 - 1)*(q + 1)
Let y be -15*6/750*-5. Determine b so that -3/5*b**3 + y*b**2 - 3/5 + 3/5*b = 0.
-1, 1
Let n(x) be the third derivative of x**7/1155 - x**6/66 + 4*x**5/55 + 8*x**4/33 - 128*x**3/33 + 44*x**2. Factor n(s).
2*(s - 4)**3*(s + 2)/11
Let w(f) = f**4 + f**3 + f**2 - f + 1. Let l(h) = 9*h**4 + 4*h**3 + 8*h**2 - 7*h + 7. Let i(n) = 3*l(n) - 21*w(n). Factor i(r).
3*r**2*(r - 1)*(2*r - 1)
Let l(o) be the first derivative of -o**4/2 + 4*o**3 - 11*o**2 + 12*o + 43. Factor l(x).
-2*(x - 3)*(x - 2)*(x - 1)
Suppose -2*s = 6*n - n - 15, 0 = -4*n + 2*s + 12. Suppose 3*i = -0 + n. Factor -i - 1 - 3*d + 4 + d**3.
(d - 1)**2*(d + 2)
Let y(r) be the first derivative of r**3/7 + 3*r**2/14 - 6*r/7 + 4. Determine f, given that y(f) = 0.
-2, 1
Let n(u) = 6*u**2 - 4*u - 26. Let k(p) = p**2 + p - 1. Let i(g) = g**3 + 6*g**2 - 2*g - 4. Let v be i(-6). Let r(m) = v*k(m) - n(m). What is q in r(q) = 0?
-3
Let v(w) = -5*w**5 - 2*w**4 + 13*w**3 + 5*w**2 - 19*w + 8. Let r(n) = -6*n**5 - 2*n**4 + 14*n**3 + 6*n**2 - 20*n + 8. Let h(g) = 3*r(g) - 4*v(g). Factor h(m).
2*(m - 1)**3*(m + 2)**2
Let l(u) = 4*u**3 + 2*u**2 - 10*u - 10. Let t(r) = -8*r**3 - 5*r**2 + 19*r + 21. Let s(x) = -5*l(x) - 2*t(x). Find w such that s(w) = 0.
-1, 2
Suppose -2*k + 1 + 23 = 0. Suppose 2*m**2 - 12*m + k*m = 0. Calculate m.
0
Let a be 2/10 + 15/675. Factor 2/9*o - 2/9*o**3 + a*o**2 - 2/9.
-2*(o - 1)**2*(o + 1)/9
Let u(p) be the first derivative of p**3/6 - p**2/4 + 10. Factor u(c).
c*(c - 1)/2
Let b(z) = 3*z - 33. Let s be b(11). Suppose -2/5*k - 2/5*k**2 + s = 0. Calculate k.
-1, 0
Let p = -10 - -16. Suppose -m = 3*y - 3, -4*y + p = -2*m + 4*m. Find w such that -6*w**2 - 2*w**3 + 0*w**m - 6*w + 1 - 3 = 0.
-1
Let g(v) be the third derivative of 1/12*v**4 + 0 - 1/30*v**5 + 0*v + 0*v**3 - 3*v**2. Factor g(y).
-2*y*(y - 1)
Let b(a) = 9*a**2 - 90*a + 105. Let v(o) = 4*o**2 - 36*o + 42. Let l(g) = 5*b(g) - 12*v(g). Let l(d) = 0. Calculate d.
-7, 1
Solve -8*g - 16*g**4 + 16*g**5 - 2*g**3 - 3*g**3 - 3*g**3 - 20*g**4 + 36*g**2 = 0.
-1, 0, 1/4, 1, 2
Suppose 4*d - 6 = -3*a - 0*a, 10 = -4*d + 5*a. Factor 0*l - 18/5*l**4 + d*l**2 + 0 - 4/5*l**3 - 14/5*l**5.
-2*l**3*(l + 1)*(7*l + 2)/5
Find n, given that -12/5*n + 9/5*n**2 - 12/5 + 12/5*n**3 + 3/5*n**4 = 0.
-2, -1, 1
Let i(k) be the second derivative of -1/5*k**2 - 1/30*k**4 + 0 + 2/15*k**3 - k. Factor i(x).
-2*(x - 1)**2/5
Factor -w + 1/2*w**2 + 1/2*w**3 + 0.
w*(w - 1)*(w + 2)/2
Let v(z) = z - 9. Let t be v(13). Let b(q) be the first derivative of -1/7*q**2 - 1 + 1/14*q**t - 2/21*q**3 + 0*q + 2/35*q**5. Suppose b(g) = 0. Calculate g.
-1, 0, 1
Find f, given that 0*f + 15/2*f**4 - 20*f**3 + 15*f**2 - 5/2 = 0.
