m.
-1, 0, 1
Suppose -5442 = -227*k + 11161 - 4345. Let 27*f - k + 45/2*f**2 + 17/4*f**3 + 1/4*f**4 = 0. What is f?
-6, 1
Let j be (-3)/(-2) + -19 + (-2478)/(-140). Factor -1/10 - j*r - 1/10*r**2.
-(r + 1)**2/10
Let p(q) be the second derivative of -5*q**7/42 + q**6/2 - q**5/2 - 5*q**4/6 + 5*q**3/2 - 5*q**2/2 + 36*q + 2. Factor p(y).
-5*(y - 1)**4*(y + 1)
Suppose -498 = -2*h - 2*r - 472, 2*r - 5 = 5*h. Let -3/2*f - 8/3*f**2 - 7/3*f**h - f**4 - 1/6*f**5 - 1/3 = 0. Calculate f.
-2, -1
Suppose 4*h + j = -7 + 25, -3*j = -4*h + 10. Let l(d) be the first derivative of 3*d**2 + 3/4*d**h + 1/10*d**5 + 13/6*d**3 + 8 + 2*d. Factor l(i).
(i + 1)**2*(i + 2)**2/2
Let l(b) = b + 4. Let i be l(0). Let m = -10435/7 - -1493. Factor 4/7*u**i + 20/7*u**2 + 0 - m*u**3 - 8/7*u.
4*u*(u - 2)*(u - 1)**2/7
Let m(f) be the second derivative of f**6/45 - f**5/15 - f**4/6 + 4*f**3/9 + 4*f**2/3 + 16*f - 1. What is k in m(k) = 0?
-1, 2
Let 0*j + 2/3 - 1/6*j**2 = 0. Calculate j.
-2, 2
Factor 4/11 + 6/11*z**2 - 14/11*z.
2*(z - 2)*(3*z - 1)/11
Let i(j) be the second derivative of j**6/6 - 11*j**5/2 + 40*j**4 + 240*j**3 + 177*j. Find b such that i(b) = 0.
-2, 0, 12
Let v(h) be the third derivative of 1/105*h**7 + 0*h + 0*h**4 + 1/30*h**6 + 10*h**2 + 1/30*h**5 + 0 + 0*h**3. Factor v(y).
2*y**2*(y + 1)**2
Factor 2/7*c**4 + 24/7 + 64/7*c + 20/7*c**3 + 58/7*c**2.
2*(c + 1)**2*(c + 2)*(c + 6)/7
Let v(q) be the first derivative of -q**3/15 - q**2/5 - 135. Factor v(b).
-b*(b + 2)/5
Let r(s) be the second derivative of 36/5*s**2 + 1/2*s**4 + 14/5*s**3 + 3/100*s**5 + s + 14. Determine i so that r(i) = 0.
-6, -2
Let j(n) = 3*n**3 + n**2 - n. Let t(i) = 22*i**3 + 10*i**2 - 6*i. Let h(s) = 6*j(s) - t(s). Solve h(w) = 0.
-1, 0
Let u(h) be the third derivative of 2*h**5/225 - h**4/45 + h**3/45 + 11*h**2 + 6*h. Factor u(c).
2*(2*c - 1)**2/15
Let b(d) be the third derivative of 5*d**8/336 + d**7/21 - d**6/8 + 51*d**2. Let b(i) = 0. Calculate i.
-3, 0, 1
Solve 0*z - 4/3*z**4 + 0*z**2 + 2/3*z**3 + 2/3*z**5 + 0 = 0 for z.
0, 1
Suppose -5*m = -c - 20, -m - 20 + 0 = -5*c. Suppose -c*u = -2*u - 9. Factor -8/5*z**u + 2/5*z**2 + 0 + 0*z + 2*z**4 - 4/5*z**5.
-2*z**2*(z - 1)**2*(2*z - 1)/5
Let x(a) = -a**2 + a. Let j(r) = r**2 - 28*r - 48. Suppose 4*b + y = -21, -6*b - 2*y = -b + 30. Let t(v) = b*x(v) - j(v). Factor t(l).
3*(l + 4)**2
Let f = 2592 - 2590. Solve 4/3*w**3 + 0 - 4*w**f + 8/3*w = 0.
0, 1, 2
Let b(s) be the first derivative of -s**6/9 - 14*s**5/15 + 41*s**4/6 - 74*s**3/9 - 40*s**2/3 + 88*s/3 - 216. Suppose b(v) = 0. What is v?
-11, -1, 1, 2
Let o(q) be the third derivative of q**5/480 - q**4/48 - 99*q**2. Determine i so that o(i) = 0.
0, 4
Let q(r) be the third derivative of -r**4/6 - 2*r**3/3 + 3*r**2. Let c be q(-5). Find l such that l**5 - l**2 + c*l**4 - 15*l**4 - l**3 + 0*l**3 = 0.
