-h(w) + 6*z(w). Factor y(v).
-5*(v - 2)*(v - 1)*(v + 2)
Let a(j) be the second derivative of -j**5/80 - 3*j**4/16 - 23*j**3/24 - 15*j**2/8 + 30*j. Factor a(v).
-(v + 1)*(v + 3)*(v + 5)/4
Let t(y) be the first derivative of y**5/300 + y**4/10 + 6*y**3/5 - 3*y**2/2 + 2. Let s(v) be the second derivative of t(v). Factor s(g).
(g + 6)**2/5
Factor -33*z - 3/4*z**2 - 363.
-3*(z + 22)**2/4
Suppose 0 = -4*u + 2*u. Let a = 4 + u. Factor -2*t**4 + 2*t**4 + t**a + 2*t**3 + t**4.
2*t**3*(t + 1)
Let t(m) be the third derivative of -m**7/210 - m**6/120 + m**5/60 + m**4/24 - 2*m**2 + 6. Factor t(h).
-h*(h - 1)*(h + 1)**2
Let w(f) = -2*f**4 - 14*f**3 - 20*f**2 - 12*f + 4. Let o(g) = -2*g**4 - 15*g**3 - 21*g**2 - 13*g + 5. Let c(k) = -4*o(k) + 5*w(k). Let c(a) = 0. What is a?
-2, -1, 0
Let p be -2 + (4/(-18) - (-20)/9). Suppose -4*s - 16 + 24 = p. Let -9/7*v**3 + 0*v**s - 3/7*v**4 + 12/7*v + 0 = 0. What is v?
-2, 0, 1
Let b(h) = 4*h + 7. Let p be b(6). Suppose y - p = -y + 5*u, 4*y + u = 7. Factor -32*c + 12*c**2 + 73 + 8*c - 57 - 2*c**y.
-2*(c - 2)**3
Suppose 53*x = -25*x. Let g(r) be the second derivative of x + 1/30*r**4 - 7/100*r**5 + 1/30*r**6 + 0*r**2 + 0*r**3 + r. Determine m so that g(m) = 0.
0, 2/5, 1
Factor -5*f**3 - 2596*f - 220 - 2552*f + 5403*f - 30*f**2.
-5*(f - 4)*(f - 1)*(f + 11)
Let m(o) = 30*o**4 - 390*o**3 - 550*o**2 - 135*o. Let t(p) = -15*p**4 + 196*p**3 + 275*p**2 + 67*p. Let b(z) = 3*m(z) + 5*t(z). Let b(y) = 0. What is y?
-1, -1/3, 0, 14
Let x = 0 - -7. Suppose 3*a + 1 = x. Factor 8*r**a - 1 - 1 - 7*r**2 - r.
(r - 2)*(r + 1)
Let l be (-26)/(1976/133)*(32/(-14) + 2). Factor 0 + 5/2*j**2 - j**5 - l*j + 7/2*j**4 - 9/2*j**3.
-j*(j - 1)**3*(2*j - 1)/2
Let v be (-60)/(-33) - (-2)/11. Suppose 2*l + 7*l**2 - 12*l**v - 2*l**3 + 4*l**2 - 6 + 7*l**2 = 0. Calculate l.
-1, 1, 3
Let n(f) be the third derivative of -f**8/1344 + 3*f**7/280 - f**6/160 - 73*f**5/240 - f**4 - 3*f**3/2 + 3*f**2 - 1. Factor n(j).
-(j - 6)**2*(j + 1)**3/4
Suppose 5*i - 59 = 3*z, 1 = 2*i + 5*z - 4. Factor 5*q**2 + i + 191*q - 102*q - 104*q.
5*(q - 2)*(q - 1)
Let j(p) be the second derivative of -3*p + 1/60*p**5 - 1/9*p**3 - 1/36*p**4 + 0 + 0*p**2. Let j(t) = 0. What is t?
-1, 0, 2
Solve -85*d + 47*d**3 - 87*d**3 + 22*d**2 + 58*d**2 + 45*d**3 = 0.
-17, 0, 1
Let u be 8 + 1 + 6 + -12. Let d(w) be the first derivative of 3/28*w**4 + 0*w + 0*w**2 + 4 - 1/21*w**u. Factor d(z).
z**2*(3*z - 1)/7
Suppose 3*y - 6 = -2*w, w + 3*w = 4*y + 12. Suppose y = -12*a + 14 + 22. Determine l, given that 105/4*l**2 - 75/8*l**3 - 33/2*l + a = 0.
2/5, 2
Let p(w) be the first derivative of 3*w**4/20 + w**3/5 - 9*w**2/5 + 51. Factor p(m).
3*m*(m - 2)*(m + 3)/5
Let n(t) be the first derivative of -4*t**3/3 - 116*t**2 - 3364*t + 61. Solve n(h) = 0.
