*3 + 0*z**3 - z**3.
-z**3
Let d be (-10)/(-25) - (-7)/70. Factor -d + 1/2*p**2 + 0*p.
(p - 1)*(p + 1)/2
Let g(l) be the third derivative of l**7/1050 - l**5/75 + 11*l**2. Factor g(u).
u**2*(u - 2)*(u + 2)/5
Let g be (2/8)/((-10)/(-64)). Let x = -2147/5 - -431. Factor -g + x*q - 2/5*q**2.
-2*(q - 2)**2/5
Suppose -3*q = -4*q - 3. Let z = q + 3. What is k in z*k**4 - 4/7*k**3 + 0*k**2 + 2/7*k**5 + 2/7*k + 0 = 0?
-1, 0, 1
Factor 2*j - 1 + 2*j**2 - 11 - 15*j + 3*j.
2*(j - 6)*(j + 1)
Let k(c) be the second derivative of -c**7/840 + c**6/240 - c**5/240 + c**2/2 - 2*c. Let f(a) be the first derivative of k(a). Find d such that f(d) = 0.
0, 1
Suppose -7/6*x + 4/3*x**2 - 1/3*x**4 + 1/6*x**5 - 1/3*x**3 + 1/3 = 0. Calculate x.
-2, 1
Factor -8/15*j**2 - 2/15*j**3 - 4/15 - 2/3*j.
-2*(j + 1)**2*(j + 2)/15
Let h = 2077 + -1298. Let x be (-4)/22 - h/(-836). Factor 3/4*o**5 + x + 3/4*o - 3/2*o**2 - 3/2*o**3 + 3/4*o**4.
3*(o - 1)**2*(o + 1)**3/4
Let y be (-2397)/(-20) + 21/(-35). Let d = y + -118. Factor d*g**4 - 5/4*g + 1/4 - 5/2*g**3 - 1/4*g**5 + 5/2*g**2.
-(g - 1)**5/4
Let i(n) be the second derivative of n**4/4 + n**3/2 - 3*n**2 + 11*n. Suppose i(c) = 0. Calculate c.
-2, 1
Let h(l) = 24*l**2 - 21*l - 6. Let c(y) = 15*y - 3*y + 16*y + 12 - 49*y**2 + 14*y. Let o(k) = 3*c(k) + 5*h(k). What is s in o(s) = 0?
-2/9, 1
Factor 0 - 2/3*m + 1/6*m**2.
m*(m - 4)/6
Factor 6/13 - 2/13*l**2 - 4/13*l.
-2*(l - 1)*(l + 3)/13
Let u(q) be the second derivative of -q**7/315 + q**5/50 - q**4/45 - 9*q. Suppose u(i) = 0. What is i?
-2, 0, 1
Factor u**3 + 203*u**4 + u**2 - 202*u**4 - 2*u**2 - u.
u*(u - 1)*(u + 1)**2
Let l be (-40)/6*(-154)/1512. Let m = -1/81 + l. Solve 0*b**2 - 1/3*b**5 + m*b**4 - 1/3*b**3 + 0*b + 0 = 0 for b.
0, 1
Suppose y + 8 = 4*u - 62, 2*y - 4*u = -144. Let t = y - -371/5. Factor 1/5 + t*l**2 + 2/5*l.
(l + 1)**2/5
Let i(z) be the third derivative of -z**7/490 - z**6/70 - 3*z**5/140 - 6*z**2 - 4. Factor i(n).
-3*n**2*(n + 1)*(n + 3)/7
Let a(w) be the first derivative of w**6/105 + w**5/35 - 2*w**3/21 - w**2/7 + 2*w - 3. Let x(f) be the first derivative of a(f). Factor x(s).
2*(s - 1)*(s + 1)**3/7
Let i = -11 - -7. Let a be (-2)/i*2/2. Factor -s**3 + 1/2*s**2 + 0*s + 0 + a*s**4.
s**2*(s - 1)**2/2
Suppose -x - 2*x + 9 = 0. Suppose -5*c**2 - c**x + 5*c**2 + c = 0. Calculate c.
-1, 0, 1
Let w = -1/275 + 1928/825. Suppose -10*z - 112 = -38*z. Factor 20/3*o**2 + w*o**z + 4/3*o + 23/3*o**3 + 0.
o*(o + 1)*(o + 2)*(7*o + 2)/3
Let q be 238/4 + (-3)/6. Let s = 237/4 - q. Factor -s*c + 1/4 + 1/4*c**3 - 1/4*c**2.
(c - 1)**2*(c + 1)/4
Let b(t) be the third derivative of 1/1050*t**7 - 1/60*t**4 + 0*t**5 + 1/300*t**6 + 8*t**2 + 0*t - 1/30*t**3 + 0. Factor b(y).
