 v**2 + v. Let m(s) = 12*s**5 - 7*s**4 - 43*s**3 - 37*s**2 - 19*s - 6. Let a(c) = 2*m(c) - 14*r(c). Let a(d) = 0. Calculate d.
-3, -1
Determine u so that -72*u**5 + 51*u**3 + 7*u**3 - 408*u**4 + 6*u**2 + 2*u**2 + 84*u**3 - 20*u**2 = 0.
-6, 0, 1/6
Let g(n) be the second derivative of n**4/108 + 151*n**3/27 + 22801*n**2/18 + 279*n. Factor g(h).
(h + 151)**2/9
Suppose 131 = 19*t - 325. Let h(w) = -w**2 + 21*w + 74. Let g be h(t). Factor -5/3*i + 1/3*i**3 - 1 - 1/3*i**g.
(i - 3)*(i + 1)**2/3
Let u(b) be the third derivative of -b**8/1680 + b**7/90 - b**6/18 - 3*b**4/4 - 2*b**2. Let n(p) be the second derivative of u(p). Factor n(o).
-4*o*(o - 5)*(o - 2)
Let y = 33040 - 165196/5. What is u in 0 - 16/5*u**2 + 0*u - y*u**4 - 4*u**3 = 0?
-4, -1, 0
Factor -6/5*p + 0 + 13/5*p**2 + 26/5*p**3 + 7/5*p**4.
p*(p + 1)*(p + 3)*(7*p - 2)/5
Let l(w) be the second derivative of 1/9*w**4 - 1/2*w**2 + 1/30*w**5 + 0 - 1/9*w**3 - 1/90*w**6 - 16*w. Determine z so that l(z) = 0.
-1, 1, 3
Let w be 1*-2*(-117)/(-6). Let l be 26/w - (-4)/(-2)*-1. What is r in 0 - 2/3*r**3 + l*r - 2/3*r**2 = 0?
-2, 0, 1
Solve -18/7 + x + 1/7*x**2 = 0 for x.
-9, 2
Let s(l) = l**3 - l**2 + l - 2. Let y be s(2). Let d be (4 - -2)*2/y. Factor -4/7*t - 8/7*t**d - 10/7*t**2 - 2/7*t**4 + 0.
-2*t*(t + 1)**2*(t + 2)/7
Let v = 1 + 2. Let q(r) = -r**3 + 7*r**2 + 4*r + 34. Let h be q(8). Factor 0*n**h + 3*n - 3*n**v + 3/2*n**4 - 3/2.
3*(n - 1)**3*(n + 1)/2
Let u(l) be the first derivative of l**6/6 - l**5/5 - l**4/4 + l**3/3 + 29. Determine t so that u(t) = 0.
-1, 0, 1
Let g(p) be the third derivative of -p**6/300 + p**5/150 + p**4/60 - p**3/15 + 436*p**2. Determine j, given that g(j) = 0.
-1, 1
Let v = 45 + 78. Solve -20*t - 123 + 20*t**2 - 50*t**5 + v + 105*t**3 - 55*t**4 = 0.
-2, -1/2, 0, 2/5, 1
Let o be (-16648)/(-36) + 8/20*5. Let z = o - 464. Determine p so that 4/9*p**2 + 1/9 + 2/9*p**3 - z*p + 2/9*p**5 - 5/9*p**4 = 0.
-1, 1/2, 1
Let z(d) = d**3 - 7*d**2 + 9*d + 10. Let g be z(5). Let h be (-253)/(-115) - (-4)/g. Factor 1/6*q**4 - 1/3*q**h + 1/6*q**2 + 0 + 0*q.
q**2*(q - 1)**2/6
Let z be (-6 - (-14 + 3)) + 57913/(-5910). Let k = 1/1182 - z. Find o such that -k - 66/5*o**2 - 87/5*o**3 - 21/5*o**5 + 18*o**4 + 108/5*o = 0.
-1, 2/7, 1, 2
Let g be 0/((-23 - -17) + 4). Find m such that 1/2*m**2 + g - 1/4*m = 0.
0, 1/2
Let k be ((-1221)/44)/111 - (1/(-4))/1. Determine q, given that -1/7*q**2 + k - 15/7*q = 0.
-15, 0
Let i(w) be the first derivative of -1/8*w**4 + 0*w + 0*w**3 + 10 + 0*w**2. Suppose i(x) = 0. What is x?
0
Let p(w) = 3*w - 16. Let d be p(6). Factor -s**4 + 9*s**3 - 346*s - 2*s**4 - 6*s**d + 346*s.
-3*s**2*(s - 2)*(s - 1)
Find k such that -56*k**3 - 4 + 4 - 196*k**2 - 4*k**4 = 0.
