 0, 1
Suppose 6*r + 30 - 42 = 0. Factor 1/4*m**4 - r + 3*m - 1/2*m**2 - 3/4*m**3.
(m - 2)**2*(m - 1)*(m + 2)/4
Find p such that -31*p**2 + 26*p + 8*p**3 + 0*p**3 + 3*p**3 + 4 - 10*p = 0.
-2/11, 1, 2
Let f(b) = -9*b**2 + 3*b - 2. Let k be 2/(-4) - 196/(-8). Let x(t) = t**2. Let a(m) = k*x(m) + 3*f(m). Factor a(p).
-3*(p - 2)*(p - 1)
Let p(g) = -7*g + 28. Let y be p(4). Let r(n) be the second derivative of -4*n + 0*n**4 - 1/2*n**3 + y + 0*n**2 + 3/20*n**5. Factor r(u).
3*u*(u - 1)*(u + 1)
Solve 5*g**3 + 13 - 13 - 20*g = 0.
-2, 0, 2
Find o, given that 0 - 2/5*o**2 + 2/5*o = 0.
0, 1
Let w = 26400 - 1715787/65. Let d = w + -27/13. Solve 0 - 1/5*n**4 + d*n**3 + 8/5*n - 12/5*n**2 = 0 for n.
0, 2
Factor -3*d**2 + 285 + 20*d - 5*d - 297.
-3*(d - 4)*(d - 1)
Let k(z) be the first derivative of z**3/12 - 3*z**2/8 - 1. Factor k(r).
r*(r - 3)/4
Let z(l) be the third derivative of l**5/30 - l**4/2 + 3*l**3 - 21*l**2. Determine v, given that z(v) = 0.
3
Let j be 1633/426 + (-2)/(-12). Solve 2/11*x**5 + 0*x**2 + 0 + 0*x - 4/11*x**j + 2/11*x**3 = 0.
0, 1
Factor -24/11*g**2 - 4/11 + 18/11*g + 10/11*g**3.
2*(g - 1)**2*(5*g - 2)/11
Let l(p) be the second derivative of -p**7/105 - p**6/75 + p**5/50 + p**4/30 - 13*p. Solve l(o) = 0.
-1, 0, 1
Let t(a) be the first derivative of a**4/16 - a**3/4 + 3*a**2/8 - a/4 - 7. Factor t(g).
(g - 1)**3/4
Let r(l) = -l**3 + 5*l**2 - 3*l**2 - 2*l**3 + 3*l - 2*l + 2. Let v(k) = 16*k**3 - 11*k**2 - 5*k - 11. Let t(w) = 11*r(w) + 2*v(w). Factor t(s).
-s*(s - 1)*(s + 1)
Let b be 2/52*(-14)/(-4). Let c = b - -3/26. Suppose 0 - 5/4*a**2 + 21/4*a**4 + 1/4*a + c*a**3 - 9/2*a**5 = 0. Calculate a.
-1/2, 0, 1/3, 1
Let u be (-8)/3*36/16. Let r = 8 + u. Factor 9*v**3 + 11*v**2 - 15*v - v**2 + r*v**2 - 6.
3*(v - 1)*(v + 2)*(3*v + 1)
Let x(r) = r**2 + 5*r - 14. Suppose 3*d + 21 = v, 4*d - 2*v + 5*v + 28 = 0. Let b be x(d). Factor 0 - 1/3*i - 1/3*i**5 + 0*i**2 + 2/3*i**3 + b*i**4.
-i*(i - 1)**2*(i + 1)**2/3
Let x = 4 + -2. Factor 8/7*q**x + 0 + 2/7*q**3 + 8/7*q.
2*q*(q + 2)**2/7
Suppose -3 + 1 = 2*v. Let k = v + 3. Find t such that 6/5*t**k + 2*t**3 + 0 - 4/5*t = 0.
-1, 0, 2/5
Let f be ((-3)/1)/3*-29. Let i = -27 + f. Solve -3/2*j**3 - 3*j + 9/2*j**i + 0 = 0 for j.
0, 1, 2
Let r(o) be the second derivative of -3/2*o**2 - 1/48*o**4 + o + 0 - 1/240*o**5 + 0*o**3. Let n(m) be the first derivative of r(m). Factor n(y).
-y*(y + 2)/4
Let x(h) be the second derivative of -h**5/15 - 2*h**4/9 + 2*h**3/9 + 4*h**2/3 - 14*h. Factor x(i).
-4*(i - 1)*(i + 1)*(i + 2)/3
Let d(q) be the second derivative of 1/12*q**4 - 1/168*q**7 + 0 + 0*q**2 + 1/30*q**6 - 2*q - 3/40*q**5 - 1/24*q**3. Let d(h) = 0. What is h?
