2 + 2. Factor u(k).
-2*k*(k + 1)**2*(3*k + 1)
Let k(w) = -w**3 + 9*w**2 + 15*w + 5. Let g(n) = -5*n**3 + 55*n**2 + 91*n + 31. Let r(b) = 6*g(b) - 34*k(b). Suppose r(m) = 0. What is m?
-4, -1
Let m(y) be the third derivative of -y**5/240 + 3*y**3/8 - 10*y**2. Factor m(h).
-(h - 3)*(h + 3)/4
Suppose 2*f = -2*f. Let b(g) = -2 + 1 + f. Let o(k) = 11*k**2 - 2*k - 4. Let l(u) = 4*b(u) - o(u). Let l(p) = 0. What is p?
0, 2/11
Let c = 23 - 20. Solve -16*k**2 - 19*k - k + k**c - 5*k**3 - 8 = 0 for k.
-2, -1
Let u = 21 - 251/12. Let r(h) be the first derivative of 0*h + u*h**3 + 1/16*h**4 + 3 + 0*h**2. Find c such that r(c) = 0.
-1, 0
Let u(o) be the second derivative of 2*o + 1/8*o**3 - 1/48*o**4 - 1/4*o**2 + 0. Factor u(n).
-(n - 2)*(n - 1)/4
Suppose 0 = -3*m + 12, 3*h + m = -0*m - 5. Let p(x) = -x - 1. Let q be p(h). Factor -4*c - 6*c**4 + 6*c - 2*c**3 + 4*c**4 + 2*c**q.
-2*c*(c - 1)*(c + 1)**2
Let a(s) be the third derivative of s**8/2800 - s**7/1400 - s**6/300 + s**3 - s**2. Let d(n) be the first derivative of a(n). Factor d(i).
3*i**2*(i - 2)*(i + 1)/5
Suppose 0*f**2 + 8*f - 3*f**2 + 3*f**3 + 0*f**3 - 14*f = 0. Calculate f.
-1, 0, 2
Let z(a) be the second derivative of -a**6/1980 - a**5/220 + a**3/3 + 3*a. Let o(b) be the second derivative of z(b). Find s, given that o(s) = 0.
-3, 0
Let k(p) = 2*p**5 - 19*p**4 + 41*p**3 - 35*p**2 + 17*p - 4. Let d(h) = -h**5 + h**4 + h**2 + h - 1. Let g(i) = 6*d(i) - 3*k(i). Solve g(r) = 0.
1/4, 1, 2
Let v(j) be the second derivative of 5*j**4/12 + 9*j**2/2 - 3*j. Let b(o) = -o**2 - 2. Let x(s) = -18*b(s) - 4*v(s). Let x(k) = 0. What is k?
0
Let d(s) be the first derivative of -s**5/5 + 3*s**4/4 - 2*s**3/3 - 4. Determine l so that d(l) = 0.
0, 1, 2
Let z(u) be the second derivative of -u**5/10 - u**4/6 + 7*u. Let z(q) = 0. What is q?
-1, 0
Let q(i) = -2*i**4 - 3*i**3 + i**2 - 2*i + 1. Let f(p) = 6*p**4 + 10*p**3 - 2*p**2 + 6*p - 4. Let j(t) = 5*f(t) + 16*q(t). Solve j(r) = 0 for r.
-1, 1, 2
Suppose 2 = -q - 1, 0 = 2*b - 2*q - 56. Let p = b + -21. Solve 3/4*w + 0 + 3/4*w**5 + 0*w**2 - 3/2*w**3 + 0*w**p = 0.
-1, 0, 1
Let h(p) be the first derivative of p**7/42 - p**6/10 + 3*p**5/20 - p**4/12 - 3*p - 4. Let u(r) be the first derivative of h(r). Find v such that u(v) = 0.
0, 1
Let d(q) be the second derivative of 2/15*q**6 + 0 + 1/3*q**3 - 1/3*q**4 - 1/21*q**7 + 0*q**2 + 0*q**5 + 5*q. Find h, given that d(h) = 0.
-1, 0, 1
Let f = -663/854 - 1582583/84546. Let h = f + 182/9. Solve -2/11*i - 8/11*i**2 - 12/11*i**3 + 0 - h*i**4 - 2/11*i**5 = 0.
-1, 0
Let r be -1 + ((-330)/50)/(3/(-47)). Factor -2/5*q**4 - 192/5*q**2 - 32/5*q**3 - r*q - 512/5.
-2*(q + 4)**4/5
Factor -6/5*m**5 + 0*m**2 + 4/5*m**3 - 2/5*m**4 + 0 + 0*m.
-2*m**3*(m + 1)*(3*m - 2)/5
Let a(q) be the second derivative of 1/36*q**4 - 1/3*q**2 - q - 1/18*q**3 + 0. Solve a(f) = 0.