(y - 1)*(y + 1)**3/5
Let t(g) be the third derivative of -g**8/252 - 16*g**7/315 - 5*g**6/18 - 38*g**5/45 - 14*g**4/9 - 16*g**3/9 - 22*g**2. Factor t(z).
-4*(z + 1)**2*(z + 2)**3/3
Let l = -2 - -8. Factor 3*d + 4*d**2 - 3*d - 4*d - l*d**2.
-2*d*(d + 2)
Let k(q) be the third derivative of q**9/3024 + q**8/840 + q**7/840 - q**3/3 - 2*q**2. Let d(n) be the first derivative of k(n). Factor d(u).
u**3*(u + 1)**2
Suppose 2*m + 5 = 11. Factor -1/3*q**m + 0 + 1/3*q**5 + 0*q**2 + 0*q + 0*q**4.
q**3*(q - 1)*(q + 1)/3
Let l = -889 + 4447/5. Determine w, given that 8/5*w - 6/5 - l*w**2 = 0.
1, 3
Let c be (-2)/((3 - 3) + -2). Let h be c*((2 - 3) + 1). Factor 2/7*w**3 + h + 2/7*w - 4/7*w**2.
2*w*(w - 1)**2/7
Let n(b) be the third derivative of b**5/180 - b**4/18 + 2*b**3/9 - b**2. Factor n(a).
(a - 2)**2/3
Let r(v) = v - 1. Let f(b) = -b**2 + 10*b - 10. Let d = 12 + -6. Let j(l) = d*r(l) - f(l). Suppose j(n) = 0. What is n?
2
Let v(w) be the second derivative of w**6/135 - w**4/54 + w + 5. Factor v(c).
2*c**2*(c - 1)*(c + 1)/9
Let f(t) be the first derivative of t**4/16 - 5*t**3/12 + 3*t**2/4 + 24. What is c in f(c) = 0?
0, 2, 3
Let t(c) = -3*c**2 + 38*c - 26. Let i(p) = -2*p**2 + 25*p - 17. Let n(a) = 8*i(a) - 5*t(a). Let w be n(9). Factor -w*g**2 - 2*g**3 + 0*g**3 + g**2.
-2*g**2*(g + 1)
Suppose 0 = -w + 5*d - 8, -w = -0*w + 5*d - 12. Factor 0 - 3*o - 2*o**5 - 2 + 2*o**w + 4*o**3 + o**5.
-(o - 2)*(o - 1)*(o + 1)**3
Let i(q) be the first derivative of 8/3*q**3 + 8*q + 4*q**4 + 2/3*q**6 - 10*q**2 - 16/5*q**5 + 7. Suppose i(w) = 0. Calculate w.
-1, 1, 2
Suppose -7*a + 2*a + 17 = -4*o, 3*o = -4*a - 5. Let y(j) be the first derivative of -1/5*j**2 - 2/15*j**3 + 0*j - a. Factor y(x).
-2*x*(x + 1)/5
Suppose -u - 3*u - 16 = 4*s, -4 = -3*s + 5*u. Let f be 1*((-8)/4 - s). Solve -5*z**4 - 3/2*z**5 + f - 6*z**3 - 1/2*z - 3*z**2 = 0 for z.
-1, -1/3, 0
Let x(z) be the third derivative of 0 - 1/2*z**4 + 1/30*z**5 + 0*z - 2*z**2 + 3*z**3. Factor x(s).
2*(s - 3)**2
Let l = 18 + -16. Solve 2/9*y**3 - 2/9*y - 2/9*y**l + 2/9 = 0 for y.
-1, 1
Let l be (-1)/3 + 28/12 - 2. Let -3/5*w**2 + l + 6/5*w = 0. What is w?
0, 2
Let m(x) be the first derivative of -x**6/3 + 4*x**5/35 + x**4 - 8*x**3/21 - x**2 + 4*x/7 - 3. Solve m(b) = 0.
-1, 2/7, 1
Let n(u) be the first derivative of 0*u**2 + 0*u**4 + 3/80*u**5 - u - 4 - 1/8*u**3. Let y(s) be the first derivative of n(s). Solve y(v) = 0 for v.
-1, 0, 1
Let g be (-20)/105 - 2/(-6). Factor -1/7*t**3 - g*t**2 + 1/7*t + 1/7.
-(t - 1)*(t + 1)**2/7
Let f(r) be the first derivative of -4*r**4/9 + 4*r**3/9 + 2*r**2/9 + 7. Let f(m) = 0. Calculate m.
-1/4, 0, 1
Suppose 16*b = 11*b + 10. Let x(d) be the second derivative of -1/105*d**7 - 1/5*d**b + 1/15*d**4 - 1/75*d**6 + 2*d - 1/15*d**3 + 1/25*d**5 + 0. Factor x(k).
