4*h**3 + 3/20*h**6 + 0*h**2 - 33/40*h**5 + 0 + 19/24*h**4 - 23*h. Factor g(u).
u*(u - 3)*(3*u - 1)**2/2
Let b(o) be the first derivative of -3*o - 1/30*o**4 + 0*o**2 + 5 - 2/15*o**3. Let s(r) be the first derivative of b(r). What is d in s(d) = 0?
-2, 0
Let h(x) be the first derivative of x**4/22 + 230*x**3/11 + 39675*x**2/11 + 3041750*x/11 - 462. Factor h(c).
2*(c + 115)**3/11
Let m(i) = 2*i**2 + 19*i - 18. Let h(d) = -2*d**2 - 18*d + 18. Let j(b) = 3*h(b) + 2*m(b). Factor j(s).
-2*(s - 1)*(s + 9)
Factor -1452/5 - 3/5*n**2 + 132/5*n.
-3*(n - 22)**2/5
Let y(c) be the first derivative of 2*c**3/51 - 32*c**2/17 + 512*c/17 - 11. Find b such that y(b) = 0.
16
Find c such that 2/7*c**2 - 16/7*c + 0 = 0.
0, 8
Let h(k) be the second derivative of -1/60*k**5 - 1/8*k**4 + 0*k**2 - 1/1080*k**6 + 0 + 1/2*k**3 - 6*k. Let j(t) be the second derivative of h(t). Factor j(u).
-(u + 3)**2/3
Suppose -3*q + 21 = 6. Suppose -5*j + 15 = 5*v, -q*v = j + 3*j - 9. Determine p, given that 73*p + j*p**2 - 8 + 2*p**3 - 73*p = 0.
-2, 1
Let h(s) = s**3 + 17*s**2 + 16*s + 2. Let m be h(-16). Factor 3*p**3 - 18 + 3*p + 9*p**2 + 8*p**m - 3*p**2 - 2*p**2.
3*(p - 1)*(p + 2)*(p + 3)
Let h(w) be the first derivative of 0*w - 26 + 1/27*w**6 + 0*w**2 + 8/27*w**3 + 0*w**4 - 2/15*w**5. Determine n so that h(n) = 0.
-1, 0, 2
Determine z, given that -3*z**3 + 5*z**5 - 2*z**5 - 8*z**3 - 16*z**3 + 24*z**4 = 0.
-9, 0, 1
Find r, given that 4688/13*r**3 + 33120/13*r**2 - 194400/13*r + 216000/13 + 172/13*r**4 + 2/13*r**5 = 0.
-30, 2
Let y(q) be the third derivative of q**5/15 - 8*q**4 + 384*q**3 + 7*q**2. Factor y(c).
4*(c - 24)**2
Let t(b) be the second derivative of -b**4/42 + b**3/7 - 2*b**2/7 - 19*b - 3. Determine k so that t(k) = 0.
1, 2
Let p(y) = 5*y**2 + y - 2. Let m be p(1). Factor -25*a**m + 10*a + 15*a**2 - 2*a**2 - a**3 - 9*a**3 + 12*a**2.
-5*a*(a - 1)*(a + 1)*(5*a + 2)
Let n be 3 + -4 - (-45)/42. Let o = 3/7 + n. Factor -3/4*f - o + 3/4*f**3 + 1/4*f**2 + 1/4*f**4.
(f - 1)*(f + 1)**2*(f + 2)/4
Let q be 75/(-21) + (-9)/21. Let u = q + 10. Suppose -3*k**3 + 2*k**4 + 3*k**2 - 3*k**3 + u*k - 6*k**4 + k**4 = 0. What is k?
-2, -1, 0, 1
Let r(x) = -7*x**3 - 27*x**2 - 4*x. Let c(u) = -13*u**3 - 54*u**2 - 7*u. Let i(g) = -4*c(g) + 7*r(g). Factor i(y).
3*y**2*(y + 9)
Let n(m) = m**2 + 24*m - 39. Let v(o) = 25*o - 40. Let r(s) = -6*s**3 + 3*s**2 - s - 1. Let i be r(1). Let h(w) = i*n(w) + 6*v(w). Factor h(p).
-5*(p - 3)**2
Suppose -47*i = -46*i + 3*r - 17, 2*i = 3*r - 11. Let 0 - 1/4*y - 1/4*y**i = 0. What is y?
-1, 0
Suppose 0 = -5*n - 25 - 20. Let h = 12 + n. Find z, given that -2*z**3 - 2*z - z**4 + 4*z**h + 0*z**3 + 1 = 0.
-1, 1
Solve p**2 - 2/3 + 1/3*p**3 - 1/3*p - 1/3*p**4 = 0 for p.
-1, 1, 2
Find l such that 14*l + 32*l - 5*l**2 + 90 - 11*l = 0.
