1
Let x(b) = -12*b**3 - 3*b**2 + 39*b + 21. Let f(y) = 6*y**3 + 2*y**2 - 20*y - 11. Let i(g) = 9*f(g) + 5*x(g). Factor i(a).
-3*(a - 2)*(a + 1)*(2*a + 1)
Let r(j) be the first derivative of -j**4/30 + j**3/15 + 2*j**2/5 + 3*j + 2. Let m(w) be the first derivative of r(w). Find s such that m(s) = 0.
-1, 2
Let q(j) be the third derivative of -j**8/5040 + j**7/2520 - 5*j**3/3 - 8*j**2. Let m(d) be the first derivative of q(d). Find i, given that m(i) = 0.
0, 1
Let d be (4/(-14))/((-12)/168). Let l be (d/2)/(6/15). Determine m, given that -4/7*m**3 + 2/7 + 2/7*m + 2/7*m**l + 2/7*m**4 - 4/7*m**2 = 0.
-1, 1
Let z be (-1)/(-1) - (-2 + 0). Let i be 35/14 + (-117)/54. Let -1/3 - i*s + 1/3*s**z + 1/3*s**2 = 0. What is s?
-1, 1
Find s such that 6*s**2 - s - 2*s**3 - s - 184 + 130 + 20*s = 0.
-3, 3
Suppose 5*p + 3 + 2 = 0. Let v be (-12)/2*p/3. Let -h**4 + 0 - v*h**3 - 1/4*h - 5/4*h**2 = 0. Calculate h.
-1, -1/2, 0
Let h(q) be the first derivative of 14*q**3/45 + 2*q**2/15 - 5. Factor h(j).
2*j*(7*j + 2)/15
Let m(t) be the third derivative of 2*t**7/525 + t**6/200 - 7*t**5/100 + 17*t**4/120 - t**3/10 + 11*t**2. Let m(c) = 0. What is c?
-3, 1/4, 1
Let h(r) be the third derivative of r**6/40 + r**5/20 - r**4/8 - r**3/2 + 4*r**2. Factor h(q).
3*(q - 1)*(q + 1)**2
Let y(r) be the first derivative of -8/3*r - 3 - 2/9*r**3 + 4/3*r**2. Factor y(h).
-2*(h - 2)**2/3
Suppose -2*w + 4*j = -14, 5*j - 20 = -5*w - 0*j. Let s(m) be the second derivative of -1/15*m**4 - 1/50*m**w - 1/15*m**3 + 0 + 0*m**2 - m. Factor s(u).
-2*u*(u + 1)**2/5
Let t(m) = -1. Let w(s) = 1. Let z(l) = -l**2 - l + 5. Let d(r) = -6*w(r) + z(r). Let o = -1 - -2. Let p(j) = o*d(j) - t(j). Factor p(n).
-n*(n + 1)
Let g(r) = -5*r**4 - 5*r**3 + 5*r**2 + r - 4. Let c(o) = -6*o**4 - 6*o**3 + 6*o**2 + o - 5. Let u(h) = -4*c(h) + 5*g(h). Suppose u(x) = 0. What is x?
-1, 0, 1
Let v(m) = 18*m**5 - 26*m**4 + 73*m**3 - 78*m**2 + 28*m - 4. Let f(s) = s**5 + s**4 - s**2. Let i(h) = -44*f(h) + 4*v(h). Factor i(k).
4*(k - 2)*(k - 1)**3*(7*k - 2)
Let t be (8/(-64))/(5/(-4) - -1). Factor -t + 1/4*j**3 - j**2 + 5/4*j.
(j - 2)*(j - 1)**2/4
Let u = 336 + -334. Factor 81*y**3 + 8/3 - 20*y + 18*y**u.
(3*y + 2)*(9*y - 2)**2/3
Let i be 17/20 + (-144)/240. Factor -1/2*c + i - 1/4*c**4 + 1/2*c**3 + 0*c**2.
-(c - 1)**3*(c + 1)/4
Suppose 4*i = -3*q + 18, 3*q = 4*q - 2. Suppose i*o - 6 + 0 = 0. Factor 0 + 0*n**o + 4/9*n**4 + 0*n - 2/9*n**3.
2*n**3*(2*n - 1)/9
Let z(y) = y - 6. Let n be z(9). Suppose 2/3*l - 4/3*l**2 + 2/3*l**n + 0 = 0. What is l?
0, 1
Factor 0 - 6/7*l**4 - 2/7*l**5 - 6/7*l**3 + 0*l - 2/7*l**2.
-2*l**2*(l + 1)**3/7
Let f be (8*(-6)/420)/((-6)/45). Factor -6/7*p - f*p**2 - 2/7 - 2/7*p**3.