-1, 2
Let a be ((-6)/36)/((-1)/(-4)*-2). Factor 1/3*g**4 + a*g - 1/3*g**3 + 0 - 1/3*g**2.
g*(g - 1)**2*(g + 1)/3
Let q(c) = -c**2 + 1. Let n(v) = 2*v**2 + 4*v - 6. Let h(a) = n(a) + 6*q(a). Suppose h(w) = 0. What is w?
0, 1
Let q(t) = -2*t**2 + 19*t - 42. Let u be q(6). Factor -4/3*c**4 + 0*c**2 + u*c - 2/3*c**5 + 0 - 2/3*c**3.
-2*c**3*(c + 1)**2/3
Let f = 2 - -2. Let n(m) = 2*m**2 + 8*m - 4. Let u(o) = o**2 + 35 - 42 + 5*o + 10*o + 3*o**2. Let l(g) = f*u(g) - 7*n(g). Factor l(p).
2*p*(p + 2)
Let y(v) be the first derivative of -v**8/2520 + v**7/630 + v**6/540 - v**5/90 - 7*v**3/3 + 7. Let p(f) be the third derivative of y(f). Factor p(g).
-2*g*(g - 2)*(g - 1)*(g + 1)/3
Let r be 4/2 - 2/1. Factor 4 - 4*s**2 + r*s - 10*s**2 + 6*s + 4*s.
-2*(s - 1)*(7*s + 2)
Let l(z) be the first derivative of -z**4/4 - 7*z**3/3 + 4*z**2 - 14. Factor l(t).
-t*(t - 1)*(t + 8)
Suppose -a = -2*j + 75, -2*a + 79 = 2*j + a. Let -x + 30*x**2 + 5*x**4 + j*x**3 + 9*x**4 - 5 + 1 + 3*x = 0. What is x?
-1, 2/7
Factor -84*m - 9*m**2 - 4*m**3 - 10*m**2 - 40 - 36*m**2 + 7*m**2.
-4*(m + 1)**2*(m + 10)
Let s(m) be the second derivative of -m**4/30 - m**3/3 - 4*m**2/5 + 9*m. Find l such that s(l) = 0.
-4, -1
Suppose 2*g + 3*g - 15 = -5*q, 6 = 5*q - 4*g. Determine f so that -2/7*f**q + 0 - 2/7*f**3 + 0*f = 0.
-1, 0
Let h(f) be the first derivative of 0*f**5 + 0*f + 0*f**2 - 1/1440*f**6 + 1/3*f**3 + 0*f**4 + 1. Let u(c) be the third derivative of h(c). Factor u(q).
-q**2/4
Let v(b) be the third derivative of 0*b**3 + 0 - 1/120*b**5 + 3*b**2 + 1/140*b**7 + 0*b**4 + 1/336*b**8 + 0*b**6 + 0*b. Factor v(q).
q**2*(q + 1)**2*(2*q - 1)/2
Let i(p) = 0*p**4 + 2*p**2 + 1 - p**5 + p**2 - p**4. Let j(x) = x**4 + x**2 - x + 1. Let c(s) = 2*i(s) - 2*j(s). Determine w, given that c(w) = 0.
-1, 0, 1
Let h(f) = -2*f**3 - f**2 + 4*f + 3. Let a(p) = 4*p**3 + 3*p**2 - 9*p - 7. Let j(d) = -4*a(d) - 9*h(d). Find v such that j(v) = 0.
-1/2, 1
Let v be 11 - 8 - 0/2. Factor v*f**3 + 16*f**4 + 9*f**3 - 8*f**3.
4*f**3*(4*f + 1)
Let l(d) be the second derivative of -d**6/90 - 3*d**5/20 - 3*d**4/4 - 3*d**3/2 - 22*d. Solve l(y) = 0 for y.
-3, 0
Let l = 28 + -26. Let h be (-1)/(-10*l/12). Factor h*j**2 + 9/5*j**3 + 0*j + 3/5*j**5 + 0 + 9/5*j**4.
3*j**2*(j + 1)**3/5
Let t be -1 + 1 - (31 - 2). Let m be (-3)/1 + t/(-9). Factor -m*f**2 + 2/9 + 2/9*f - 2/9*f**3.
-2*(f - 1)*(f + 1)**2/9
Suppose 0 = 6*i - 7*i. Factor 2/3*z**3 + 0*z**2 + 0 + i*z - 2/3*z**5 + 0*z**4.
-2*z**3*(z - 1)*(z + 1)/3
Let f(x) = -x**3 - 7*x**2 + 7*x. Let d(m) = m**3 + 5*m**2 - 5*m. Suppose -6*l = -2*l - 28. Let o(t) = l*d(t) + 5*f(t). Factor o(s).
2*s**3
Suppose -16/7*v + 4/7*v**3 + 2/7*v**4 - 8/7 - 6/7*v**2 = 0. Calculate v.