-2, 9
Let d(f) = 357*f**2 - 402*f - 63. Let w(r) = 102*r**2 - 115*r - 17. Let x(v) = 5*d(v) - 18*w(v). Find b such that x(b) = 0.
3/17, 1
Suppose -4*c + 2*c = -8. Suppose -2*a + 40 = 2*a. Factor 5*t**3 + 4 + 8*t**2 - 11*t**3 - a*t + c*t**3.
-2*(t - 2)*(t - 1)**2
Let h = -25 + 41. Suppose -h = -0*b - 2*b. Solve 2*d**4 - 6*d - 4*d**3 - 6*d**3 + 8*d**2 - 2*d**2 + b*d**2 = 0.
0, 1, 3
Let y = -15 + 19. Factor 16*o**5 + 60*o**3 - 33*o**4 + 4*o + 28*o**2 - 32*o**y + 117*o**4.
4*o*(o + 1)**3*(4*o + 1)
Factor -335/4*c - 65/4*c**3 + 5/4*c**4 + 255/4*c**2 + 35.
5*(c - 7)*(c - 4)*(c - 1)**2/4
Let g(y) = 7*y**4 + 2*y**3 + 11*y**2 - 8*y - 6. Let s(l) = -13*l**4 - 4*l**3 - 20*l**2 + 15*l + 11. Let d(a) = -11*g(a) - 6*s(a). Let d(b) = 0. What is b?
-2, -1, 0, 1
Factor 64/5*j**3 + 0*j + 0 + 12*j**2 + 4/5*j**4.
4*j**2*(j + 1)*(j + 15)/5
Let q(y) be the second derivative of y**3/2 + 3*y**2/2 + y. Let c(k) = k**2 + 3*k + 2. Suppose -4*f + 9 = -f. Let g(b) = f*c(b) - 4*q(b). Factor g(z).
3*(z - 2)*(z + 1)
Let t(q) be the second derivative of 1/8*q**2 + 1/40*q**5 + 0 - 1/12*q**3 - 1/48*q**4 - 23*q. Find y, given that t(y) = 0.
-1, 1/2, 1
Factor -1152*w + 4/3*w**4 + 480*w**2 - 136/3*w**3 - 4608.
4*(w - 12)**3*(w + 2)/3
Suppose 32*p - 36*p + 12 = 0. Let i(f) = -f**2 - f - 1. Let x(b) = -4*b**4 - 12*b**3 + b**2 + 9*b - 3. Let d(n) = p*i(n) - x(n). Factor d(o).
4*o*(o - 1)*(o + 1)*(o + 3)
Let i(h) be the first derivative of 2*h**5/35 - 4*h**3/21 + 2*h/7 - 41. Factor i(q).
2*(q - 1)**2*(q + 1)**2/7
Let c = 5887 - 29417/5. Factor c*m + 2/5*m**3 + 12/5*m**2 + 0.
2*m*(m + 3)**2/5
Let c be 4/(-5) + 85*6/600. Let t(w) be the third derivative of 1/8*w**4 + 0*w - 8*w**2 - w**3 + c*w**5 + 0. Factor t(b).
3*(b - 1)*(b + 2)
Factor 18*w + 25*w**2 - 11*w**2 - 27 - 17*w**2.
-3*(w - 3)**2
Let r(j) be the second derivative of 0 + 1/6*j**6 + 5/6*j**3 - 4*j + 3/4*j**5 + 5/4*j**4 + 0*j**2. Determine w, given that r(w) = 0.
-1, 0
Factor -4/5*w**2 + 44/5 + 8*w.
-4*(w - 11)*(w + 1)/5
Let l(j) = -j - 1. Let m(x) = 5*x**2 - 31 - 28*x - 10*x + 10*x + 2*x. Let g(u) = -6*l(u) + m(u). Let g(w) = 0. What is w?
-1, 5
Let q(d) = d**2 - 12*d + 39. Let m be q(6). Find n such that 4*n + m*n**2 - 2*n**3 - 2*n - n**2 - 2 = 0.
-1, 1
Let p = 30 - 56. Let g = p + 30. Find y such that -y**3 + 1/2*y**4 - 3/2*y**2 + g*y - 2 = 0.
-2, 1, 2
Let j(y) be the second derivative of 2/33*y**4 + 3/110*y**5 + 12*y + 0*y**2 - 4/33*y**3 - 1/231*y**7 + 0 - 2/165*y**6. Solve j(d) = 0.
-2, 0, 1
Factor -38 + 21*u - 10 + 5*u**2 - 10*u - 3*u**2 + 35*u.
2*(u - 1)*(u + 24)
Let s(n) be the second derivative of 2*n**7/21 + 4*n**6/15 - 4*n**5/5 - 2*n**4/3 + 2*n**3 + 53*n. Factor s(m).
4*m*(m - 1)**2*(m + 1)*(m + 3)
Factor 149*n**3 + 92*n**4 - 394*n**3 - 167*n + 326*n**2 - 5*n**5 - 31*n**3 + 30.