-1, 0, 1
Let t(j) be the second derivative of j**6/120 + 3*j**5/40 + j**4/16 - 5*j**3/12 - 268*j. Determine m so that t(m) = 0.
-5, -2, 0, 1
Solve -20 + u**2 - 53*u + 33*u - 1 = 0.
-1, 21
Let u(j) be the second derivative of -1/5*j**4 + 0 + 1/5*j**2 - 12*j + 0*j**3 - 4/25*j**5 - 1/25*j**6. Factor u(c).
-2*(c + 1)**3*(3*c - 1)/5
Let o be (2 - (-44)/(-20)) + 7738/40. Let v = o + -192. Factor -v*l**2 + 1/2 - 3/4*l.
-(l + 1)*(5*l - 2)/4
Let m = -3373/5 + 677. Factor -m*d**3 + 0 + 0*d + 2/5*d**4 + 18/5*d**2.
2*d**2*(d - 3)**2/5
Let t(b) = -b**3 - 8*b**2 - 14. Let q be t(-8). Let z be q/(-6)*1*(-4)/(-7). Factor z - 4*p + 3*p**2.
(3*p - 2)**2/3
Factor -8/11*i + 16/11*i**2 + 2/11*i**4 - 10/11*i**3 + 0.
2*i*(i - 2)**2*(i - 1)/11
Let k(j) be the first derivative of -j**4/8 - j**3/2 + 5*j**2/2 - 274. Solve k(h) = 0 for h.
-5, 0, 2
Let x be ((-3862)/6 + 3)/((-21)/9). Let z = x + -274. Factor 2/7 + 2/7*q**5 - 6/7*q + z*q**2 + 4/7*q**3 - 6/7*q**4.
2*(q - 1)**4*(q + 1)/7
Let q(k) = k**3 + 4*k**2 - 14*k - 8. Let v be q(-6). Suppose -3*t = p, v*t = -p + 6*t. Find h such that 1/4*h + 1/4*h**5 + p + 3/2*h**3 - h**4 - h**2 = 0.
0, 1
Factor 97/4*o**2 + 5 + 15/4*o**4 - 18*o - 1/4*o**5 - 59/4*o**3.
-(o - 10)*(o - 2)*(o - 1)**3/4
Let r(g) be the first derivative of 4/5*g + 4/15*g**3 + 4/5*g**2 - 19. Solve r(a) = 0 for a.
-1
Let p be (147/196 + (-27)/20)*-2. Suppose 4*z = -0*n + 2*n + 18, 4*z = 4*n + 28. Solve -27/5*o - 9/5*o**3 + 6*o**z + p = 0 for o.
1/3, 1, 2
Factor -708*p - 3*p**2 + 138*p - 27572 + 2*p**2 - 4510 - 49143.
-(p + 285)**2
Let q(m) = m**2 - 9*m + 16. Let h(g) = 2*g**2 - 18*g + 33. Let f(n) = -4*h(n) + 7*q(n). Factor f(o).
-(o - 5)*(o - 4)
Let o(x) = x**3 + 6*x**2 + 8*x + 3. Let f be o(-3). Factor -4*a + 46*a**2 + 8*a**3 + f*a**3 + 16*a.
2*a*(a + 3)*(7*a + 2)
Let p(r) = r**3 - r**2 + 4. Let u be p(0). Suppose 0 = -3*i + 4*x + x - 1, u*i = x + 10. Solve 21*s + 64*s**2 + i + 9 - 8 + 11*s = 0 for s.
-1/4
Let u(m) = -2*m**3 - 14*m**2 - 38*m + 8. Let r be u(-6). Let s = 493/3 - r. Suppose 0 + s*x**2 - 2/3*x = 0. Calculate x.
0, 2
Let s(m) = -4*m**2 - 111*m - 673. Let d be s(-9). Determine u so that -3/8*u**d + 15/8*u + 9/4 = 0.
-1, 6
Let o(m) be the second derivative of m**6/60 + 31*m**5/40 + 59*m**4/24 + 29*m**3/12 + 30*m + 3. Factor o(t).
t*(t + 1)**2*(t + 29)/2
Let r(b) be the third derivative of b**6/660 + b**5/165 + 388*b**2. Factor r(z).
2*z**2*(z + 2)/11
Let w be 660/(-132) + (1 + 6)*1. Let d(v) be the third derivative of 0*v**5 + 0*v + 0*v**3 + 1/1050*v**7 + 0 + 1/600*v**6 + 4*v**w + 0*v**4. Solve d(b) = 0.
-1, 0
Let j(r) be the first derivative of -17 - 1/15*r**3 + 1/5*r + 0*r**2. Let j(o) = 0. Calculate o.
