3)*(m - 1)*(41*m + 2)
Let w(c) be the second derivative of -c**4/20 - 7*c**3/10 - 3*c**2 - 243*c. Suppose w(x) = 0. What is x?
-5, -2
Suppose -4*p = 4*h - 0*p - 12, -5*p = 2*h - 6. Let s be (-2 + -1)*(-4)/4*1. Suppose -o**s - 4*o**2 + 11*o**h - 6*o**3 + 4*o**3 + 12*o**4 = 0. Calculate o.
-1, 0, 1/3
Factor 120 - 15*o**2 - 4*o**4 - 236 + 116 + 20*o**3 - o**4.
-5*o**2*(o - 3)*(o - 1)
Let f = -2/9945 - 17692147/39780. Let d = 447 + f. Find t, given that 1/4*t**2 + 11/4*t**4 + 0 - d*t**3 - t**5 + 1/4*t = 0.
-1/4, 0, 1
Let d(h) be the third derivative of 7*h**7/45 - 1379*h**6/18 + 966277*h**5/90 + 46295*h**4/3 + 8836*h**3 + 2*h**2 - 535*h. Factor d(i).
2*(i - 141)**2*(7*i + 2)**2/3
Let t(l) be the first derivative of -l**6/15 - 26*l**5/25 - 24*l**4/5 - 24*l**3/5 - 14. Let t(a) = 0. Calculate a.
-6, -1, 0
Let h(o) be the first derivative of 20 - 1/28*o**4 + 8/21*o**3 - 13/14*o**2 + 6/7*o. Determine p, given that h(p) = 0.
1, 6
Let s(p) = -2*p**3 - 7*p**2 + 49*p. Let q(m) = -3*m**3 - 10*m**2 + 73*m. Let v(y) = -5*q(y) + 8*s(y). Determine i so that v(i) = 0.
-9, 0, 3
Let l(u) = -5*u**4 + 10*u**3 + 4*u**2 - 6*u - 6. Let s(p) = 4*p**4 - 9*p**3 - 4*p**2 + 5*p + 5. Let h(i) = -5*l(i) - 6*s(i). Factor h(v).
v**2*(v + 2)**2
Let p = 1/93 - -835/186. Let r = p + -3. What is i in 0 + 0*i**4 + 0*i**2 - 3/2*i**5 + 3*i**3 - r*i = 0?
-1, 0, 1
Let b be ((-304)/38 - (-10 - -2))/1. Suppose b*n**3 - 9/4 - 6*n - 9/2*n**2 + 3/4*n**4 = 0. Calculate n.
-1, 3
Let r(k) be the first derivative of 28/5*k**5 - 32*k**2 + 40*k**4 + 176/3*k**3 + 0*k + 4. Find n such that r(n) = 0.
-4, -2, 0, 2/7
Let a(t) be the third derivative of t**8/168 - 8*t**7/105 + 3*t**6/10 - 8*t**5/15 + 5*t**4/12 - 146*t**2. Find u such that a(u) = 0.
0, 1, 5
Factor 11/4*a**4 - 5*a**3 + 0 - a**2 + 0*a.
a**2*(a - 2)*(11*a + 2)/4
Let r(q) be the second derivative of -q**5/60 - 5*q**4/36 - q**3/9 + 4*q**2/3 - q + 19. Factor r(j).
-(j - 1)*(j + 2)*(j + 4)/3
Let q be ((-48)/(-27))/4*3/(-10)*-5. Factor -16/3 + 4/3*j**2 - q*j**3 + 8/3*j.
-2*(j - 2)**2*(j + 2)/3
Factor 1380*p**2 + 34385/3*p + 60835/6 + 175/3*p**3 + 5/6*p**4.
5*(p + 1)*(p + 23)**3/6
Let p(b) = -b**2 - 20*b - 15. Let h be p(-19). Let z be (0 - -3 - 5) + h. Factor 12/5*d**z - 6/5*d**5 - 2/5*d - 24/5*d**3 + 0 + 4*d**4.
-2*d*(d - 1)**3*(3*d - 1)/5
Let f(o) = -2*o**2 + 18*o - 16. Let l(w) = -7 - 25 - 5*w**2 + 26*w + 11*w. Let c(m) = -13*f(m) + 6*l(m). Factor c(h).
-4*(h - 1)*(h + 4)
Let l(g) = g**3 + 28*g**2 - 93*g. Let v be l(-31). Solve 2/3*j**3 - 2/3*j**4 + v*j + 0 - 2/3*j**5 + 2/3*j**2 = 0 for j.
-1, 0, 1
Let y(c) be the second derivative of 5*c**3/6 + 37*c**2/2 + c - 12. Let q be y(-7). Determine g so that -4/9*g**q - 2/9 - 8/9*g**3 + 2/3*g**4 + 8/9*g = 0.
