e of -j**6/280 - j**5/140 + j**4/14 + 2*j**3/7 + 8*j**2. Factor k(p).
-3*(p - 2)*(p + 1)*(p + 2)/7
Let j(p) be the third derivative of p**6/180 - p**5/60 - p**3/2 - p**2. Let c(a) be the first derivative of j(a). Factor c(n).
2*n*(n - 1)
Let f(j) = 3*j**4 - 20*j**3 + 18*j**2 - 2*j. Let k(p) = 35*p**4 - 240*p**3 + 215*p**2 - 25*p. Let i(y) = 25*f(y) - 2*k(y). Factor i(w).
5*w**2*(w - 2)**2
Suppose -32 = -2*n - 3*n - 4*w, 0 = -5*n + 4*w + 8. Let g(f) be the first derivative of -4 + 0*f + 0*f**3 + 1/2*f**2 - 1/4*f**n. Find c such that g(c) = 0.
-1, 0, 1
Factor -27/8*r + 27/8 - 9/4*r**2 + 1/8*r**5 + 7/8*r**4 + 5/4*r**3.
(r - 1)**2*(r + 3)**3/8
Let u(b) be the second derivative of b**8/4200 - b**6/900 + b**3/3 + 4*b. Let a(n) be the second derivative of u(n). Factor a(z).
2*z**2*(z - 1)*(z + 1)/5
Let v be 4 - (2 - 6/(-11)). Let d(u) be the first derivative of 9/22*u**4 - 14/11*u**3 + v*u**2 - 8/11*u + 3. Find m, given that d(m) = 0.
2/3, 1
Suppose 75*p**2 + 3*p - 8*p - 449*p**3 + 245*p**4 + 134*p**3 = 0. What is p?
0, 1/7, 1
Let c(t) = -3*t**2 - 3*t - 1. Suppose -z = -0*z + 3. Let j(m) = -1. Let r(b) = -b**2 - b - 4. Let w(g) = z*j(g) + r(g). Let l(d) = -c(d) + w(d). Factor l(s).
2*s*(s + 1)
Let z = 4 - 2. What is g in g**3 - 2*g**2 - 2*g**2 + 4*g**z - g = 0?
-1, 0, 1
Let 8*w**2 - 10*w + 8/3*w**3 + 8/3 = 0. Calculate w.
-4, 1/2
Let t = -63 + 43. Let f be (-72)/t - (-2)/5. Factor -n + 4*n**f + 0*n**3 + 4*n**2 + 7*n**3 - 2*n**2.
n*(n + 1)**2*(4*n - 1)
Let p(o) = -o**3 - 6*o**2 - 4*o + 5. Let c be p(-5). Solve -3/2*l**2 + 0 - 3/2*l**3 + c*l = 0 for l.
-1, 0
Let z(s) be the third derivative of -s**5/12 + 5*s**4/2 - 30*s**3 + 9*s**2 - s. Factor z(q).
-5*(q - 6)**2
Suppose v**2 - 3*v + v**2 - 3*v = 0. Calculate v.
0, 3
Let x(n) be the first derivative of -n**6/300 - n**5/50 + 4*n**3/15 - n**2/2 + 8. Let v(o) be the second derivative of x(o). Determine p, given that v(p) = 0.
-2, 1
Factor 0*n**3 + 0 + 0*n**2 + 8/15*n**4 + 0*n - 2/15*n**5.
-2*n**4*(n - 4)/15
Let c(r) = -r**3 - 9*r**2 + r + 11. Let a be c(-9). Factor 38/7*d**4 - a*d**5 - 30/7*d**3 + 4/7*d + 0 + 2/7*d**2.
-2*d*(d - 1)**3*(7*d + 2)/7
Let q(d) be the first derivative of 1/8*d**2 + 0*d + 1/8*d**4 + 1/4*d**3 - 3. Factor q(t).
t*(t + 1)*(2*t + 1)/4
Solve -30*o + 25*o**3 - 28*o**2 + 35*o**4 - 60*o**5 - 5 - 10*o**4 + 65*o**3 + 8*o**2 = 0 for o.
-1, -1/3, -1/4, 1
Let f be (-20)/(2*-2) + -3. Factor -d**f + 8*d + 1 - 5*d - 3*d.
-(d - 1)*(d + 1)
Let g(z) = 4*z**3 - 4*z**2 - 8*z. Let j(b) = -20*b**3 + 20*b**2 + 40*b. Let d(u) = 11*g(u) + 2*j(u). Factor d(r).
4*r*(r - 2)*(r + 1)
Let q = 64/95 - 2/285. Let g = q - 1/3. Solve 3*z**2 - 2*z + g = 0.