-1, 1
Solve 4*z**2 + 21*z**3 + 23312*z**4 - 23263*z**4 + 7*z**3 = 0 for z.
-2/7, 0
Let n(y) = y**2 - 13*y + 38. Let w(z) = 2. Let b(x) = -n(x) + 4*w(x). Find p, given that b(p) = 0.
3, 10
Determine f, given that 168/5*f - 2/5*f**2 - 3528/5 = 0.
42
Let p = 16292 + -48400/3. Let c = p - 158. Find a such that -c + 2/3*a**3 + 2/3*a**2 - 2/3*a = 0.
-1, 1
Let u be (11/((-110)/8))/((-1)/5). Suppose -12*s + 32 = u*s. Suppose 1/3 - 1/6*t**s + 1/6*t = 0. Calculate t.
-1, 2
Factor 5/3*n**4 + 0 + 1/3*n**5 + 7/3*n**2 + 2/3*n + 3*n**3.
n*(n + 1)**3*(n + 2)/3
Find r such that 26/5*r**2 + 6 - 58/5*r + 2/5*r**3 = 0.
-15, 1
Let c(g) be the third derivative of -2*g**5/3 + 125*g**4/24 - 5*g**3/2 - 165*g**2. Suppose c(l) = 0. What is l?
1/8, 3
Let w(d) = -2*d**2 + 114*d + 1718. Let z(l) = l**2 - 120*l - 1720. Let g(p) = 4*w(p) + 5*z(p). Factor g(n).
-3*(n + 24)**2
Let l(x) be the first derivative of -2*x**3/27 - 25*x**2/9 - 16*x/3 - 138. Factor l(i).
-2*(i + 1)*(i + 24)/9
Suppose 4*p + 9 = -3*w, -w = -3*p - 0*p + 3. Let m = -4563/905 + 985/181. Factor -1/5*x**2 + m*x + p.
-x*(x - 2)/5
Let f = -4015 + 4017. What is a in 14/9*a**4 - 20/9*a**f + 4/9*a**5 + 0*a**3 + 2/3 - 4/9*a = 0?
-3, -1, 1/2, 1
Let k(t) be the first derivative of -9/2*t**2 + 1/3*t**3 - 10*t + 5. Factor k(p).
(p - 10)*(p + 1)
Let j(a) be the third derivative of a**5/240 - 9*a**4/32 - 15*a**3/4 + 7*a**2. Suppose j(y) = 0. Calculate y.
-3, 30
Suppose -29*q + 59 = -57. Let l(z) be the first derivative of 56*z**4 - q + 512*z**2 + 34/5*z**5 + 704/3*z**3 + 1/3*z**6 + 512*z. What is c in l(c) = 0?
-4, -1
Let c(f) be the third derivative of 0*f**3 - 43/12*f**6 - 10*f**2 - 5/3*f**5 + 0 + 35/6*f**7 + 5/3*f**4 - 35/16*f**8 + 0*f. Suppose c(t) = 0. What is t?
-2/7, 0, 2/7, 2/3, 1
Let y(f) = -f**4 - 7*f**3 - 9*f**2 + 7*f + 4. Let o(p) = p**3 - p**2 - p - 2. Let q(c) = 6*o(c) - 3*y(c). Solve q(r) = 0 for r.
-8, -1, 1
Let l(q) be the third derivative of -q**6/240 + q**5/120 + q**4/6 - q**3 + 214*q**2. Factor l(f).
-(f - 2)**2*(f + 3)/2
Factor -138 - 4*y**2 - 6 - 132*y + 16.
-4*(y + 1)*(y + 32)
Let p(c) be the second derivative of -c**6/9 - 7*c**5/15 - 7*c**4/18 + 2*c**3/9 + 40*c. Find m such that p(m) = 0.
-2, -1, 0, 1/5
Suppose 13*c + 21 = 20*c. Suppose 5*d + 3*y - 2*y + c = 0, 6 = -2*y. Determine x, given that 2/13*x + d + 2/13*x**2 = 0.
-1, 0
Let n(z) be the second derivative of -z**4/54 - 2*z**3/9 + 8*z**2 + 461*z. Factor n(a).
-2*(a - 6)*(a + 12)/9
Suppose 0*m - 8*m + 16 = 0. Let z = 52 + -152/3. Solve z*h**m - h - 1/3 = 0.
-1/4, 1
Let r(s) = 8*s**4 + 11*s**3 + 10*s**2 + s + 6. Let l(o) = -7*o**4 - 10*o**3 - 9*o**2 - o - 5. Let y(u) = -6*l(u) - 5*r(u). Factor y(q).
q*(q + 1)**2*(2*q + 1)
Solve -14/9*b**2 + 0 + 4/3*b = 0.
0, 6/7
Let n(g) be the second derivative of g**4/24 