- m*k**3.
-3*k*(k + 1)**2*(3*k - 1)/2
Let l(y) = 4*y**2 - 6*y - 2. Let h be l(3). Solve 21*g**2 + 15*g - 15*g**3 + 4 - 16 - 7*g + h*g = 0 for g.
-1, 2/5, 2
Let d(p) = -13*p + 13. Let q(m) = -3*m + 3. Let w(n) = -2*d(n) + 9*q(n). Let b be w(-5). Factor -7*u**2 - 9 + 6*u + 7*u + u**3 - 4*u + b*u.
(u - 3)**2*(u - 1)
Suppose 13*s - u = 10*s + 12, 3*u = -18. Factor 3/8*i + 0 + 15/8*i**s + 3/2*i**3.
3*i*(i + 1)*(4*i + 1)/8
Suppose -2*f + 3*f = -3. Let y be 240/70 - f/(-7). Solve 6*b**5 - 18*b**4 + 0*b**y - 2*b**3 - 20*b**5 - 2*b**3 = 0 for b.
-1, -2/7, 0
Let z(l) be the third derivative of -l**5/15 + 13*l**4 - 1014*l**3 - 34*l**2 + 5. Factor z(q).
-4*(q - 39)**2
Let f(b) = 25*b + 177. Let q be f(-7). Factor 5/2*l**q - 4*l - 2.
(l - 2)*(5*l + 2)/2
Let b(c) be the second derivative of 1/420*c**5 - 1/1260*c**6 - 4*c + c**3 + 1/42*c**4 + 0*c**2 + 0. Let d(y) be the second derivative of b(y). Factor d(m).
-2*(m - 2)*(m + 1)/7
Suppose j - 2*f - 248 = -617, 2*f + 756 = -2*j. Let h be 2/(-16) - j/120. Suppose -1/2*p**h + p**2 + 0*p + 0 - 1/2*p**4 = 0. What is p?
-2, 0, 1
Let d(r) be the second derivative of r**4/96 - 2*r**3/3 - 33*r**2/16 + 23*r. Solve d(b) = 0.
-1, 33
Let o(m) be the first derivative of -m**3/5 + 3*m**2/5 + 9*m/5 - 80. Factor o(n).
-3*(n - 3)*(n + 1)/5
Suppose 74 = 26*i - 30. Let y(m) be the third derivative of m**i + m**2 + 1/20*m**5 + 0 + 0*m + 8*m**3. Determine n, given that y(n) = 0.
-4
Let p = 244 - 256. Let a be 65/(-120) - p/18. Factor 1/4 - a*u**3 + 1/8*u - 1/4*u**2.
-(u - 1)*(u + 1)*(u + 2)/8
Let a(u) = -2*u - 26. Let r = -270 + 257. Let k be a(r). Let -2/7*d + k - 4/7*d**5 + 6/7*d**3 + 2/7*d**4 - 2/7*d**2 = 0. What is d?
-1, -1/2, 0, 1
Let t be (-20)/6*18*4/(-16). Let j = 17 - t. What is y in 0*y + 0 - 3/5*y**3 + 6/5*y**j = 0?
0, 2
Let u(m) be the first derivative of 0*m + m**3 - 4 + 3/2*m**2. Find o, given that u(o) = 0.
-1, 0
Let m = -33 - -22. Let q(t) = t**2 + 19*t - 11. Let x(z) = -1 + 17*z - 7*z - 5. Let b(p) = m*x(p) + 6*q(p). Suppose b(d) = 0. Calculate d.
-2/3, 0
Let v(b) = b**4 + b**2. Let i be 24/(-9)*(-9)/(-6). Let w be -10 + (0 - i/4). Let h(u) = 5*u**4 + 3*u**2 - u. Let y(a) = w*v(a) + 2*h(a). Factor y(j).
j*(j - 2)*(j + 1)**2
Let w be (18*5/(-10))/(-1) + -5 + -2. Factor 0 - 3/4*b - 3/4*b**4 + 3/4*b**w + 3/4*b**3.
-3*b*(b - 1)**2*(b + 1)/4
Let j(z) be the first derivative of 2/5*z**5 + 2*z - 25 - 1/2*z**2 - 1/6*z**6 + 1/2*z**4 - 4/3*z**3. Determine y so that j(y) = 0.
-1, 1, 2
Factor 64 - 64 - 6*z - 83*z**2 + z**4 - 36*z - 40*z**3.
z*(z - 42)*(z + 1)**2
Solve -141/4*o**2 + 0*o + 36*o**3 - 3/4*o**4 + 0 = 0 for o.
0, 1, 47
Let x be (-19)/(-36) - (-18)/81. Let s(u) be the second derivative of -1/6*u**3 - 1/24*u**4 + 11*u + x*u**2 + 0. Solve s(f) = 0.