1/3
Let m(b) be the second derivative of b**8/6720 + b**7/1260 + b**6/720 - b**4/4 - 3*b. Let t(x) be the third derivative of m(x). Factor t(a).
a*(a + 1)**2
Let b = -69587/20 - -3476. Let k = b - -18/5. Factor 1/4*t - 1/2*t**2 + 1/4 - 1/2*t**3 + 1/4*t**4 + k*t**5.
(t - 1)**2*(t + 1)**3/4
Factor 6*f**2 + 14*f**2 + 28*f**3 + 4*f - 12*f.
4*f*(f + 1)*(7*f - 2)
Let g(s) = -7 + 12*s - 2*s + 2*s**2 - 10*s**2. Let j(m) = -24*m**2 + 30*m - 22. Let a(x) = 16*g(x) - 5*j(x). Factor a(l).
-2*(l - 1)*(4*l - 1)
Let g(j) = -6*j**5 + 9*j**4 - 9*j**3 + 15*j**2 - 9*j. Let p(m) = -3*m**5 + 5*m**4 - 5*m**3 + 7*m**2 - 4*m. Let u(z) = 4*g(z) - 9*p(z). Factor u(v).
3*v**2*(v - 1)**3
Let o(t) be the first derivative of 2 + 2/5*t**3 - 2/5*t**2 + 0*t. Suppose o(m) = 0. What is m?
0, 2/3
Let l = 6 + -2. Suppose -l*i + 4 = -4. Find z such that 0*z**i + z - 2*z - z**2 = 0.
-1, 0
Let l be (-240)/1000*(-1 + (-434)/6). Let 8/5 + 242/5*j**2 - l*j = 0. What is j?
2/11
Let k = 679 - 674. Factor 0 - 6/7*f**3 - 8/7*f**2 + 2/7*f**k + 4/7*f**4 + 8/7*f.
2*f*(f - 1)**2*(f + 2)**2/7
Let -6*t + 3/2*t**2 + 9/2 = 0. Calculate t.
1, 3
Let k(h) be the first derivative of -h**3/3 + 3*h**2 + 6*h - 5. Let w be k(6). Suppose w*s**4 - 10*s**4 + 6*s**4 - 2*s**3 = 0. What is s?
0, 1
Let w(l) = -l**2 + 11*l - 8. Let x be w(10). Let 2/3*h + 0 + 1/3*h**x = 0. Calculate h.
-2, 0
Let s(b) be the third derivative of 0*b**3 + 0*b + 0*b**4 + b**2 + 0*b**5 + 1/40*b**6 + 0. Solve s(z) = 0.
0
Suppose 0 = 3*p - 3 - 3. Let w be 5/p*(-32)/(-20). Factor 2*n**4 + 4*n**3 - 2*n - 2*n**5 - 4*n**w - 2 - n**2 + 5*n**2.
-2*(n - 1)**2*(n + 1)**3
Let k(u) be the second derivative of -u**4/72 + u**3/9 - u**2/4 - 12*u. Let k(p) = 0. What is p?
1, 3
Let v = 6 + -4. Factor -1 + 2*i**4 + 1 + i**2 - i**4 - v*i**3.
i**2*(i - 1)**2
Determine a so that -8/11*a**3 - 8/11*a**4 + 10/11*a + 4/11*a**2 + 4/11 - 2/11*a**5 = 0.
-2, -1, 1
Let i(n) = n**5 - 8*n**4 + 4*n**3 - 10*n**2 + 11*n + 2. Let o(d) = d**4 - d**3 + d**2 - d. Let b(s) = -3*i(s) - 24*o(s). Factor b(p).
-3*(p - 2)*(p - 1)*(p + 1)**3
Let o(l) be the first derivative of l**7/1050 + l**6/300 - l**5/300 - l**4/60 - 5*l**2/2 - 3. Let b(w) be the second derivative of o(w). Solve b(m) = 0 for m.
-2, -1, 0, 1
Let 65*n**3 - 13*n - 30*n**4 - 26*n - 10 + 10*n**2 + 4*n = 0. What is n?
-1/2, -1/3, 1, 2
Let k be (2 + 1)/(9/12). Determine n so that 3*n**k + n**3 - 6*n**2 - 4*n**4 - 7*n**3 - 2*n - n**4 = 0.
-1, 0
Let a(c) = c**5 + 3*c**3 - 5*c**2 - 9*c + 5. Let g(r) = -2*r**5 - 4*r**3 + 8*r**2 + 14*r - 8. Let i(x) = 8*a(x) + 5*g(x). Factor i(p).
-2*p*(p - 1)**2*(p + 1)**2
Let w = -13 + 19. Let h be (w/45)/(4/6). What is u in h*u**2 + 4/5*u + 4/5 = 0?
-2
Let i = 7 + -2. Let g(p) be the second derivative of -1/15*p**3 + 1/50*p**i + 0*p**2 - 2*p + 0*p**4 + 0. Let g(z) = 0. Calculate z.