-1, 1/3, 1
Let m(j) be the second derivative of -j**7/147 - 4*j**6/21 - 72*j**5/35 - 72*j**4/7 - 144*j**3/7 + 87*j. Solve m(i) = 0 for i.
-6, -2, 0
Factor 45 + 30*i**2 + 419*i**4 + 12*i**3 - 207*i**4 - 215*i**4 - 84*i.
-3*(i - 5)*(i - 1)**2*(i + 3)
Determine p so that 167*p - 5*p**2 + 83*p - 268 + 90*p - 5512 = 0.
34
Suppose 0*v = 5*v. Let k be v + (1 + -2 - -3). Suppose 1 + 2*g**2 - 5*g**3 + 3*g + 0*g**5 - k*g**3 - 3*g**4 + 5*g**3 - g**5 = 0. Calculate g.
-1, 1
Factor 5*y + 277 + 2*y**2 - 265 + 5*y.
2*(y + 2)*(y + 3)
Suppose -r = 4*k - 26, -4*r = -4*k - 5 - 19. Suppose -42 = -5*j - 3*v, 4*j - 30 - r = -4*v. Let -8*t - 5*t**2 + j + 0 + 7*t**2 + 2 = 0. What is t?
2
Let t(c) be the second derivative of c**6/90 - c**5/10 + c**4/4 + 12*c + 3. Factor t(h).
h**2*(h - 3)**2/3
Let c(i) = i**2 - 4*i + 7. Let t be c(0). Determine y, given that t*y + 3*y**2 - 5*y - 9 - y + 5*y = 0.
-3, 1
Let g be 0*(6/(-16))/((-9)/12). Let b(j) be the second derivative of 1/30*j**5 + 0 + 0*j**2 + g*j**3 - 1/18*j**4 - 2*j. Let b(z) = 0. What is z?
0, 1
Let w = 117 + -115. Factor -45*c**2 - 11 + 44*c**w - 5 + 8*c.
-(c - 4)**2
Let w(v) = 4*v**4 + 10*v**3 - 12*v**2 - 12*v + 12. Let h(a) = a**4 + a**2 - a. Let i(f) = 2*h(f) - w(f). Find q such that i(q) = 0.
-6, -1, 1
Let m(d) be the first derivative of 670*d**3 + 13 + d**4 + 5*d**4 - 671*d**3 + 3*d**4. Factor m(b).
3*b**2*(12*b - 1)
Let -1/7*f**2 - 10/7 + f = 0. Calculate f.
2, 5
Suppose 53 + 49 - 158 - 2825*k**3 - 1970*k**2 + 35*k**5 - 360*k - 1180*k**4 + 56 = 0. Calculate k.
-1, -2/7, 0, 36
Let m = 918 + -2752/3. Let f = -83/2 + 263/6. Factor f*h**4 + 11/3*h**2 - 16/3*h**3 - m*h + 0.
h*(h - 1)**2*(7*h - 2)/3
Factor -6*w**2 - 21 + 2*w**4 + 9 + 12 - 14*w**3 - 30*w**2.
2*w**2*(w - 9)*(w + 2)
Let z(j) be the second derivative of j**5/10 - j**4/2 - 3*j**3 + 27*j**2 - 22*j. Factor z(q).
2*(q - 3)**2*(q + 3)
Let a(i) = 2*i**2 - 16*i - 16. Let w(k) = 3*k**2 - 16*k - 16. Let s be 6 + 0 + (-5)/5. Let f = s + -11. Let l(o) = f*w(o) + 7*a(o). Find n such that l(n) = 0.
-2
Let a(k) be the first derivative of -11/6*k**3 - 1/2*k**2 + 0*k - 2. Factor a(b).
-b*(11*b + 2)/2
Let a be (-30)/18*2 - -4. Let p(u) be the first derivative of a*u**2 + 5 + 0*u + 16/9*u**3 + u**4. Factor p(v).
4*v*(v + 1)*(3*v + 1)/3
Let u be (5 + 644/(-120))*12/(-33). Let g = 31 + -27. Solve 0 - 4/15*r**2 + u*r**g + 0*r - 2/15*r**3 = 0 for r.
-1, 0, 2
Let b(j) be the first derivative of 375/4*j**4 - 28 + 525*j**3 + 2205/2*j**2 + 1029*j. Determine p, given that b(p) = 0.
-7/5
Suppose -118/13*k**3 + 48/13 + 276/13*k**2 - 200/13*k - 24/13*k**4 + 18/13*k**5 = 0. What is k?
-3, 2/3, 1, 2
Let t(o) be the second derivative of 1/9*o**4 + 4/9*o**3 + 0*o**2 + 0 + 26*o - 1/15*o**5. Find z, given that t(z) = 0.