0, 1
Let f(m) be the second derivative of m**7/42 + m**6/5 + 3*m**5/5 + 5*m**4/6 + m**3/2 + 6*m. Let f(d) = 0. What is d?
-3, -1, 0
Let a(p) = -4*p + 76. Let l be a(18). Let y(r) be the third derivative of r**3 - 3/8*r**l + 0*r - 3/70*r**7 - r**2 + 7/40*r**6 + 0 - 3/20*r**5. Factor y(f).
-3*(f - 1)**3*(3*f + 2)
Let j(b) = -b**3 + b**2 + 2. Let r be j(2). Let z be (r/(-5))/(1/8). Determine x so that z*x**2 + 14/5*x**3 - 8/5*x + 0 - 2*x**4 = 0.
-1, 0, 2/5, 2
Let y(s) be the second derivative of -s**7/21 + 9*s**5/10 + 21*s. Factor y(w).
-2*w**3*(w - 3)*(w + 3)
Let n(s) = 56*s**3 + s**2 + 2*s + 1. Let d be n(-1). Let c be 16/d - 4/(-14). Factor c + 1/4*x**2 - 1/4*x.
x*(x - 1)/4
Let x be (1*-2 - -2) + 0. Let v(i) = -i**2 + i + 11. Let u be v(x). Let g(s) = 5*s**3 + 3*s. Let p(b) = -14*b**3 - 8*b. Let n(j) = u*g(j) + 4*p(j). Factor n(a).
-a*(a - 1)*(a + 1)
Let l(u) = -9*u**4 - 24*u**3 - 4*u**2 + 6*u + 5. Let k(h) = 18*h**4 + 48*h**3 + 9*h**2 - 12*h - 9. Let b(s) = 5*k(s) + 9*l(s). Find d, given that b(d) = 0.
-2, -1, 0, 1/3
Let c be (8/48)/(2/42). Factor c*i**2 - i - 4*i**3 + 3/2*i**4 + 0.
i*(i - 1)**2*(3*i - 2)/2
Let c(w) = -11*w**3 + 15*w**2 - 4*w. Let y(t) = -10*t**3 + 15*t**2 - 5*t. Let q(m) = -5*c(m) + 6*y(m). Let q(v) = 0. Calculate v.
0, 1, 2
Let d be 2/(-4) + (-345)/(-6). Let a be (-5)/(-9)*d - -1. Factor 0 - 218/3*g**3 + 84*g**4 + 24*g**2 - 8/3*g - a*g**5.
-2*g*(g - 1)**2*(7*g - 2)**2/3
Let j(v) be the third derivative of -v**6/160 - 7*v**5/240 - v**4/24 + 36*v**2. Factor j(z).
-z*(z + 1)*(3*z + 4)/4
Let o(k) = 3*k**3 - 25*k**2 + 15*k + 45. Let f(q) = -8*q**3 + 75*q**2 - 45*q - 135. Let m(b) = -2*f(b) - 7*o(b). Determine s so that m(s) = 0.
-1, 3
Let d = -851/5 + 171. Let 2*a**2 - d*a + 0 = 0. What is a?
0, 2/5
Let q = 3461/5 - 692. Factor 3/5*o**2 + 3/5*o + q*o**3 + 1/5.
(o + 1)**3/5
Let z(y) be the second derivative of 5*y**7/168 - y**6/18 + y**5/30 - y**3/2 - y. Let k(b) be the second derivative of z(b). Solve k(s) = 0 for s.
0, 2/5
Let r(y) be the second derivative of -3*y**2 + 3/2*y**3 + 0*y**4 + 0 + 5*y - 3/20*y**5. Factor r(m).
-3*(m - 1)**2*(m + 2)
Let d be -4*(3 - 26/8). Let f(q) = 2*q**2 + 8*q + 2. Let i(b) = -1. Let l(n) = d*f(n) - 6*i(n). Factor l(m).
2*(m + 2)**2
Let f = 380 + -554. Let l = -863/5 - f. Factor v**3 + l*v + 9/5*v**2 + 2/5 + 1/5*v**4.
(v + 1)**3*(v + 2)/5
Let g(t) be the second derivative of 7*t**6/6 - t**5/2 - 35*t**4/12 + 5*t**3/3 - 3*t. Factor g(d).
5*d*(d - 1)*(d + 1)*(7*d - 2)
Let h be ((-48)/2)/(-3) + -2. Let n be 6/h*0/2. Factor n*b + 1/4*b**3 + 0*b**2 + 0.
b**3/4
Factor -13*y**2 + 62*y**2 - 6*y**4 + 15*y**4 + y**5 + 63*y**3 + 6*y**4.
y**2*(y + 1)*(y + 7)**2
Let x(y) be the third derivative of y**7/10080 + y**4/3 - 7*y**2. Let d(t) be the second derivative of x(t). Suppose d(z) = 0. What is z?
