
1/4, 2
Let x(d) = -3*d**4 + 2*d**3 - 5*d**2 - 5*d - 5. Let u(r) = 5*r**4 - 3*r**3 + 8*r**2 + 8*r + 8. Let h(j) = 5*u(j) + 8*x(j). Factor h(n).
n**3*(n + 1)
Let j(i) be the first derivative of -i**6/840 - 3*i**5/280 + 2*i**3/3 - 4. Let l(h) be the third derivative of j(h). Find o, given that l(o) = 0.
-3, 0
Let z(f) = -f**2 - 14*f + 6. Let v be z(-15). Let k(h) = -h**3 - 8*h**2 + 8*h - 6. Let p be k(v). Suppose 16*t + 14*t**2 - 98/3*t**p + 8/3 = 0. Calculate t.
-2/7, 1
Let u(t) be the third derivative of t**7/630 - t**5/90 + t**3/18 - 4*t**2. Factor u(z).
(z - 1)**2*(z + 1)**2/3
Let i(h) be the second derivative of 1/7*h**2 + 0 + 1/14*h**4 + 1/7*h**3 + h + 1/70*h**5. What is p in i(p) = 0?
-1
Let w(o) = 46*o + 5*o**2 + 2 - o**3 - 5 - 48*o. Let k be w(4). Factor -2/7*v - 2/7*v**4 + 4/7*v**2 - 2/7 + 4/7*v**3 - 2/7*v**k.
-2*(v - 1)**2*(v + 1)**3/7
Let i(f) = f**3 + 6*f**2 + f. Let y be i(-3). Let v be 2 - (-14)/y*-3. Find m such that -v*m**2 - 1/4*m + 0 = 0.
-1, 0
Let n(p) be the first derivative of 3 + 11/8*p**2 - 9/16*p**4 - p**3 - 1/2*p. Factor n(c).
-(c + 2)*(3*c - 1)**2/4
Let d be ((-8)/10)/(-1)*(-1)/(-2). Solve 0 + d*p - 2/5*p**2 = 0.
0, 1
Let w(z) be the third derivative of -z**7/1050 + z**6/120 - 3*z**5/100 + 7*z**4/120 - z**3/15 - 3*z**2. Let w(y) = 0. Calculate y.
1, 2
Let z(n) = -10*n**2 + 10*n - 11. Let t(c) = -c**2 + c - 1. Let y(v) = 22*t(v) - 2*z(v). Factor y(a).
-2*a*(a - 1)
Let f(z) be the third derivative of 3*z**7/1120 + z**6/96 + z**5/160 - z**4/32 + z**3/2 - 4*z**2. Let c(i) be the first derivative of f(i). Factor c(v).
3*(v + 1)**2*(3*v - 1)/4
Let o = -3152 + 661921/210. Let k(x) be the third derivative of 0*x**3 + 2*x**2 + 0*x**5 + 0*x - 1/240*x**6 + 0*x**4 + 0 + o*x**7. Let k(i) = 0. What is i?
0, 1/2
Let r be 11/(-33)*(-5 + -1). Factor 10*c**2 + 3*c**r + 8*c - 9*c**2 + 4.
4*(c + 1)**2
Let k = -143/3 - -48. Factor 0 - 1/3*l**3 - k*l**2 + 0*l.
-l**2*(l + 1)/3
Let m(y) be the third derivative of -y**7/840 + y**6/480 + y**5/240 - y**4/96 - 6*y**2. Determine i, given that m(i) = 0.
-1, 0, 1
Let t(f) be the third derivative of 2/105*f**7 - 1/12*f**4 + 0*f**3 + 0 + 1/168*f**8 - 1/15*f**5 + 0*f + 0*f**6 - f**2. Determine x so that t(x) = 0.
-1, 0, 1
Let c = 288 - 1408/5. Factor 16/5*w**2 + 0 + 8/5*w**3 - c*w - 4/5*w**4.
-4*w*(w - 2)**2*(w + 2)/5
Suppose 1 = -3*n + 4, 2*j = -2*n + 20. Let y be (-5 + j)*1/3. Suppose 2/3*s**2 - y*s + 2/3 = 0. What is s?
1
Let k(f) be the second derivative of -5*f**4/12 - 5*f**3/3 - 9*f. Suppose k(g) = 0. Calculate g.
-2, 0
Let l(h) be the second derivative of -h**5/110 - h**4/33 + h**3/11 + 29*h. Let l(t) = 0. What is t?
-3, 0, 1
Let p = 6/7 - 4/7. Find i such that -p*i**2 + 0 - 2/7*i = 0.
-1, 0
Factor -2 + 0*u + 31/2*u**2 + 53/2*u**3 + 33/2*u**4 + 7/2*u**5.