-29
Let o = 7 - 4. Suppose 5*h - o*u - 77 = 0, -5*h + 3*h - 3*u + 14 = 0. Solve 4*y + 1 + 11*y**2 - h*y**2 - 3 = 0 for y.
1
Factor 5765 - 5637 - 202*o + 14*o - 6*o**2.
-2*(o + 32)*(3*o - 2)
Suppose -4*x + 412 = 3*h, 36 = x + 5*h - 50. Let -x*o**4 - 30*o**2 - 37*o**2 + 56*o**3 + 59*o**2 + 40*o**5 = 0. What is o?
0, 1/4, 2/5, 2
Let m(b) = b**3 - 9*b**2 + 8*b + 4. Let w be m(8). Let d(u) be the second derivative of 1/4*u**3 - 4*u + 0 + 0*u**2 + 1/120*u**5 + 1/12*u**w. Factor d(c).
c*(c + 3)**2/6
Let g be 2*((-2)/6 + 39/(-18)). Let x(z) = 13*z + 68. Let q be x(g). Suppose -6/5*o**2 + 3/5*o**q + 0 + 0*o = 0. Calculate o.
0, 2
Let a(b) be the second derivative of -b**4/3 - 2*b**3 + 2*b + 43. Solve a(q) = 0 for q.
-3, 0
Factor -184/7 - 4/7*t**2 + 188/7*t.
-4*(t - 46)*(t - 1)/7
Let s be (-10)/130 - (-53)/13. Let r(z) be the second derivative of 0*z**3 + 2/75*z**6 - 2/25*z**5 + 1/15*z**4 + 0*z**2 - s*z + 0. Factor r(t).
4*t**2*(t - 1)**2/5
Let t be 2/24*8/3. Suppose 51*x = 615 - 513. Let 0*d + t*d**x - 2/9 = 0. What is d?
-1, 1
Let j be -4*(-2 - (-160)/88). Find o such that j + 16/11*o + 10/11*o**2 + 2/11*o**3 = 0.
-2, -1
Let f(z) be the first derivative of 0*z**3 - 13/2*z**2 + 0*z + 0*z**4 + 1/90*z**5 - 6. Let w(t) be the second derivative of f(t). Factor w(g).
2*g**2/3
Let u(q) be the third derivative of 2*q**7/105 - 11*q**6/5 + 1088*q**5/15 + 11*q**4 - 726*q**3 - 2*q**2 + 141*q. Suppose u(l) = 0. Calculate l.
-1, 1, 33
Let w(m) be the first derivative of -2*m**5/5 - 319*m**4/8 + 40*m**3/3 + 955. Find u such that w(u) = 0.
-80, 0, 1/4
Let i(v) = 4*v - 37. Let s be i(10). Determine j so that 2*j**2 - 5*j + 11*j - 6*j - j**s = 0.
0, 2
Suppose 0 = -4*v + 178 + 18. Let c be -7*(-42)/v*(-1)/(-2). Factor -8/9*i**2 - 2/9*i**c - 10/9*i - 4/9.
-2*(i + 1)**2*(i + 2)/9
Factor 3/5*k**2 - 21/5 + 18/5*k.
3*(k - 1)*(k + 7)/5
Let n(m) = 12*m**4 - 25*m**3 + 16*m**2 - m + 2. Let a(b) = 12*b**4 - 24*b**3 + 15*b**2 + 3. Let f(t) = 2*a(t) - 3*n(t). Factor f(l).
-3*l*(l - 1)**2*(4*l - 1)
Let r(b) = -6*b**4 + 15*b**3 + 9*b**2 + 3*b. Let m(p) = p**4 - 2*p**3 + p**2 - p. Let o(k) = -3*m(k) - r(k). Factor o(d).
3*d**2*(d - 4)*(d + 1)
Let m be (38/(-209))/(1/(-11)). Let 0 - 9/2*g**m - 3*g - 3/2*g**3 = 0. What is g?
-2, -1, 0
Let b(q) be the second derivative of -q**8/6720 - q**7/6720 + q**6/2880 - 13*q**3/3 + 21*q. Let u(k) be the second derivative of b(k). Factor u(m).
-m**2*(m + 1)*(2*m - 1)/8
Suppose -2931*i + 2940*i - 18 = 0. Let -3/4 - c - 1/4*c**i = 0. What is c?
-3, -1
Factor 3*k**2 - 60 + 2*k**2 + 138*k - 65*k - 93*k.
5*(k - 6)*(k + 2)
Suppose -72*s**2 + 2*s + 6 + 51*s**2 - 21*s + 4*s**3 = 0. What is s?
-1, 1/4, 6
Let y(i) be the third derivative of -i**8/6720 + i**7/840 + 7*i**5/30 - 4*i**2. Let o(n) be the third derivative of y(n). Solve o(g) = 0 for g.