-2*(k - 1)**2*(k + 1)**3/5
Factor -6*z**3 + 15/2*z**2 + 0 + 3/2*z**4 - 3*z.
3*z*(z - 2)*(z - 1)**2/2
Let y(h) be the first derivative of 0*h**2 - 2*h + 2/3*h**3 - 1. Solve y(p) = 0.
-1, 1
Let n be (-2)/4*(-4 - 2). Suppose p + 4 = n*p. Factor -4*b**p + 4*b - b - 2*b**2 + 3*b**2.
-3*b*(b - 1)
Let w = -13 - -17. Let s(y) be the first derivative of -2/9*y + 1/9*y**2 - 2/45*y**5 - 1/9*y**w + 4/27*y**3 + 2 + 1/27*y**6. Let s(a) = 0. Calculate a.
-1, 1
Let h(g) be the second derivative of 3*g**5/10 - g**4/4 - g**3 + 3*g**2/2 - 4*g. What is f in h(f) = 0?
-1, 1/2, 1
Factor -9 + 2*i**3 + 3 - 5*i**3 + 3*i**4 - 6*i**3 + 3*i**2 + 9*i.
3*(i - 2)*(i - 1)**2*(i + 1)
Let v(a) be the first derivative of 1/16*a**4 + 2 + 0*a - 1/2*a**3 + 9/8*a**2. Factor v(n).
n*(n - 3)**2/4
Let c(w) be the second derivative of w**4/42 - w**3/21 - 2*w**2/7 + w. Find b, given that c(b) = 0.
-1, 2
Let b be (0/23)/(10/(-2)). Let p(j) be the first derivative of -1/6*j**2 + 1/18*j**6 + 2/15*j**5 - 2/9*j**3 + 4 + 0*j**4 + b*j. What is q in p(q) = 0?
-1, 0, 1
Let c(r) be the first derivative of -5*r**3/3 + 10*r**2 - 15*r + 16. Factor c(a).
-5*(a - 3)*(a - 1)
Suppose 15*n - 4*n - 22 = 0. Factor 27/2*q - 3/2 - 81/2*q**n + 81/2*q**3.
3*(3*q - 1)**3/2
Factor 1/5*u**2 - 4/5*u + 4/5.
(u - 2)**2/5
Let p(z) be the third derivative of -z**8/1680 - z**7/525 - z**6/600 - 8*z**2. Factor p(i).
-i**3*(i + 1)**2/5
Factor 6*i**3 - 35 + 35*i**2 - i**3 - 333*i + 328*i.
5*(i - 1)*(i + 1)*(i + 7)
Let h(l) be the second derivative of l**5/10 + l**4/3 + l**3/3 - 3*l. Factor h(c).
2*c*(c + 1)**2
Let f(n) be the third derivative of 0*n**3 + 4*n**2 + 1/32*n**4 + 0 + 0*n + 1/80*n**5. What is g in f(g) = 0?
-1, 0
Let l be 0 + -1*0/(4 + -3). Let d(a) be the first derivative of l*a + 0*a**4 - 1/5*a**5 + 1/3*a**3 + 0*a**2 + 3. Factor d(j).
-j**2*(j - 1)*(j + 1)
Let z(c) = -2 - 9*c + 1 + 18*c**2 + 15*c. Let m(p) = 37*p**2 + 11*p - 3. Let k(o) = -2*m(o) + 5*z(o). Determine r so that k(r) = 0.
-1/4
Determine x, given that 3*x**2 + x - 8*x**2 + 9*x**3 + 2*x - 4*x**2 - 3*x**4 = 0.
0, 1
Let f be 2/(-6) - (-110)/33. Let o(k) be the third derivative of 1/420*k**6 + 2*k**2 + 1/84*k**4 + 0 + 0*k**f + 1/105*k**5 + 0*k. Let o(j) = 0. Calculate j.
-1, 0
Suppose -51 = -2*i + 455. Factor 3*x**2 + 253 - i.
3*x**2
Let q(j) = j**2 - j - 1. Let d(k) = -28*k + 26. Let g(t) = -d(t) + 2*q(t). Solve g(w) = 0.
-14, 1
Let a(r) be the first derivative of r**7/280 - r**6/120 - r**5/8 - 3*r**4/8 + 5*r**3/3 - 1. Let y(b) be the third derivative of a(b). Factor y(z).
3*(z - 3)*(z + 1)**2
Suppose 0 = 4*j + 4 - 12. Suppose -j*m - 3 = -3*m. Factor -7*p**3 + m*p**2 + 6*p**3 + 0*p - 2*p.
-p*(p - 2)*(p - 1)
Let t(n) be the first derivative of -4*n**6/9 + 8*n**5/3 - 25*n**4/6 - 20*n**3/9 + 20*n**2/3 + 16*n/3 - 6. L