-7, 0
Let b(a) be the first derivative of -2/7*a - 7 + 1/21*a**3 - 3/14*a**2 + 1/35*a**5 + 3/28*a**4. Factor b(d).
(d - 1)*(d + 1)**2*(d + 2)/7
Let k(g) be the third derivative of -g**5/15 + 13*g**4/6 - 8*g**3 + 2*g**2 + 2. Factor k(u).
-4*(u - 12)*(u - 1)
Let z(u) be the second derivative of u**5/30 - u**4/2 - 7*u**3/3 - 11*u**2/3 - 168*u. Factor z(i).
2*(i - 11)*(i + 1)**2/3
Let v(y) be the first derivative of y**5/20 - 15*y**4/16 + 7*y**3/6 + 526. Factor v(a).
a**2*(a - 14)*(a - 1)/4
Let c(m) be the third derivative of -m**11/665280 + m**10/302400 - m**5/5 + 8*m**2. Let f(y) be the third derivative of c(y). Let f(d) = 0. What is d?
0, 1
Let o be ((-90)/70)/(12/(-28)). Factor -6/5 + 3/5*l**2 + 9/5*l**o + 3/5*l**4 - 9/5*l.
3*(l - 1)*(l + 1)**2*(l + 2)/5
Let s(r) be the third derivative of 0*r + 36*r**2 - 1/180*r**6 + 0*r**3 + 0 + 0*r**5 + 0*r**4. Factor s(z).
-2*z**3/3
Let i be (-20)/24*18/(-720). Let a(s) be the third derivative of 1/480*s**5 - 8*s**2 + 0 - 1/96*s**4 + i*s**3 + 0*s. Factor a(k).
(k - 1)**2/8
Let t(a) = -5*a**2 + 22*a + 7. Let m(p) = -7*p**2 + 23*p + 5. Let n(d) = -4*m(d) + 5*t(d). What is v in n(v) = 0?
-5, -1
Let w be ((-90)/27 - -8)*(-6)/(-7). Let g(z) be the second derivative of 10*z + 5/78*z**w + 0 + 6/13*z**2 - 17/39*z**3. Solve g(u) = 0 for u.
2/5, 3
Let y = 5/23 - -3/92. Let r(n) be the first derivative of -1/3*n**3 + 0*n**2 + 0*n - 3 + y*n**4. Factor r(i).
i**2*(i - 1)
Let t(q) = -q**2 - 7*q + 11. Suppose -4*x - 31 = 4*g - 5*x, -5*x - 13 = g. Let j be t(g). Find c such that -4*c**2 + j - 2*c - 2*c**3 - 3 + 0 = 0.
-1, 0
Let u = 111/205 - 14/41. Suppose 2/5*v**2 + 0 + 0*v + u*v**4 - 3/5*v**3 = 0. Calculate v.
0, 1, 2
Let q(r) = -r**3. Let b(k) = 3*k**3 + 47*k**2 - 264*k - 144. Let m(n) = b(n) + 5*q(n). Factor m(p).
-(p - 12)**2*(2*p + 1)
Let w be (0 + 0)*3/(-6). Let g(j) be the first derivative of -1/5*j**5 + 1/6*j**6 + 5 + 0*j + 0*j**4 + 0*j**3 + w*j**2. Determine k so that g(k) = 0.
0, 1
Let -11 - 24*q + 55718*q**2 - 55717*q**2 - 41 = 0. Calculate q.
-2, 26
Suppose 2*w = -3*w - 125. Let b be -2*10*2/w. Determine s so that -10*s**2 - b*s + 10*s**3 + 8/5 = 0.
-2/5, 2/5, 1
Let d(j) be the second derivative of -98*j**6/45 - 7*j**5/15 - j**4/36 + 9*j + 3. Factor d(w).
-w**2*(14*w + 1)**2/3
Let l(g) be the third derivative of -1/28*g**5 - 1/28*g**4 + 0*g + 1/98*g**7 + 0 + 0*g**3 + g**2 + 1/140*g**6. Suppose l(z) = 0. Calculate z.
-1, -2/5, 0, 1
Let y = 96413/36 + -2678. Let a(w) be the third derivative of -5*w**2 - y*w**4 + 0 - 1/90*w**5 - 4/9*w**3 + 0*w. Factor a(q).
-2*(q + 1)*(q + 4)/3
Let -18/5*f + 0 - 24/5*f**3 + 39/5*f**2 + 3/5*f**4 = 0. Calculate f.
0, 1, 6
Let a(i) be the second derivative of -i**5/5 + i**4 + 2*i**3/3 - 6*i**2 + 63*i. Determine w, given that a(w) = 0.
-1, 1, 3
Let d(a) be the second derivative of a**5/210 - 4*a**3/63 + 52*a. Let d(j) = 0. What is j?