0, 2
Let t(i) be the first derivative of 0*i**2 + 0*i - 4 + 1/7*i**4 + 0*i**3. Solve t(z) = 0.
0
Let w = 765 + -759. Let m(p) be the first derivative of 5*p**3 - 8 - 3/5*p**5 + 0*p - 3*p**2 + 1/2*p**w - 9/4*p**4. Solve m(q) = 0 for q.
-2, 0, 1
Let i(f) = -1 + 1 + f**2 + f. Let j(d) = 30*d - d**2 - 31*d + 2*d**2 - 9 - 9*d**2. Let c(p) = 21*i(p) + 3*j(p). Factor c(q).
-3*(q - 3)**2
Suppose -4*o + 0*o + 4 = 0. Let t = 209 + -207. Factor 63/2*z**3 + 49/4*z**4 + 109/4*z**t + o + 9*z.
(z + 1)**2*(7*z + 2)**2/4
Let v(k) = -k**3 - 8*k**2 - 8*k - 2. Let g be v(-7). Solve -7 + d**2 + g*d + 17 - 5*d**2 - d**2 = 0.
-1, 2
Let a(k) = k**3 - 2*k**2 + k + 5. Let i be 4 + -9 - (-1)/1. Let s(q) = q**3 - 2*q**2 + q + 4. Let h(g) = i*a(g) + 5*s(g). Factor h(m).
m*(m - 1)**2
Let v(k) be the second derivative of 1/3*k**5 - 5/9*k**4 - 1/3*k**2 + 0 + 5*k - 1/9*k**6 + 5/9*k**3 + 1/63*k**7. Let v(d) = 0. Calculate d.
1
Let r(q) = q**3 + 2*q**2 - q - 10. Let g be r(0). Let v be (-6)/18 + g/(-3). Factor -8/5*i + 0 + 6/5*i**v - 2/5*i**4 + 0*i**2.
-2*i*(i - 2)**2*(i + 1)/5
Let l(m) = m**3 + 8*m**2 + 52*m + 317. Let q be l(-7). Factor 33/7*z**q + 0 + 9/7*z**3 + 18/7*z.
3*z*(z + 3)*(3*z + 2)/7
Let v(x) = 9*x**5 - x**4 + 5*x**3 - 15*x**2 + 2*x. Let d(m) = 8*m**5 - 2*m**4 + 6*m**3 - 14*m**2 + 2*m. Let n(w) = 7*d(w) - 6*v(w). Factor n(o).
2*o*(o - 1)**4
Let d(v) be the second derivative of 1/20*v**5 - v**3 - 1/8*v**4 + 0 - v**2 + 3*v. Let x(r) be the first derivative of d(r). Factor x(t).
3*(t - 2)*(t + 1)
Let d(m) be the third derivative of -m**6/1080 + m**4/8 + m**3/3 + 26*m**2. Let p(u) be the first derivative of d(u). Factor p(i).
-(i - 3)*(i + 3)/3
Let g = -26 - -28. Factor 5*k + 0*k**2 - 2*k**2 - 5*k**2 + 3*k**g - 2 + k**3.
(k - 2)*(k - 1)**2
Let u(r) be the second derivative of 0 + 0*r**3 - 4/5*r**2 - 1/50*r**5 + 1/10*r**4 + 30*r. Suppose u(a) = 0. What is a?
-1, 2
Suppose -4*l + 4*h = -28, -4*l + 4*h = -h - 33. Let j be (8/8)/(2/6). Factor -l*m**2 + 15*m**4 - 6*m**j + 0*m - 5*m**2 + 6*m - 8*m**2.
3*m*(m - 1)*(m + 1)*(5*m - 2)
Let m(d) = d**3 + 3*d**2 - 2*d - 1. Let w be m(-3). Let 5*x**3 - 15*x**5 - 24*x**4 + 10*x**3 + x**w + 18*x**2 + 5*x**5 = 0. What is x?
-3, -2/3, 0, 1
Suppose -3*y + i = 22 - 54, -3*i = -y. Suppose -44*g + y = -38*g. Suppose 22/5*m**3 + 0 + 18/5*m**g - 4/5*m = 0. Calculate m.
-1, 0, 2/11
Factor 13 + 0 - 1 - 18*d + 27*d**2 + 6*d**3 + 54*d.
3*(d + 2)**2*(2*d + 1)
Solve -6/7 + 2/7*v**2 - 4/7*v = 0.
-1, 3
Let k = -34 + 16. Let m(d) = -d**3 - 19*d**2 - 19*d - 14. Let x be m(k). Factor -2/13*z**3 + 0*z**2 - 2/13*z**x + 0 + 0*z.
-2*z**3*(z + 1)/13
Let i(x) be the first derivative of -x**6/270 - x**5/60 + 2*x**3/27 + 16*x - 50. Let p(c) be th