-3, 1
Let p = -47 + 47. Suppose 0 = -p*x - x + 3. Factor -2/3 + 2*a - 4/3*a**x - 4/3*a**2 - 2/3*a**5 + 2*a**4.
-2*(a - 1)**4*(a + 1)/3
Solve -8*g**3 + 8*g - 591 - 592 - 10*g**2 + 26*g**2 - 4*g**4 + 1171 = 0 for g.
-3, -1, 1
Factor 6/7*w + 2/7*w**4 + 0 + 10/7*w**3 + 2*w**2.
2*w*(w + 1)**2*(w + 3)/7
Let z(q) = -q**2 + 11*q - 6. Suppose 21 + 29 = 5*f. Let b be z(f). Factor 2*s**2 - 2*s**2 - 18*s - b*s**3 + 16*s**2 + 2*s.
-4*s*(s - 2)**2
Let a(p) = p + 18. Let b be a(-13). Suppose 2 = b*t - 8. Factor v - v**2 - v**2 + v**t.
-v*(v - 1)
Factor -1/2*k**2 + 3/8*k**4 - 1/4*k + 1/8 + 1/4*k**3.
(k - 1)*(k + 1)**2*(3*k - 1)/8
Let u(f) be the third derivative of -f**5/20 - 9*f**4/4 - 556*f**2. Let u(n) = 0. What is n?
-18, 0
Let m(n) = 2*n**2 + n. Let s(r) = 15*r**3 + 12*r**2 - 9*r - 10. Let t(z) = -4*m(z) - s(z). Factor t(a).
-5*(a + 1)**2*(3*a - 2)
Let c(j) be the first derivative of -j**6/3960 + j**5/440 - 10*j**3 + 14. Let i(w) be the third derivative of c(w). Suppose i(f) = 0. Calculate f.
0, 3
Let x be 0 + 0 - ((-64)/24)/4. Let w(z) be the first derivative of 4 - x*z + 7/6*z**2 - 5/9*z**3. Let w(f) = 0. What is f?
2/5, 1
Let u(v) be the first derivative of v**6/1080 + v**5/120 + v**4/36 - 11*v**3/3 - 4. Let p(d) be the third derivative of u(d). Let p(z) = 0. What is z?
-2, -1
Let k(f) be the third derivative of -f**6/780 - 3*f**5/65 + 90*f**2 + 2*f. Let k(g) = 0. Calculate g.
-18, 0
Let c = -148 + 151. Determine a so that 3*a**4 - 6*a**4 + 11*a**3 + a**c = 0.
0, 4
Let n(q) be the first derivative of -q**7/1960 + q**6/280 + 5*q**3/3 - 11. Let i(m) be the third derivative of n(m). Factor i(a).
-3*a**2*(a - 3)/7
What is p in 22/7*p**3 + 0*p + 0 - 8/7*p**4 - 10/7*p**5 - 4/7*p**2 = 0?
-2, 0, 1/5, 1
Let f = 7 + -4. Let k(t) = -36*t**3 - 36*t**2 + 16. Let j(r) = 7*r**3 + 7*r**2 - 3. Let g(i) = f*k(i) + 16*j(i). Factor g(w).
4*w**2*(w + 1)
Let -11/5*j**4 + 2/5*j - j**5 + 11/5*j**2 + 0 + 3/5*j**3 = 0. Calculate j.
-2, -1, -1/5, 0, 1
Suppose 0 = 4*a + 2 - 10. Let m(j) be the first derivative of 2/35*j**5 + 0*j + 1/7*j**a + 5 + 2/7*j**3 + 3/14*j**4. Factor m(s).
2*s*(s + 1)**3/7
Let b(t) be the second derivative of -t**4/6 + 8*t**3/3 - 16*t**2 + 9*t - 3. Find x, given that b(x) = 0.
4
Let v(y) be the third derivative of -y**11/554400 + y**9/100800 - 3*y**5/20 - 9*y**2. Let i(n) be the third derivative of v(n). What is f in i(f) = 0?
-1, 0, 1
Let j(z) be the third derivative of z**7/840 - z**5/40 + z**4/12 - z**3/2 + 7*z**2. Let t(q) be the first derivative of j(q). Solve t(r) = 0 for r.
-2, 1
Let k(j) = 9*j**2 + j. Let p be (45/(-10) - -4)/(3/(-36)). Let v(r) = 8*r**2 + 2*r. Let g(s) = p*k(s) - 7*v(s). What is y in g(y) = 0?
-4, 0
Suppose 0 = 5*d - 3*u - 45, 7*d - 9*d - 5*u - 13 = 0. Let t be (2 - (d + -3))/((-54)/96). Factor -2/9*m**4 - 8/9*m - 10/9*m**3 + 0 - t*m**2.