-2*(p + 1)**3/7
Let j(x) = x**3 - 7*x**2 + 4. Let n be j(7). Let 3*p + n*p**3 - 6*p**3 - p = 0. Calculate p.
-1, 0, 1
Let q = 73 - 73. Factor -1/5*t**4 + q + 1/5*t**2 - 1/5*t + 1/5*t**3.
-t*(t - 1)**2*(t + 1)/5
Let z(f) be the first derivative of -3*f**4/4 + f**3 - 2. Let z(o) = 0. What is o?
0, 1
Find i such that -3/2 + 3/8*i**3 - 3/8*i + 3/2*i**2 = 0.
-4, -1, 1
Let z(g) be the second derivative of 7*g + 1/5*g**3 - 3/50*g**5 + 0*g**4 - 3/10*g**2 + 0 + 1/50*g**6. Factor z(m).
3*(m - 1)**3*(m + 1)/5
Let p = 2 + 13. Solve 2 - 3*q**3 - 11 + 0*q**3 - 3*q**2 + p*q = 0.
-3, 1
Find b, given that 0 - 2/7*b**2 - 8/7*b = 0.
-4, 0
Let u = 15 + -12. Factor -2*i**u - 2*i**4 + 3*i**3 + 3*i**4.
i**3*(i + 1)
Factor 2*w**2 + w + w**3 + w**3 + 6 - 11*w.
2*(w - 1)**2*(w + 3)
Solve -2/9*s**2 - 4/9 + 2/3*s = 0.
1, 2
Let d(o) be the first derivative of -2*o**5/65 + 2*o**4/13 - 33. Factor d(w).
-2*w**3*(w - 4)/13
Let m(f) be the second derivative of -f**8/16800 + f**7/2100 - f**6/900 - 2*f**4/3 + 6*f. Let j(g) be the third derivative of m(g). Factor j(i).
-2*i*(i - 2)*(i - 1)/5
Suppose 0 = -5*h - 22 + 212. Determine d, given that 104/7*d - h*d**3 - 16/7 + 42*d**4 - 116/7*d**2 = 0.
-2/3, 2/7, 1
Let z(g) be the first derivative of -1/3*g**3 + 1/540*g**6 - 1/36*g**4 + 0*g - 1/120*g**5 + 0*g**2 + 3. Let c(d) be the third derivative of z(d). Factor c(j).
(j - 2)*(2*j + 1)/3
Let f(q) be the third derivative of -q**7/945 - q**6/270 - q**5/270 + 4*q**2. Let f(l) = 0. Calculate l.
-1, 0
Let o(n) be the second derivative of 25*n**7/126 - 4*n**6/9 + n**5/10 + 2*n**4/9 + n**3/18 + 9*n. Factor o(f).
f*(f - 1)**2*(5*f + 1)**2/3
Let y(t) be the first derivative of 0*t - 1/8*t**4 + t**3 - 4 - 1/20*t**5 + 1/2*t**2. Let j(s) be the second derivative of y(s). Find v such that j(v) = 0.
-2, 1
Let x be (-3 - (-58)/20)/((-4)/10). Factor -1/4*c**3 + x*c**4 - 1/2 - 3/4*c**2 + 5/4*c.
(c - 1)**3*(c + 2)/4
Let g(r) = -3*r**2 + 11*r + 29. Let h(t) = t**2 - 5*t - 15. Let j(x) = 3*g(x) + 5*h(x). Suppose j(l) = 0. Calculate l.
-1, 3
Let a(p) be the third derivative of -p**6/420 + p**5/42 - p**4/14 + 15*p**2. Suppose a(r) = 0. Calculate r.
0, 2, 3
Let r = -173/68 + 56/17. Let -3/4*c - 1/2*c**4 + 1/4 + 1/4*c**2 + r*c**3 = 0. Calculate c.
-1, 1/2, 1
Determine w so that 3*w + 0*w + 2*w**3 + 0*w**2 + 6*w**2 + w**3 = 0.
-1, 0
Let n = 2/123 - -236/615. Factor 2/5*h + 4/5 - n*h**2.
-2*(h - 2)*(h + 1)/5
Factor 1 - 4/3*t + 1/3*t**2.
(t - 3)*(t - 1)/3
Let w(v) = 7*v**3 - 7*v + 6. Let n(u) be the second derivative of 2*u**5/5 - 4*u**3/3 + 7*u**2/2 - 3*u. Let q(p) = -6*n(p) + 7*w(p). Factor q(o).
o*(o - 1)*(o + 1)
Let m(s) be the first derivative of -2*s + 0*s**2 + 2/3*s**3 - 1. Solve m(v) = 0.
-1, 1
Let w(p) be the second derivative of 3*p**5/100 - 8*p. Factor w(j).