-2, -1, 2
Let a(i) be the first derivative of -i**6/5 - 4*i**5/25 + i**4/10 - 7. Factor a(z).
-2*z**3*(z + 1)*(3*z - 1)/5
Let a(m) be the second derivative of m**6/240 - m**4/48 + 3*m**2/2 - m. Let o(s) be the first derivative of a(s). Solve o(i) = 0 for i.
-1, 0, 1
Let j(f) be the first derivative of -5*f**4/4 - 10*f**3/3 - 5*f**2/2 - 18. Factor j(l).
-5*l*(l + 1)**2
Suppose 3*j - 8 = -2*k, 7*k - 1 = 2*k + 2*j. Let t = k + 1. Find l, given that -l**2 + l**2 + 3*l + 3*l**t = 0.
-1, 0
Let o be (-3 + 23)/(-5) + 4. Let s(t) be the third derivative of 0 + t**2 + 1/210*t**5 - 1/21*t**3 + o*t + 0*t**4. Factor s(y).
2*(y - 1)*(y + 1)/7
Suppose 0 = 9*j + 71 - 71. Let 1/3*l + 1/3*l**2 + j = 0. Calculate l.
-1, 0
Determine f so that -14/3*f - 2/3*f**4 - 4/3 - 6*f**2 - 10/3*f**3 = 0.
-2, -1
Let f(t) = t**2 - 7*t + 15. Let h be f(3). Solve 0*d - 2/3*d**2 + 0 - 1/3*d**h = 0 for d.
-2, 0
Let n(o) be the third derivative of -5*o**2 - 1/16*o**4 + 0*o + 1/120*o**5 + 0*o**3 + 0. Determine c so that n(c) = 0.
0, 3
Factor 4*o + 6*o**2 + 7 - 4 - 3 + 2*o**3.
2*o*(o + 1)*(o + 2)
What is a in 6*a**2 - 3*a**5 + 11*a - 12*a**4 + 4 + 2 + 4*a - 12*a**3 = 0?
-2, -1, 1
Factor 3/2 - 1/2*a**2 - a.
-(a - 1)*(a + 3)/2
Let q(m) = -7*m**3 - m**2 - m + 3. Let f = 7 + -5. Let l(b) = -b - 5*b**2 + b - 3*b**3 + 4*b**2 - b + 1. Let p(o) = f*q(o) - 5*l(o). Factor p(g).
(g + 1)**3
Let x = -76 - -81. Solve 2/5*d**4 + 0 - 4/5*d - 6/5*d**x + 2*d**3 - 2/5*d**2 = 0 for d.
-1, -2/3, 0, 1
Let b(h) be the first derivative of h**3/3 - h**2 + h + 2. Suppose b(x) = 0. Calculate x.
1
Let s(r) be the third derivative of 3*r**6/200 - r**5/20 + r**4/20 + 12*r**2. Solve s(p) = 0 for p.
0, 2/3, 1
Let p(q) be the first derivative of 3 - 4/15*q**5 - 1/12*q**4 + 0*q + 0*q**3 + 0*q**2. Factor p(a).
-a**3*(4*a + 1)/3
Let x(w) = 4*w - 4. Let c be x(3). Let d be -1 + (c - (4 - 1)). Factor 0 - 3/4*g**2 - 1/2*g + 3/4*g**d + 1/2*g**3.
g*(g - 1)*(g + 1)*(3*g + 2)/4
Let v(m) = -m**2 - 15*m - 23. Let k be v(-13). Factor 0 + i**2 + 1/2*i**k + 1/2*i.
i*(i + 1)**2/2
Let f(w) = -8*w**5 + 16*w**4 - 8*w**3 + 4*w - 4. Let z(x) = 7*x**5 - 15*x**4 + 9*x**3 - x**2 - 3*x + 3. Let j(b) = -3*f(b) - 4*z(b). Let j(d) = 0. Calculate d.
0, 1
Let i(j) be the first derivative of -5*j**3 - 3*j**2 - 4. Factor i(t).
-3*t*(5*t + 2)
Suppose -32*y - 8 = -36*y. Let l(m) be the third derivative of 2*m**y + 0*m - 1/35*m**7 - 1/2*m**3 + 0 - 9/20*m**5 + 5/8*m**4 + 7/40*m**6. Factor l(k).
-3*(k - 1)**3*(2*k - 1)
Suppose 0 = -0*i + 4*i - 24. Let v = i + -4. Factor 0 - 2/3*u**v + 0*u.
-2*u**2/3
Let r(c) be the second derivative of -c**5/5 + 2*c**4/3 + 2*c**3 + 31*c. Determine p so that r(p) = 0.
-1, 0, 3
Let t be (0 - (3 + 28/(-12))) + 4. Factor -2*z**5 + 0 - 2/3*z**