(u + 1)**3*(u + 2)*(7*u - 2)/2
Let a be 0*(3 + 1 + -1 + -4). Factor -39/2*c**2 + a - 3*c - 33/2*c**3.
-3*c*(c + 1)*(11*c + 2)/2
Let a be 2 - (-2 - (-2 + 1)). Factor 2*l + 3*l**2 - 8*l - 2*l**3 - 2*l**a + 7*l**3.
3*l*(l - 1)*(l + 2)
Suppose -7*i = -11*i + 12. Let a(k) be the second derivative of 0 + 1/70*k**5 + 0*k**i + 0*k**2 - 1/42*k**4 - 3*k. Factor a(q).
2*q**2*(q - 1)/7
Let f = -50 + 52. Suppose -2*y - 3*s + f - 11 = 0, -4*y + 2*s = -22. Factor 0*l - l**4 + 0 - 1/3*l**2 - 1/3*l**5 - l**y.
-l**2*(l + 1)**3/3
Let o be 4/(-14) + (-72)/(-56). Let n be 2 - (o + 15/18). Find p such that -n*p**2 + 1/3 - 1/6*p = 0.
-2, 1
Let m be -1 - 4/(20/(-7)). Let t(l) be the first derivative of -1/5*l**2 + 0*l + 2 - 1/5*l**4 - m*l**3. Factor t(y).
-2*y*(y + 1)*(2*y + 1)/5
Let g = -1 - -6. Suppose -g*y + 28 - 8 = 0. Factor -3*a**4 + 2*a**4 + 0*a**y + a**2.
-a**2*(a - 1)*(a + 1)
Let n(q) be the third derivative of q**8/392 - 11*q**7/735 + q**6/30 - q**5/35 - q**4/84 + q**3/21 - 42*q**2. Solve n(w) = 0.
-1/3, 1
Let o be (5 - 3/1) + (-19)/12. Let j(v) be the third derivative of 3*v**2 + 0*v + o*v**4 + 2/3*v**3 - 7/10*v**6 - 19/30*v**5 + 0. Solve j(t) = 0.
-1/2, -2/7, 1/3
Let l(f) be the first derivative of f**5/10 - f**4/6 - 2*f**3/3 - f - 1. Let g(b) be the first derivative of l(b). Let g(k) = 0. Calculate k.
-1, 0, 2
Let t(g) = -g**3 - 2*g**2 - 7*g - 12. Let m be t(-2). Solve 0 + 0*y**3 + 4/5*y**5 + 0*y + 0*y**m - 2/5*y**4 = 0 for y.
0, 1/2
Let o(b) = b**2 + 7*b + 8. Let v be o(-6). Let p be v*(-3 + (-26)/(-8)). Let 0 - 1/4*r + 1/4*r**5 + 0*r**3 - 1/2*r**2 + p*r**4 = 0. What is r?
-1, 0, 1
Let a be (2 + -2 + 1)*(-24)/(-5). Factor -114/5*w**2 - a*w**4 - 24/5 + 84/5*w + 15*w**3 + 3/5*w**5.
3*(w - 2)**3*(w - 1)**2/5
Let d(h) = -11*h**2 - 29*h - 19. Let t(o) = -6*o**2 - 15*o - 9. Let l(a) = 3*d(a) - 5*t(a). Let l(q) = 0. Calculate q.
-2
Let q(h) be the third derivative of 2*h**7/105 - h**5/5 + h**4/3 + 10*h**2. Factor q(r).
4*r*(r - 1)**2*(r + 2)
Let i(x) be the first derivative of -x**4 + 2*x**2 - 3. Solve i(h) = 0.
-1, 0, 1
Let x = -5 - -10. Find i, given that x*i**3 - 3*i**2 - 33*i**4 - 6*i - 12*i**5 + 9*i - 32*i**3 = 0.
-1, 0, 1/4
Let b be (-9)/(-15) + (-53)/105. Let q(z) be the first derivative of 0*z - b*z**3 + 2 + 0*z**2. Determine k, given that q(k) = 0.
0
Let y be (-1)/2*-6 + -1. Suppose 4 = 3*u + 5*v - 7, 2*u = -3*v + 7. Factor -d**y + 3*d**u + d**4 + d**4 + 4*d**3.
2*d**2*(d + 1)**2
Let p(j) be the first derivative of j**5/20 - j**3/2 - j**2 + j - 1. Let g(u) be the first derivative of p(u). Solve g(n) = 0 for n.
-1, 2
Let w(y) be the first derivative of -y**4/6 + 2*y**3/3 - y**2 - y + 7. Let i(t) be the first derivative of w(t). Factor i(z).
-2*(z - 1)**2
Let q = -101 - -104. Factor 1/4*s**q + 0*s**2 + 0 - 1/4*s.
s*(s - 1)*(s + 1)/4
Let i(x) be the third derivative of 0*x**4 + 1/270*x**5 + 0*x**3 - 1/540*x**6 - 3*x**2 + 0 + 0*x. Factor i(t).