-1, 0, 2
Suppose -60*n + 7 + 14 - 21 = 0. Factor 15/8*j**3 + n + 3/4*j + 21/8*j**2.
3*j*(j + 1)*(5*j + 2)/8
Let m(p) be the third derivative of -p**8/1344 - p**7/168 - 3*p**6/160 - 7*p**5/240 - p**4/48 + 4*p**2 - 16*p. Factor m(f).
-f*(f + 1)**3*(f + 2)/4
Let u be -15 + 20 + -2*2. Let w be (-600)/(-90) - 4*u. Find m, given that -4/3*m**4 + 4/3*m**3 + 0*m + 0 + w*m**2 = 0.
-1, 0, 2
Let y = 54 + -57. Let d be -3*y/18 + (-4)/24. Let d*p + p**3 + p**2 + 1/3*p**4 + 0 = 0. Calculate p.
-1, 0
Let w(p) be the third derivative of p**8/13440 + p**7/3360 - p**5/480 + 7*p**4/24 + 7*p**2. Let c(u) be the second derivative of w(u). Factor c(r).
(r + 1)**2*(2*r - 1)/4
Let r = -669 - -669. Let b(j) be the third derivative of -1/660*j**6 - 4*j**2 - 2/33*j**3 + r*j**5 + 0*j + 1/44*j**4 + 0. Solve b(g) = 0.
-2, 1
Let i(h) be the second derivative of 0 - 3*h**4 + 8*h**2 + 32/3*h**3 - 16*h. Find m such that i(m) = 0.
-2/9, 2
Let q(m) be the second derivative of -6*m**2 - 19*m + 0 + 4/3*m**3 + 1/3*m**4. Find p, given that q(p) = 0.
-3, 1
Let p(s) be the second derivative of -1/3*s**4 - 14*s + 0 - 2*s**2 - 5/3*s**3. Find b such that p(b) = 0.
-2, -1/2
Factor 1/2*j**4 + 15/2*j**2 + 13/2*j + 7/2*j**3 + 2.
(j + 1)**3*(j + 4)/2
Let o(z) be the first derivative of -z**5/160 + z**4/96 + z**3/48 - z**2/16 - 6*z - 13. Let a(n) be the first derivative of o(n). Factor a(v).
-(v - 1)**2*(v + 1)/8
Let l = 7/744 - -411/248. What is p in 0 + 1/3*p**2 + l*p = 0?
-5, 0
Let r(y) be the second derivative of 7*y + 0 + 2*y**2 - 1/4*y**4 - 1/30*y**5 - 2/3*y**3. Let m(q) be the first derivative of r(q). Factor m(g).
-2*(g + 1)*(g + 2)
Let p = 3 + -1. Let i(d) = d**3 + 12*d**2 + 8*d - 30. Let h be i(-11). Suppose z**2 - 2*z**h - 3*z**2 + p*z + 2*z**2 = 0. Calculate z.
-1, 0, 1
Let m = -1/36 - -19/360. Let d(n) be the third derivative of 2*n**2 + 0*n**3 + m*n**5 + 0*n + 0 + 0*n**4 + 1/80*n**6. Factor d(i).
3*i**2*(i + 1)/2
Let m(p) = -148*p**4 + 292*p**3 - 148*p**2 - 8*p + 4. Let a(l) = -2*l**4 + 2*l**2 - l - 1. Let t(j) = -4*a(j) + m(j). Suppose t(g) = 0. What is g?
-1/5, 2/7, 1
Let j(u) = -u**3 - 124*u**2 - 4804*u - 63996. Let g(a) = a**2 + a - 1. Let c(f) = -12*g(f) - 3*j(f). Factor c(k).
3*(k + 40)**3
Let u(l) be the first derivative of l**4/4 - 10*l**3/3 + 33*l**2/2 - 36*l + 845. Factor u(q).
(q - 4)*(q - 3)**2
Let v(z) be the third derivative of -z**5/60 + z**3/6 - 51*z**2. Find u such that v(u) = 0.
-1, 1
Factor -1/4*r - 1/4*r**3 + r**2 - 3/2.
-(r - 3)*(r - 2)*(r + 1)/4
Let v(d) be the third derivative of -d**7/105 + d**6/15 - d**5/15 - d**4/3 + d**3 + d**2 + 53*d. Determine m, given that v(m) = 0.
-1, 1, 3
Let l(y) = y**3 - 2*y**2 + 5*y - 197. Let t be l(0). Let u = t + 197. Factor 0*a + 0 - 1/2*a**5 + u*a**2 + 0*a**4 + 1/2*a**3.
-a**3*(a - 1)*(a + 1)/2
Let