-(n - 15)*(n - 1)**3*(5*n - 2)
What is s in 106*s + 73/2*s**2 + 1/2*s**3 + 70 = 0?
-70, -2, -1
Let w be -3 + 26/10 + (-110)/(-25). Let h(x) be the first derivative of -x**2 - 1/6*x**4 + 0*x - w - 8/9*x**3. Factor h(a).
-2*a*(a + 1)*(a + 3)/3
Let v(z) = 4*z**2 - 778*z - 52251. Let b(s) = s**2 - 260*s - 17418. Let q(o) = -21*b(o) + 6*v(o). Suppose q(l) = 0. Calculate l.
-132
Let l be 6/(4 - 2) + (-2 - -1). What is q in -40*q**3 - 89*q**2 + 10*q - 6*q**l - 40*q + 25*q**4 = 0?
-1, -2/5, 0, 3
Let r = 1907 + -9533/5. Find o, given that -r*o**2 - 18/5 + 12/5*o = 0.
3
Let m be (1/3)/((-1)/(-318)). Factor -r**2 - 158*r + 56 - 3*r**2 + m*r.
-4*(r - 1)*(r + 14)
Let t(r) be the first derivative of 2*r**3/51 - 120*r**2/17 + 7200*r/17 - 13. Factor t(v).
2*(v - 60)**2/17
Determine i so that -4*i**2 + 138*i**3 - i**4 - 132*i**3 + 2*i**4 - 3*i**2 = 0.
-7, 0, 1
Suppose 1/2*t**2 - 4 + 15*t - 15*t**3 + 7/2*t**4 = 0. Calculate t.
-1, 2/7, 1, 4
Factor 1634*h**3 - 400/7 + 896*h**4 + 4040/7*h + 98*h**5 - 13036/7*h**2.
2*(h + 5)**2*(7*h - 2)**3/7
Let y(i) be the first derivative of -23 + 0*i - 2/5*i**2 + 2/5*i**3 - 1/10*i**4. Factor y(j).
-2*j*(j - 2)*(j - 1)/5
Solve -8*o**2 - 1562 - 5*o + 14*o**3 - 9*o + 786 + 784 = 0.
-1, 4/7, 1
Let v = -94 + 97. Let d(m) be the first derivative of 0*m**2 - 1/20*m**5 + 1/6*m**v + 0*m**4 - 1/4*m - 1. Suppose d(c) = 0. Calculate c.
-1, 1
Let x(c) = -7*c - 24. Let m be x(-4). Factor -79*d**2 + d + m*d + 10*d**3 + 64*d**2.
5*d*(d - 1)*(2*d - 1)
Suppose t - 2*t = 0. Suppose 2 + t = j. Let -j*l**4 - l**5 + 5*l**4 + l**4 - 4*l**2 + 2*l - l**5 = 0. What is l?
-1, 0, 1
Let p = -34 + 37. What is r in 2*r**3 + 4*r - r**3 - 5*r**p = 0?
-1, 0, 1
Let a(s) be the first derivative of -s**4/24 + s**3/3 - s**2 - s + 18. Let d(t) be the first derivative of a(t). Factor d(z).
-(z - 2)**2/2
Factor -8*a**2 + 426 - 5*a**3 - 22*a**2 - 266.
-5*(a - 2)*(a + 4)**2
Let r be ((-3)/4)/(-1) + 30/(-60). Solve -1/4 + 1/2*l**3 - 1/2*l + 0*l**2 + r*l**4 = 0.
-1, 1
Factor -308 + 244 - 108*h**2 + 141*h + 11*h + 16*h**3 + 2*h**4 + 2*h**4.
4*(h - 2)*(h - 1)**2*(h + 8)
Let h(b) = 3*b**3 + 12*b**2 + 2. Let c be h(-4). Let t(g) be the second derivative of 0 + 6*g + 1/6*g**c + 0*g**3 - 1/36*g**4. Solve t(f) = 0.
-1, 1
Suppose 11*z**3 - 4*z - 4 + 9*z**2 - 3*z**5 - 5*z**4 + 5*z**3 - 3*z**3 - 6*z**3 = 0. Calculate z.
-2, -1, -2/3, 1
Let i(c) = 15*c**4 + 65*c**3 - 40*c**2 - 235*c - 140. Let b(q) = -7*q**4 - 33*q**3 + 19*q**2 + 117*q + 70. Let g(y) = -5*b(y) - 2*i(y). Factor g(h).
5*(h - 2)*(h + 1)**2*(h + 7)
Suppose 2/7*i**3 + 12/7 + 12/7*i**2 + 22/7*i = 0. What is i?
-3, -2, -1
Factor 18/7*w - 2/7*w**2 - 16/7.
-2*(w - 8)*(w - 1)/7
Let f be (-4)/(-10)*30/3. Suppose 0 = f*