0
Let f = -5 + 9. Suppose 3*z + 2*z - 6*z - 2*z**2 - 3*z**5 + 2*z**4 + f*z**5 = 0. Calculate z.
-1, 0, 1
Suppose 0 = -2*y - 2*h + 16, 4*y - 25 - 4 = -3*h. Suppose y*s - s = 8. Determine k, given that 3*k - 2*k + 0*k + k**3 - k**s + k**4 - 2*k = 0.
-1, 0, 1
Suppose 4*z = -z - 105. Let j be 8/(-16) + z/(-10). Factor -6/5*q**5 - 2/5*q**3 + 0*q**2 + 0*q + 0 - j*q**4.
-2*q**3*(q + 1)*(3*q + 1)/5
Let u(o) be the first derivative of 4/9*o**2 + 4 + 2/45*o**5 + 2/9*o + 4/9*o**3 + 2/9*o**4. Suppose u(p) = 0. What is p?
-1
Let k be (-10)/(-1)*(-1)/(-2). Factor k*z + 0*z**2 + 0*z**2 + z - 9 - z**2.
-(z - 3)**2
Let q be ((-6)/(-9))/((-30)/(-72)). What is p in -16/5*p**2 + 22/5*p**3 + 0 - q*p + 6*p**4 = 0?
-1, -2/5, 0, 2/3
Let b(i) = 142*i**4 + 98*i**3 - 54*i**2 + 6*i - 8. Let d(m) = 95*m**4 + 65*m**3 - 36*m**2 + 4*m - 5. Let o(n) = 5*b(n) - 8*d(n). Let o(k) = 0. What is k?
-1, 0, 1/5
Let n(k) = k**5 - 4*k**4 - 2*k**3 + 4*k**2 + k - 4. Let x(f) = f**4 - f**2 + 1. Let v = 3 + -2. Let g(r) = v*n(r) + 4*x(r). Find m such that g(m) = 0.
-1, 0, 1
Let y(t) be the third derivative of -t**8/1008 + t**7/630 + t**6/72 + t**5/60 - 16*t**2. Factor y(s).
-s**2*(s - 3)*(s + 1)**2/3
Let o(k) = -3*k**3 + 7*k**2 - 3*k - 1. Let r(q) = 3*q**3 - 6*q**2 + 2*q + 1. Let y(m) = -5*o(m) - 6*r(m). Solve y(l) = 0.
-1, 1/3, 1
Let d(b) be the first derivative of -3*b**4/28 + 3*b**2/14 + 5. Factor d(p).
-3*p*(p - 1)*(p + 1)/7
Let h be 4*(1 - 0/(-1)). Let y be -2*h/64*-2. Factor 0 + 1/4*i + y*i**4 - 1/4*i**3 - 1/4*i**2.
i*(i - 1)**2*(i + 1)/4
Let i(f) = f**3 + 1. Let d be (4/8)/(1/2). Let j be i(d). Solve 4/7*u + j*u**2 + 0 + 10/7*u**3 = 0 for u.
-1, -2/5, 0
Let g be (-12)/(-8) - (-2)/4. Let k = 0 + g. Factor -2*p**5 + 8*p**4 - 2*p**4 - 4*p**2 - k - 2*p**3 - 4*p + 10*p - 2*p**3.
-2*(p - 1)**4*(p + 1)
Let i(v) = -17*v**4 - 4*v**3 + 16*v**2 + 29*v - 13. Let h(s) = 4*s**4 + s**3 - 4*s**2 - 7*s + 3. Let m(r) = 26*h(r) + 6*i(r). Let m(j) = 0. Calculate j.
-2, -1, 0, 2
Factor 0*d + 2/13*d**3 - 6/13*d**2 + 8/13.
2*(d - 2)**2*(d + 1)/13
Let p(z) = 2*z**3 - 5*z**2 - 4*z + 1. Let f be p(5). Let g = f - 522/5. Factor -8/5*h - 2/5*h**4 - g*h**3 - 2/5 - 12/5*h**2.
-2*(h + 1)**4/5
Let h(b) = 6*b**3 - 6*b**2 - 6*b + 2. Let c(g) = -g**3 + g**2 + g + 1. Let k(m) = -2*c(m) - h(m). Factor k(w).
-4*(w - 1)**2*(w + 1)
Let f(w) = w**3 + 7*w**2 + 10*w + 3. Let o be f(-5). Let c = o - -1. Let 686/9*a**5 + 0*a - 196/9*a**c + 0 + 16/9*a**2 - 56/9*a**3 = 0. Calculate a.
-2/7, 0, 2/7
Let p be ((-24)/16 + 1)*0. Determine k, given that p*k**2 + 2/15*k - 2/15*k**3 + 0 = 0.
-1, 0, 1
Let b(h) be the first derivative of 2 - 25*