t + 1 + 2/3*t**3 - 2/5*t**5 + 0*t**2. Factor n(m).
2*m**2*(m - 1)**2*(m + 1)
Let t(m) = 2*m**3 - 9*m**2 - 6*m - 11. Let o(z) = 5*z**3 - 26*z**2 - 20*z - 32. Let b(f) = 3*o(f) - 8*t(f). Solve b(v) = 0 for v.
-2
Let b(l) be the third derivative of -l**7/1260 + l**6/360 - l**4/72 + l**3/36 + 668*l**2. Factor b(q).
-(q - 1)**3*(q + 1)/6
Let p = -14 + 22. Find y such that -7*y**2 - 4*y**4 + 0*y**3 + 3*y**2 - p*y**3 + 0*y**2 = 0.
-1, 0
Factor 320/21 + 4/3*q**3 + 72/7*q**2 + 464/21*q - 2/21*q**4.
-2*(q - 20)*(q + 2)**3/21
Factor 14 + 118*a + 140 + 159*a + 5*a**2 + 110*a.
(a + 77)*(5*a + 2)
Let d = 1/351 + 5609/2457. What is k in 4/7*k**2 + d + 16/7*k = 0?
-2
Let b(m) be the third derivative of m**8/168 - 2*m**7/21 - 5*m**6/6 - 8*m**5/3 - 55*m**4/12 - 14*m**3/3 - 599*m**2. Factor b(z).
2*(z - 14)*(z + 1)**4
Let z(f) be the second derivative of f**8/1008 + f**7/315 + f**6/360 - 11*f**2/2 - 27*f. Let y(x) be the first derivative of z(x). What is q in y(q) = 0?
-1, 0
Let t(v) be the first derivative of -4*v**3/3 - 16*v**2 - 28*v + 56. Factor t(c).
-4*(c + 1)*(c + 7)
Let n(g) be the second derivative of -g**7/14 - 3*g**6/10 + 15*g + 2. Find v, given that n(v) = 0.
-3, 0
Let o(t) be the first derivative of -t**6/2 + 3*t**4/4 + 15. Let o(l) = 0. Calculate l.
-1, 0, 1
Let f(l) be the third derivative of -4/735*l**7 + 0*l**3 - 2/21*l**5 + 0 - 21*l**2 - 17/420*l**6 - 1/21*l**4 + 0*l. Suppose f(b) = 0. What is b?
-2, -1/4, 0
Let v(q) = q**2 + q - 106. Let o be v(-11). Let h(s) be the first derivative of 1/3*s**6 + 0*s**o + 0*s - 4/5*s**5 + 6 + 4/3*s**3 - s**2. Factor h(n).
2*n*(n - 1)**3*(n + 1)
Let n(w) be the third derivative of w**7/1260 + w**6/440 - w**5/330 - w**4/12 + 2*w**2. Let o(g) be the second derivative of n(g). Solve o(t) = 0 for t.
-1, 2/11
Suppose -3*y + 24 = 15. Let h(k) be the first derivative of 3/7*k**2 - 3/7*k + 2 - 1/7*k**y. Find n such that h(n) = 0.
1
Suppose 4*d + 2*a + 9 = 3, -4*a = -4*d + 12. Suppose d = -2*g - 3*g. Factor 8*r - 4*r + 0*r + g*r - 4*r**2 + r**3.
r*(r - 2)**2
Let v(u) be the first derivative of 1/5*u**2 - 1 - 1/5*u**4 - 3/25*u**5 + 0*u + 1/3*u**3. Factor v(d).
-d*(d - 1)*(d + 2)*(3*d + 1)/5
Let o = -1/40 - -977/680. Let r = o - 86/85. Factor -8/15*j**3 + 0*j**2 + 2/15 + r*j.
-2*(j - 1)*(2*j + 1)**2/15
Suppose -8*h = -13*h - 50. Let g = 9 + h. Let y(f) = -f**3 - f**2 + f - 1. Let i(l) = -7*l**3 + 17*l**2 - 29*l + 13. Let m(d) = g*i(d) + 3*y(d). Factor m(u).
4*(u - 2)**2*(u - 1)
Let p(o) be the second derivative of o**7/504 + o**6/48 - o**5/6 - 11*o**4/12 + 3*o. Let z(s) be the third derivative of p(s). Factor z(w).
5*(w - 1)*(w + 4)
Suppose 493*i - 453*i = 0. Factor 1/7*q**3 + 5/7*q - 6/7*q**2 + i.
q*(q - 5)*(q - 1)/7
Let a(i) be the first derivative of -i**4/4 + 4*i**3/3 + 5*i**2/2 - 6*i - 3. Let u be a(4). Solve -8*n**2 + 2*n**3 + u*n**2 + n**3 = 0 for n.