3*j**3/5
Let t(v) be the second derivative of v**6/660 - v**5/165 - 2*v**2 - 3*v. Let g(d) be the first derivative of t(d). Factor g(l).
2*l**2*(l - 2)/11
Let u(d) be the third derivative of 0*d**3 + 1/840*d**8 + 1/100*d**6 + 0*d + 1/175*d**7 + 0*d**4 - d**2 + 1/150*d**5 + 0. What is c in u(c) = 0?
-1, 0
Let v be 1*(-1 - 1) + -2. Let t be (-2)/v*2 + 1. Factor -4*p**2 + p**2 - 2*p - p**t.
-2*p*(2*p + 1)
Let d(s) be the first derivative of 1/6*s**4 - 2*s - 1/10*s**5 - 1 + 0*s**2 + 0*s**3. Let v(g) be the first derivative of d(g). Factor v(o).
-2*o**2*(o - 1)
Let w be 2/5 + 36/135. Factor 2/3*h**3 + 2/9*h**5 + 0*h + 2/9*h**2 + 0 + w*h**4.
2*h**2*(h + 1)**3/9
Let j(n) be the second derivative of -n**7/13860 - n**4/4 + 5*n. Let u(i) be the third derivative of j(i). Factor u(y).
-2*y**2/11
Let j be 3/(-21) + (-4)/(-28). Factor -3/2*a + j - 9/2*a**3 - 3/2*a**4 - 9/2*a**2.
-3*a*(a + 1)**3/2
Let o be (-8)/3*(-45)/(-20). Let v be (24/84)/(o/(-14)). Solve 0*l**2 + 0 + 2/3*l**3 - v*l = 0.
-1, 0, 1
Factor -3*v**2 + 153*v - 26 - 49 - 123*v.
-3*(v - 5)**2
Let x(u) be the second derivative of 343/45*u**6 - u + 0 - 35/3*u**4 - 8/3*u**2 + 76/9*u**3 + 49/30*u**5. Factor x(p).
2*(p + 1)*(7*p - 2)**3/3
Let s = 13 + -13. Let m(d) be the second derivative of 0 - 3*d - 1/2*d**4 - 1/5*d**5 + s*d**2 - 1/3*d**3. Find o, given that m(o) = 0.
-1, -1/2, 0
Factor 4*a**2 + 15*a**3 - 20*a**3 - 6*a**2 + 7*a**2.
-5*a**2*(a - 1)
Let m(d) be the first derivative of -3*d**3 - 3/4*d**4 - 9/2*d**2 + 2 - 3*d. Factor m(v).
-3*(v + 1)**3
Let s be 6/15*5/(-3). Let c = s - -13/6. Factor 3 + 27/2*a**2 + c*a**4 - 15/2*a**3 - 21/2*a.
3*(a - 2)*(a - 1)**3/2
Let o be ((-418)/(-12))/11 - 3. Let g(q) be the first derivative of -1 + 0*q + o*q**4 + 0*q**2 + 0*q**3. Factor g(p).
2*p**3/3
Let x(y) be the first derivative of -3 - 1/12*y**3 + 0*y + 1/8*y**2. Factor x(c).
-c*(c - 1)/4
Let h = 30 + -17. Let j = 40/3 - h. Factor -j*d**2 + 0*d + 1/3.
-(d - 1)*(d + 1)/3
Let w = -74 + 74. Factor 1/4*s**2 + 0*s + w.
s**2/4
Suppose 5*d + 5 = 2*k, -4 = -2*d + 2*k - 0. Let r be -3*((-8)/d)/(-2). Factor 10*u**2 - 2 - u**4 - 7*u**5 + 4*u**3 + u - 7*u**r + 2*u**5.
-(u - 1)*(u + 1)**3*(5*u - 2)
Let x = 10 + -16. Let f be x/(-27) + (-25)/(-9). Factor -6*v - f*v**2 + 5*v**2 + 4*v.
2*v*(v - 1)
Factor 7*i**4 - 2*i**4 + i**4 - 5*i**3 - i**4.
5*i**3*(i - 1)
Let r be (-711)/(-756) - 8/96. Factor 2/7*l**5 - 10/7*l**2 + 0 - r*l**3 - 4/7*l + 2/7*l**4.
2*l*(l - 2)*(l + 1)**3/7
Let i(p) be the first derivative of 1/18*p**4 + 0*p + 1/9*p**2 + 1 - 4/27*p**3. Factor i(j).
2*j*(j - 1)**2/9
Let q(o) be the third derivative of -o**6/80 - o**5/10 - 5*o**4/16 - o**3/2 + 6*o**2. Factor q(m).
-3*(m + 1)**2*(m + 2)/2
Determine h, given that -192 - 13*h - 21*h**2 - 3*h**3 - 15*h**2 - 131*h = 0.
-4
Let w(q) = q**2 + 7*q