-1, 0, 1
Let j(o) be the second derivative of 0 + 5/6*o**4 - 4*o + 8/3*o**3 - 4*o**2. Factor j(l).
2*(l + 2)*(5*l - 2)
Factor 1/5*a**3 + 1/5*a + 0 - 2/5*a**2.
a*(a - 1)**2/5
Suppose -1 - 5 = 2*d + 4*m, 0 = -4*d + m + 15. Factor 5*o**2 + 2*o + 2*o**3 + o**4 + o**d + 3*o**3 - 2*o**3.
o*(o + 1)**2*(o + 2)
Let b(d) = 2*d**2 - 6 + 4*d - 2*d + 2*d + 2 - 2*d**3. Let l(f) = -3*f**3 + 2*f**2 + 5*f - 5. Let g(h) = -5*b(h) + 4*l(h). Factor g(n).
-2*n**2*(n + 1)
Let g be (1 + -2)*(1 + -3). Let r = 0 + g. Factor 2*f - 2*f - f**r + 1.
-(f - 1)*(f + 1)
Let s(d) be the third derivative of 1/30*d**5 + 0 + 1/12*d**4 + 9*d**2 + 0*d - 1/168*d**8 + 1/30*d**7 - 1/6*d**3 - 1/15*d**6. Factor s(r).
-(r - 1)**4*(2*r + 1)
Let t be (17/12 + (-9)/12)*3. Let p(i) be the second derivative of 1/4*i**4 - 1/20*i**5 - t*i**2 - i + 0*i**3 + 0. Determine u so that p(u) = 0.
-1, 2
Suppose -5*a + 8 = -a. Factor -7*j**3 - 9*j**2 - 2*j**3 - 3*j + 21*j**a.
-3*j*(j - 1)*(3*j - 1)
Let h = 1 + 1. Find i such that -i**3 - 1 - 3*i**h - 2*i - 3*i + 2*i = 0.
-1
Let y be ((-1)/5)/(7/(-35)). Let l be y*(-2 - -3) - -3. Factor -1/2*b**3 + 1/6*b - 1/3*b**5 - 5/6*b**l + 0 + 1/6*b**2.
-b*(b + 1)**3*(2*b - 1)/6
Let t be 1 + 1 + 3162/(-15). Let q = 210 + t. Let -q*m + 11/5*m**2 + 1/5 + 8/5*m**5 - 12/5*m**4 - 2/5*m**3 = 0. Calculate m.
-1, 1/2, 1
Let h(z) be the second derivative of z**4/6 + z**3/3 - 2*z**2 + 3*z. Factor h(d).
2*(d - 1)*(d + 2)
Let t(z) be the first derivative of z**6/1440 - z**3 - 2. Let g(k) be the third derivative of t(k). Determine d so that g(d) = 0.
0
Suppose 4*y = 3*y + 2*y. Let o(l) be the first derivative of -9/2*l**6 - 9*l**4 + 3 + y*l**2 + 0*l + 8/3*l**3 + 54/5*l**5. Let o(p) = 0. Calculate p.
0, 2/3
Let g = -655/9 + 73. Solve 2/9*y**4 + 0 - g*y**3 - 2/9*y**2 + 2/9*y = 0 for y.
-1, 0, 1
Let h = -79/4 - -253/12. Determine n so that 2/3*n - 2/3*n**3 - 4/3*n**2 + h = 0.
-2, -1, 1
Let f(l) be the first derivative of 64*l**5/15 + 8*l**4/3 + 4*l**3/9 + 11. Suppose f(s) = 0. What is s?
-1/4, 0
Determine p, given that 4/3*p + 1/3*p**2 + 4/3 = 0.
-2
Solve 1/2*v**2 + 5*v + 25/2 = 0 for v.
-5
Let n be 9/(-6) + 9/6. Let u(f) be the second derivative of 2*f + n*f**2 + 4/45*f**6 - 1/9*f**3 + 2/9*f**4 + 0 - 1/63*f**7 - 1/5*f**5. Factor u(s).
-2*s*(s - 1)**4/3
Let b = -65 - -67. Let i(a) be the first derivative of -1/15*a**5 + 0*a - 1/12*a**4 + b + 1/6*a**2 + 1/9*a**3. Determine n so that i(n) = 0.
-1, 0, 1
Let p(v) be the third derivative of v**8/1680 + v**7/840 - v**6/360 - v**5/120 + v**3/6 + 3*v**2. Let r(b) be the first derivative of p(b). Factor r(s).
s*(s - 1)*(s + 1)**2
Let c(h) be the first derivative of -3/4*h**2 - 1/4*h**3 + 6 + 0*h. Factor c(p).
-3*p*(p + 2)/4
Suppose 3*m - 5*s = 4, 0*m + 3 = 2*m - 3*s. Suppose 0 = 2*i + i - 6. Factor 2*y**2 + 6*y**m + 4*y*