-2, 0, 2
Factor 9*o + 10 - 30 + 14 + 15*o**2.
3*(o + 1)*(5*o - 2)
Let t(h) be the second derivative of h**6/15 + 17*h**5/20 + 4*h**4 + 26*h**3/3 + 8*h**2 - 930*h. Determine u, given that t(u) = 0.
-4, -2, -1/2
Let u(w) = -20*w**4 - 30*w**3 + 8*w**2 - 6*w + 6. Let d(b) = -b**4 + 155*b**2 - b - 1 - b**3 - 155*b**2 + 2. Let m(q) = 6*d(q) - u(q). Factor m(f).
2*f**2*(f + 2)*(7*f - 2)
Suppose -3*w + 2*k = 40, -25 = w + 2*w + k. Let a = 16 + w. What is p in p**5 - a*p**3 + 8*p - 5*p**5 - 8*p**4 + 8*p**2 + 2*p**5 = 0?
-2, -1, 0, 1
Let j(v) be the second derivative of v**8/336 - v**6/24 - v**5/12 + 3*v**3 - 28*v. Let q(f) be the second derivative of j(f). Determine g so that q(g) = 0.
-1, 0, 2
Let h be (0 - 7)*(-167)/167. Let t(r) be the second derivative of 0 + 0*r**2 - h*r + 1/150*r**5 - 1/30*r**4 + 2/45*r**3. Factor t(y).
2*y*(y - 2)*(y - 1)/15
Factor -3*o**2 - 1/9*o**3 - 56/3*o + 196/9.
-(o - 1)*(o + 14)**2/9
Let r(y) = y**2 + 17*y + 30. Let i(p) = -p - 2. Let a(c) = -6*i(c) - r(c). Factor a(v).
-(v + 2)*(v + 9)
Let c(p) be the third derivative of 1/84*p**8 + 2/15*p**6 + 2/15*p**5 - 8/105*p**7 + 20*p**2 + 0*p - 5/6*p**4 + 4/3*p**3 + 0. Determine b so that c(b) = 0.
-1, 1, 2
Let c = 436/9 + -424/9. Factor 4/3 + 1/3*k**4 - c*k - k**2 + 2/3*k**3.
(k - 1)**2*(k + 2)**2/3
Suppose -4*h - 3*y = -14, 2*h - 3*y + 6*y - 4 = 0. Let c(s) = s**3 - 5*s**2 - s + 8. Let n be c(h). Factor 0*i**n + 1/2*i**4 + 0*i + 0 - 1/2*i**2.
i**2*(i - 1)*(i + 1)/2
Determine f, given that -9/5 - 1/5*f**4 + 24/5*f - 22/5*f**2 + 8/5*f**3 = 0.
1, 3
Let 5*k**4 + 60*k**2 - 32*k + 80 + 160*k**3 - 59*k**2 - 119*k - 20*k**5 - 169*k - 41*k**2 = 0. Calculate k.
-2, 1/4, 2
Let j(g) be the first derivative of 6 + 19*g**2 - 14/3*g**3 + 12*g. Suppose j(w) = 0. Calculate w.
-2/7, 3
Factor -1/3*k**3 + 0 + 0*k + k**4 + 0*k**2 - 2/3*k**5.
-k**3*(k - 1)*(2*k - 1)/3
Let z(i) = i**2 + 29*i + 192. Let v be z(-19). Determine l, given that -9/2*l**v - 3 + 21/2*l = 0.
1/3, 2
Factor 56/15 - 2/15*l**3 + 52/15*l**2 + 22/3*l.
-2*(l - 28)*(l + 1)**2/15
Suppose -2*w + 29 = 2*l + 25, -11 = -2*l + 5*w. Let b(m) be the first derivative of -3/5*m**5 - 11/4*m**4 + 8*m + 6*m**2 + 2 - 2*m**l. Factor b(p).
-(p - 1)*(p + 2)**2*(3*p + 2)
Solve 0 + 1/4*r**2 - 1/4*r = 0 for r.
0, 1
Suppose r - o - 21 = 2*o, 0 = r + 5*o + 19. Let w be r/25*-10*(-3)/3. Factor 12/5*t**3 + 8/5 - 8/5*t**2 - w*t.
4*(t - 1)*(t + 1)*(3*t - 2)/5
Let y = 9/518 - -2955/8806. Factor 4/17 + 0*v**2 + y*v - 2/17*v**3.
-2*(v - 2)*(v + 1)**2/17
Let i(c) be the second derivative of 1/8*c**4 + 3/2*c**2 + 1/200*c**6 + 1/25*c**5 + 2*c + 0 + 1/5*c**3. Let t(p) be the first derivative of i(p). Factor t(u).
3*(u + 1)**2*(u + 2)/5
Solv