-2, 0
Suppose 2*a = -j + 4, 17*a - 12*a + 28 = 7*j. Factor 1/5*w**2 - 1/5*w + a.
w*(w - 1)/5
Let v(b) be the first derivative of -25 + 28*b**2 + 46/3*b**3 + 24*b + 4*b**4 + 2/5*b**5. Find o, given that v(o) = 0.
-3, -2, -1
Let i = 2441/6 + -813/2. Factor 1/3*t**5 + 0 - t**3 - i*t**4 - 2/3*t + 5/3*t**2.
t*(t - 1)**3*(t + 2)/3
Let n(g) be the first derivative of -g**6/18 - 4*g**5/15 - 5*g**4/12 - 2*g**3/9 + 50. Solve n(q) = 0 for q.
-2, -1, 0
Let h(u) be the second derivative of -u**6/240 - u**5/40 + u**3/2 - 10*u. Let m(o) be the second derivative of h(o). Factor m(x).
-3*x*(x + 2)/2
Let f(k) be the third derivative of -k**6/810 - 2*k**5/135 - 4*k**3/3 + 28*k**2. Let o(n) be the first derivative of f(n). Let o(t) = 0. What is t?
-4, 0
Determine u so that 1 - 1/6*u - 1/6*u**2 = 0.
-3, 2
Let b be 567/(-27) + 410/18. Factor 4/3*y**2 + b*y + 2/3 - 2/9*y**4 + 0*y**3.
-2*(y - 3)*(y + 1)**3/9
Let n(a) = -a - 1. Let s be n(1). Let j be (s - (-2 + -1))*0. Factor -4*z + 76*z**2 - 78*z**2 + j*z.
-2*z*(z + 2)
Factor -28*z**3 + 478*z**2 - 62*z - 24 - 546*z**2 - 4*z**4 - 6*z.
-4*(z + 1)**2*(z + 2)*(z + 3)
Let w(l) be the second derivative of l**6/90 + l**5/30 + l**4/36 - l + 89. Let w(i) = 0. What is i?
-1, 0
Let v(w) be the first derivative of -11 - 5*w**3 + 15*w + 5/4*w**4 - 5/2*w**2. What is t in v(t) = 0?
-1, 1, 3
Let a(t) be the third derivative of -t**8/1008 + t**7/105 - t**6/180 - 4*t**5/45 + t**4/24 + 5*t**3/9 - 368*t**2. Determine w so that a(w) = 0.
-1, 1, 2, 5
Let w(y) be the second derivative of y**4/102 - 3*y**3/17 - 93*y. Solve w(h) = 0 for h.
0, 9
Let y(b) be the second derivative of b**6/60 - b**5/5 + b**4 - 8*b**3/3 + 4*b**2 + 2*b - 19. Factor y(p).
(p - 2)**4/2
Let b(s) = 3*s**3 + 31*s**2 + s - 29. Let w(d) = -16*d**3 - 155*d**2 - 6*d + 144. Let o(k) = -33*b(k) - 6*w(k). Suppose o(t) = 0. Calculate t.
-31, -1, 1
Factor -12*h - 195*h**4 - h**2 - 3*h**3 - 13*h**3 - 25*h**2 + 193*h**4.
-2*h*(h + 1)**2*(h + 6)
Let w(j) be the third derivative of 0 + 5/6*j**4 - 4*j**3 + 0*j + 1/15*j**5 - 10*j**2. Factor w(q).
4*(q - 1)*(q + 6)
Let b(a) = 9*a**4 + 18*a**3 + 61*a**2 + 47*a - 7. Let m(f) = 4*f**4 + 9*f**3 + 30*f**2 + 24*f - 3. Let t(r) = 3*b(r) - 7*m(r). Factor t(j).
-j*(j + 3)**3
Let o(d) = -d**3 + 4*d**2 + 34*d + 4. Let l be o(8). Factor 4 - y**4 + 2*y**3 - 24*y**2 - 11*y**3 + y**3 - 32*y - l.
-(y + 2)**4
Let c(o) be the second derivative of -o**7/210 + o**6/30 - o**5/10 + o**4/6 - o**3/6 + o**2/10 + o - 112. Suppose c(r) = 0. What is r?
1
Let a be ((-4)/3)/((-70)/15 - -4). Find x, given that 3*x**4 + 7*x**5 - a*x**5 + 0*x**5 - 2*x**5 = 0.
-1, 0
Let m(c) = -8*c**2 - 44*c + 94. Let h(o) = 3*o**2 + 15*o - 32. Let l(n) = 11*h(n) + 4*m(n). Factor l(k).