-1/3, 1
Let a(v) be the third derivative of v**5/210 + 11*v**4/84 + 70*v**2. Solve a(q) = 0.
-11, 0
Suppose -2 = -2*g - 4. Let i be g/2 + 1/2. Factor 0 + 0*w + 25/4*w**5 + 5*w**4 + w**3 + i*w**2.
w**3*(5*w + 2)**2/4
Let s(h) be the third derivative of h**7/1260 + h**6/144 + h**5/45 + h**4/36 + 8*h**2. Let s(j) = 0. What is j?
-2, -1, 0
Let f(z) be the second derivative of -z**4/18 - 10*z**3/9 - 8*z + 2. Factor f(d).
-2*d*(d + 10)/3
Let i(s) = s**3 + 24*s**2 + 45*s + 24. Let b be i(-22). Let o(n) be the second derivative of 0*n**2 + b*n + 1/12*n**4 - 1/24*n**3 + 0. Factor o(j).
j*(4*j - 1)/4
Let t be ((-60)/(-2))/3 + -3. Let i(y) be the third derivative of 0*y + 1/6*y**4 + 0*y**5 + 1/105*y**t + 0 - 1/30*y**6 - 1/3*y**3 - y**2. Factor i(w).
2*(w - 1)**3*(w + 1)
Let z(o) = o - 3. Suppose 4*h = -2 + 26. Let x be z(h). Factor -2*n**3 + 3*n**2 - x*n**2.
-2*n**3
Determine y so that 3/4*y**2 + 9/4 + 3*y = 0.
-3, -1
Let l(g) be the third derivative of -g**5/480 - 11*g**4/192 - 3*g**3/8 - 2*g**2 + 6*g. Factor l(p).
-(p + 2)*(p + 9)/8
Factor -4*b**2 + b**3 + 15*b**4 + b**3 - 13*b**4.
2*b**2*(b - 1)*(b + 2)
Let o = 27 + -24. Factor 1/4*m**o - 1/4*m**2 - 1/2*m + 0.
m*(m - 2)*(m + 1)/4
Let w(i) be the first derivative of i**5/10 + i**4/36 - 2*i**3/9 + i**2/6 - i + 2. Let b(o) be the first derivative of w(o). Solve b(m) = 0 for m.
-1, 1/3, 1/2
Let f(w) be the first derivative of -w**4 - 4*w**3 + 65. Factor f(a).
-4*a**2*(a + 3)
Suppose 0 = 3*j - 5 - 4. Let 1/4*h**4 + 0 - 1/2*h + 5/4*h**2 - h**j = 0. What is h?
0, 1, 2
Let z(i) be the second derivative of 9*i**6/10 - 9*i**5/20 - 2*i**4 + 2*i**3 + 6*i. Find l such that z(l) = 0.
-1, 0, 2/3
Let w = 12 - 7. Determine j, given that -j**w + 0 + 1/4*j**4 + 0*j + j**3 - 1/4*j**2 = 0.
-1, 0, 1/4, 1
Let w(s) be the third derivative of -s**6/120 - s**5/180 + s**4/9 - 2*s**3/9 + 3*s**2. Factor w(y).
-(y - 1)*(y + 2)*(3*y - 2)/3
Find r such that 264 - 248 + 484*r**3 + 192*r + 1054*r**2 - 394*r**2 = 0.
-1, -2/11
Let b(r) be the third derivative of 2*r**7/735 - r**6/105 - 4*r**5/105 + r**4/21 + 2*r**3/7 - 23*r**2. Factor b(w).
4*(w - 3)*(w - 1)*(w + 1)**2/7
Let z(i) be the third derivative of i**6/240 - i**5/60 + i**4/48 + 5*i**2. What is a in z(a) = 0?
0, 1
Let u(f) = f**2 - 1. Let o(b) = -20*b**2 - 2*b + 22. Let a(k) = 2*o(k) + 44*u(k). Factor a(t).
4*t*(t - 1)
Let d(l) be the second derivative of -2/105*l**6 + l + 0 + 0*l**2 + 0*l**3 + 0*l**4 + 1/147*l**7 + 1/70*l**5. Factor d(x).
2*x**3*(x - 1)**2/7
Let s be 4/((-40)/25) + (-3)/(-1). Solve -1/4 - s*t - 1/4*t**2 = 0 for t.
-1
Suppose -4*s + 8*s + 8 = 0. Let h be -1 + (-3*2)/s. Find a such that -2*a**3 - 2*a**2 + 0*a**5 + 0*a**4 + 2*a**5 + 0*a**5 + h*a**4 = 0.
-1, 0, 1
Suppose 7*k = 2*k + 3*m + 16, -2*k + 12 = -4*m. Let h = 275 - 2471/9. Factor 0 + 2/9*r**k + h*r.