-2*m*(m + 1)*(m + 2)**2/9
Suppose -71 = 8*l - 103. Let -2/15*a**l + 0*a + 0*a**3 + 4/15*a**2 - 2/15 = 0. Calculate a.
-1, 1
Factor 18/5*g + 3/5*g**2 - 81/5.
3*(g - 3)*(g + 9)/5
Let x(t) = -t**3 - 829*t**2 - 29394*t - 28566. Let f(i) = -i**3 - 415*i**2 - 14697*i - 14283. Let h(g) = -5*f(g) + 2*x(g). Find q such that h(q) = 0.
-69, -1
Let h(i) = -2*i**2 + 13*i + 47. Let o = -25 + 34. Let x be h(o). Factor -2/3*c**x + 2/3*c**4 - 2/3*c**3 + 2/3*c**5 + 0*c + 0.
2*c**2*(c - 1)*(c + 1)**2/3
Let d = -21 - -15. Let b be -1 - (5 - (-40)/d). Solve b*p**4 + 2/3*p**3 + 0*p + 0*p**2 + 0 = 0.
-1, 0
Solve 96/17 - 14/17*j**4 + 208/17*j - 6/17*j**3 + 118/17*j**2 - 2/17*j**5 = 0.
-4, -1, 3
Let i(t) be the third derivative of 7/20*t**5 + 0 + 0*t - 3/8*t**4 + 0*t**3 + 8*t**2 + 1/70*t**7 - 1/8*t**6. Determine c so that i(c) = 0.
0, 1, 3
Let r(t) = 9*t + 45. Suppose -20 = 3*v + v. Let d be r(v). Factor -1/2*n**2 + d + 1/2*n**4 + 0*n**3 + 0*n.
n**2*(n - 1)*(n + 1)/2
Factor 28 - 4/3*w**2 - 16/3*w.
-4*(w - 3)*(w + 7)/3
Let y be (-16)/98*-7 + (-16)/28. Factor 2*s**3 + 0 - y*s + 10/7*s**2.
2*s*(s + 1)*(7*s - 2)/7
Find o such that 0 + 4/3*o**2 - 2/9*o + 14/9*o**3 = 0.
-1, 0, 1/7
Let d(a) be the first derivative of 1/34*a**4 - 4 + 0*a + 0*a**3 + 0*a**2 - 2/85*a**5. Factor d(k).
-2*k**3*(k - 1)/17
Let g(h) be the second derivative of 18*h**4 - 72*h**3 + 162*h**2 + 2/15*h**6 + 0 - 35*h - 12/5*h**5. Factor g(z).
4*(z - 3)**4
Determine a so that 57*a**3 + 22*a - 11*a**3 - 7*a**5 + 13*a**5 - a**5 + 46*a**2 + 22*a**4 + 4 - a**5 = 0.
-2, -1, -1/2
Let b(q) be the third derivative of 16*q**2 + 1/42*q**4 + 1/210*q**5 + 0*q + 1/21*q**3 + 0. Determine c so that b(c) = 0.
-1
Let z(m) be the second derivative of 1/6*m**3 + 0*m**2 + 1/6*m**4 + 1/180*m**6 + 1/20*m**5 - 6*m + 0. Let y(a) be the second derivative of z(a). Factor y(b).
2*(b + 1)*(b + 2)
Let r(w) = -w**3 - 3*w**2 + 12*w + 12. Let u be r(-5). Suppose 109*f**2 - 11 + u - 106*f**2 - 6*f = 0. Calculate f.
-1, 3
Let i(h) be the third derivative of h**6/30 - h**5/3 + 2*h**4/3 - 357*h**2. Factor i(n).
4*n*(n - 4)*(n - 1)
Suppose 0 = 5*c - 3*a + 49 - 59, 5*c - 10 = 2*a. Let h(m) be the first derivative of 5/3*m**3 + 8 + 5/4*m**4 - 5*m - 5/2*m**c. Suppose h(v) = 0. What is v?
-1, 1
Let c(i) be the second derivative of -i**6/90 - i**5/60 + i**4/6 + 2*i**3/9 - 4*i**2/3 + 639*i. Factor c(z).
-(z - 2)*(z - 1)*(z + 2)**2/3
Suppose 2*w + 2*w - 24 = -4*c, 3*w - c - 6 = 0. Suppose 0 = -4*j - w*a + 4, 5*a = a. Find g, given that 2*g**2 + 3*g**2 + g + g - j - 6*g**2 = 0.
1
Suppose -32*f + 30*f + 4 = 0. Find l, given that -9/4*l + 1/4*l**f - l**5 + 1/2 - 3/4*l**4 + 13/4*l**3 = 0.
-2, -1, 1/4, 1
Let l(m) be the third deriva