(k - 8)*(k - 3)
Let b(q) = -11*q**3 + 4*q**2 - 3*q + 2. Let n be b(2). Let y = -73 - n. Factor 1/2*s**y + 0*s - 1/6*s**2 - 1/3*s**4 + 0.
-s**2*(s - 1)*(2*s - 1)/6
Let l(t) be the second derivative of -1/6*t**4 - 23*t + 0*t**2 + 1/20*t**5 + 0*t**3 + 1/30*t**6 + 0. Factor l(x).
x**2*(x - 1)*(x + 2)
Let c be 2/3 + 8/6. Let d be (-20)/(-15)*3/c. What is z in 0*z**3 - z**3 - 2*z**3 + z**2 - 7*z**d = 0?
-2, 0
Let h(t) be the first derivative of -t**2/2 + 8*t + 4. Let f be h(6). Let -3*m + 3*m**5 + 4*m - 4*m**3 + 2*m - f*m**3 = 0. Calculate m.
-1, 0, 1
Let i be ((-9)/((-45)/3740))/1. Suppose -748 + 20*z**2 + 20*z**3 + i + 5*z**4 = 0. Calculate z.
-2, 0
Let u(a) be the first derivative of -3*a**5/40 - 3*a**4/16 + 9*a**3/2 - 33*a**2/2 + 24*a - 419. Factor u(z).
-3*(z - 2)**3*(z + 8)/8
Let t be -7 + (-14)/(-49) + 42/6. Factor -t*k**2 + 10/7 - 8/7*k.
-2*(k - 1)*(k + 5)/7
Let o = 1816 + -1816. Let f(s) be the third derivative of 1/15*s**3 + 0 - 6*s**2 + o*s**5 - 1/150*s**6 + 1/30*s**4 + 0*s - 1/525*s**7. Factor f(l).
-2*(l - 1)*(l + 1)**3/5
Let p = 230909/4224 - -1/1408. Let y = p - 54. Factor -y - 3*o - 14/3*o**3 - 16/3*o**2 - 2*o**4 - 1/3*o**5.
-(o + 1)**4*(o + 2)/3
Let d(p) be the third derivative of -p**8/784 + 8*p**7/245 + 4*p**6/35 - 192*p**5/35 - 288*p**4/7 + 492*p**2. Factor d(i).
-3*i*(i - 12)**2*(i + 4)**2/7
Let d(j) = 4*j**3 + 20*j**2 + 26*j - 66. Let h(k) = k**3 + 4*k**2 + 5*k - 13. Let q(f) = 3*d(f) - 14*h(f). Solve q(r) = 0 for r.
-2, 2
Suppose 4*q - 4*m = q + 27, 2*m = 2*q - 16. Let d(u) be the third derivative of 0 - 2/3*u**3 + 5*u**2 + 1/30*u**q + 0*u + 1/12*u**4. Solve d(a) = 0.
-2, 1
Let t(u) be the third derivative of u**8/2016 - u**7/252 - 13*u**6/720 - 7*u**5/360 - 91*u**2. Factor t(w).
w**2*(w - 7)*(w + 1)**2/6
Factor -13 - 5 + 420*r**2 + 44*r + 53*r - 72 + 45*r**3 + 28*r.
5*(r + 9)*(3*r - 1)*(3*r + 2)
Let z(m) be the second derivative of 4/7*m**2 - m + 1/35*m**5 + 0 + 4/21*m**4 + 10/21*m**3. Factor z(a).
4*(a + 1)**2*(a + 2)/7
Factor 0*l**2 + 0*l + 0 - 1/7*l**4 + 7*l**3.
-l**3*(l - 49)/7
Let s(n) = -n**2 + 2. Let c be s(0). Let x(g) = 2*g. Let d(m) = -m**2 - m + 1. Let y(u) = c*d(u) + x(u). Determine b, given that y(b) = 0.
-1, 1
Let k(t) = t + 12. Let i = 93 + -103. Let d be k(i). Determine s, given that 0*s + 0 + 2/7*s**4 + 0*s**d - 6/7*s**3 = 0.
0, 3
Let y(z) be the third derivative of z**6/60 - z**4/4 + 2*z**3/3 + 2*z**2 - 40*z. Determine c, given that y(c) = 0.
-2, 1
Suppose -2*l + 6*c = -34, -c + 5 = 11*l - 6*l. Suppose 4/13*o**l + 4/13 - 10/13*o - 8/13*o**4 + 8/13*o**3 + 2/13*o**5 = 0. Calculate o.
-1, 1, 2
Let -15*d**3 + 8*d - 6*d + 26 - 69*d**2 + 4*d + 9*d - d**4 + 44*d**2 = 0. What is d?
-13, -2, -1, 