2*r*(r + 2)/9
Let n(c) be the second derivative of c**8/1680 + c**7/2520 - c**6/540 + 4*c**3/3 + 4*c. Let w(o) be the second derivative of n(o). Suppose w(h) = 0. What is h?
-1, 0, 2/3
Suppose 2*t = 6*t - 72. Let v = 20 - t. Factor 0 + 0*x + 2/7*x**v.
2*x**2/7
Let g(y) be the third derivative of -y**7/735 - 2*y**6/105 - 3*y**5/35 + 9*y**3/7 + 9*y**2. Let g(n) = 0. What is n?
-3, 1
Let t = 10 + -10. Let b(h) be the third derivative of 0 + t*h + 1/30*h**5 + 1/12*h**4 + 2*h**2 + 0*h**3. Let b(j) = 0. What is j?
-1, 0
Let l = 203 + -201. Let 2/3*b**3 + 0*b**l - 2*b**4 - 8/3*b**5 + 0*b + 0 = 0. What is b?
-1, 0, 1/4
Let w(n) = n**3 + 5*n**2 - 7*n - 3. Let v be w(-6). Let g be 2/v*(-30)/(-8). Factor g*o**2 + 0 + 7/2*o**3 - o.
o*(o + 1)*(7*o - 2)/2
Let h be (-6)/10 - 767/(-295). Factor -1/3*a**4 - a**h + 0 + 1/3*a + a**3.
-a*(a - 1)**3/3
Factor 15*q**2 - 7*q + 16*q - 5*q**3 - 15*q - 4*q.
-5*q*(q - 2)*(q - 1)
Let a(s) = s**4 - 2*s**3 + 3*s**2 - 2*s + 2. Let t(z) = -2*z**4 + 3*z**3 - 4*z**2 + 3*z - 3. Let o(v) = 3*a(v) + 2*t(v). What is i in o(i) = 0?
-1, 0, 1
Let s(w) be the second derivative of 16*w**6/15 - 4*w**5 + 3*w**4/2 + 13*w**3/3 + 2*w**2 + 25*w. Factor s(k).
2*(k - 2)*(k - 1)*(4*k + 1)**2
Let i = 386 + -2692/7. Factor -10/7*b**2 - 5/7*b**4 - 1/7 + i*b**3 + 1/7*b**5 + 5/7*b.
(b - 1)**5/7
Let x(u) be the first derivative of 3*u**4/4 - 3*u**3 - 6*u**2 - 29. Factor x(t).
3*t*(t - 4)*(t + 1)
Let s(w) be the first derivative of -2/3*w + 3 + 1/6*w**4 + 1/6*w**2 + 5/9*w**3. Factor s(t).
(t + 1)*(t + 2)*(2*t - 1)/3
Let d = -24 - -32. Let b = 11 - d. Find y such that -3/2*y**b + 1/2*y**2 + 3/2*y + 1/2 - y**4 = 0.
-1, -1/2, 1
Let t = 4 - 2. Suppose 7*o + q + 2 = 9*o, 5*o = 3*q + 6. Factor o*i - 2/5*i**t + 2/5.
-2*(i - 1)*(i + 1)/5
Let j(t) be the first derivative of -32*t**5/55 + 4*t**4/11 + 14*t**3/33 + t**2/11 - 17. Factor j(n).
-2*n*(n - 1)*(4*n + 1)**2/11
Suppose -4/5*z**2 - 1/5 - 4/5*z = 0. What is z?
-1/2
Suppose 5*g - 4*g - 2 = o, 5*g - 6 = 3*o. Let z(t) be the third derivative of 3*t**2 - 1/40*t**5 + g + 0*t + 1/4*t**3 + 0*t**4. Find u, given that z(u) = 0.
-1, 1
Suppose -14/9*d**2 + 10/3*d - 2 + 2/9*d**3 = 0. What is d?
1, 3
Suppose -2*o = 5*o. Let t(i) be the first derivative of -1/9*i**3 + 1/3*i + o*i**2 + 3. Factor t(w).
-(w - 1)*(w + 1)/3
Let k(x) be the third derivative of -x**5/60 - x**4/8 - 7*x**2. Factor k(h).
-h*(h + 3)
Let j = 1850/51 - 50/17. Let s = -33 + j. Solve 4/3*g - s*g**2 - 4/3 = 0.
2
Let v(r) be the third derivative of -5*r**2 + 2/9*r**3 + 0 + 0*r + 5/36*r**4 - 7/90*r**5. Suppose v(b) = 0. Calculate b.
-2/7, 1
Suppose 2 = -3*p - 2*o + 3, -p = 2*o + 5. Let j(n) be the first derivative of -n + 2 + 9/4*n**2 - 2*n**p + 5/8*n**4. Factor j(m).
(m - 1)**2*(5*m - 2)/2
Suppose -4*c + 5*q = -21 - 12,