-2*t**2*(t - 1)/9
Factor 2/3 - 1/3*n**3 + 1/3*n - 2/3*n**2.
-(n - 1)*(n + 1)*(n + 2)/3
Let p be (-16)/10 - 6/(-10). Let l be (-2)/(-7)*(8 + p). Factor 4/3*n + 2/3*n**l + 2/3.
2*(n + 1)**2/3
Let f(x) be the first derivative of x**7/70 - x**6/40 - x**5/20 + x**4/8 + 3*x**2/2 - 4. Let h(d) be the second derivative of f(d). Factor h(r).
3*r*(r - 1)**2*(r + 1)
Let w(q) = 23*q**3 + 5*q**2 + 9*q. Let j(t) = -8*t**3 + 0*t - 2*t**2 - 4*t - 3*t**3. Let s(b) = 9*j(b) + 4*w(b). Suppose s(x) = 0. Calculate x.
0, 2/7
Factor -d - 12*d**4 - 4*d**2 + 16*d**4 + d.
4*d**2*(d - 1)*(d + 1)
Let z = 49 + -47. Let -t**4 + t**3 + 7/2*t + 1 - 1/2*t**5 + 4*t**z = 0. What is t?
-1, 2
Let p(z) be the third derivative of -z**5/30 + z**4/36 + 2*z**3/9 - 2*z**2. Determine c so that p(c) = 0.
-2/3, 1
Let v(a) = -a**3 + 7*a**2 - 7*a + 8. Let i be v(6). Let d be ((-2)/2)/(i/(-4)). Determine o, given that -4*o + 2*o - o**2 - o**d + 2*o**3 + 2 = 0.
-1, 1
Let l(n) = 3*n**3 + 2*n - 1. Let c be l(1). Find a such that -c*a**2 + a**2 + 0*a**2 + 4*a**2 = 0.
0
Let u(o) be the second derivative of o**5/160 + 5*o**4/96 + o**3/6 + o**2/4 - 8*o - 4. Factor u(b).
(b + 1)*(b + 2)**2/8
Suppose -2*s + 3 = 3*o, -1 = -2*s + o + 6. Suppose -s*d = -3*n - 9, 3*n - d = -3*d + 16. Factor 2*q - 2 + q**3 - 3*q**3 + 0*q**2 + 2*q**n.
-2*(q - 1)**2*(q + 1)
Factor 8*j**2 + 3 - 34*j - 3 + 0 + 8.
2*(j - 4)*(4*j - 1)
Let p be 0 + 75/140 - (-1)/(-4). Factor 4/7*d**3 + 0*d - p*d**2 - 2/7*d**4 + 0.
-2*d**2*(d - 1)**2/7
Determine t so that -2/9 - 8/9*t + 16/9*t**3 + 4/9*t**2 - 8/9*t**5 - 2/9*t**4 = 0.
-1, -1/4, 1
Suppose -5*c + 20 = -0*c, -5*p + 3*c + 3 = 0. Determine y so that y**3 + y**3 + y**3 + 0*y**p = 0.
0
Solve 36/5*w**2 + 0 + 108/5*w + 3/5*w**3 = 0 for w.
-6, 0
Let y(g) = g**2 + 16*g - 17. Let x be y(-17). Let i(c) = -c**2 - 9*c + 12. Let o be i(-10). Factor x + 1/4*t + 3/4*t**3 + t**o.
t*(t + 1)*(3*t + 1)/4
Let d(o) be the second derivative of -9*o**5/20 + 2*o**4 + 3*o**3/2 - 11*o. Suppose d(i) = 0. Calculate i.
-1/3, 0, 3
Let i(s) = -s**2 - 22*s - 21. Let f be i(-21). Factor v + 3/2*v**2 + 1/2*v**3 + f.
v*(v + 1)*(v + 2)/2
Let r = 0 + 0. Let p(z) = z - 11. Let n be p(13). Factor 2*s**n + r*s**3 - 2*s + 3*s**4 + 2*s**3 - 5*s**4.
-2*s*(s - 1)**2*(s + 1)
Suppose 8 = 2*i + 2*i. Let -4*d**2 + 0*d**3 + 2*d**3 + 6*d**i = 0. What is d?
-1, 0
Determine i, given that -178 - 15*i**5 + 12*i**4 + 4*i**3 + 7*i**5 - 12*i**2 + 4*i + 178 = 0.
-1, 0, 1/2, 1
Let w = -2/191 - -400/1719. Let b(m) be the first derivative of 1/3*m**2 - 3 - w*m**3 + 0*m. Factor b(s).
-2*s*(s - 1)/3
Let y(a) be the