0 - 4/5*q**4 + 2/5*q**5 + s*q + 0*q**2 = 0.
0, 1
Suppose 10*t - 3216 = 7*t. Factor 12*s**3 + 8*s**2 + 1072*s - 4*s**5 - t*s.
-4*s**2*(s - 2)*(s + 1)**2
Suppose 22*x = 27*x - 15. Suppose 3*p = -x*a + 15, 4*a - 3 - 15 = -3*p. Factor -1/2*u + 0 - 1/4*u**4 - 5/4*u**p - u**3.
-u*(u + 1)**2*(u + 2)/4
Let r(a) = -8*a**3 - 15*a**2 - 5*a - 5. Let c(b) = b**3 + b + 1. Let f be (-1 - -3)*(-6)/((-60)/25). Let h(z) = f*c(z) + r(z). Factor h(x).
-3*x**2*(x + 5)
Let b(z) be the first derivative of z**4 + 32*z**3/3 + 40*z**2 + 64*z + 322. Solve b(s) = 0 for s.
-4, -2
Let w be ((-2)/12)/(1/(-3)). Let t(g) = -2*g**2 + 622*g - 3056. Let b be t(5). Solve -w*h**3 + 1/2*h**2 - 1/2*h**b + 1/2*h + 0 = 0 for h.
-1, 0, 1
Suppose 13 = n + 4*a + 28, 3*a = -n - 11. Let l be n/(-5) + 210/50. Factor 7*b**3 + 2*b**2 - 4*b**l + 2*b**4 - 5*b**3 - 2*b**5.
-2*b**2*(b - 1)*(b + 1)**2
Let p(a) = a**2 + 5*a. Let m be p(-6). What is y in 32*y**4 - 6*y**5 - m - 16*y**3 - 24*y**2 + 31*y - 3*y - 2 - 6*y**5 = 0?
-1, 2/3, 1
Let s(q) be the first derivative of 0*q - 11 - 1/6*q**3 - 1/8*q**2 - 1/16*q**4. Suppose s(a) = 0. Calculate a.
-1, 0
Let r be (-54)/(-8) + (-4)/(-16). Let l = 13 - r. Find w, given that -8*w + 11 - 26*w**2 - 10*w**3 + 3 - l = 0.
-2, -1, 2/5
Let u be 1*(1 - 3)*-1. Let -12 - l**u + 3 - 7 - 8*l = 0. Calculate l.
-4
Let k(v) be the first derivative of 2*v**3/3 - 6*v**2 + 10*v + 211. Suppose k(l) = 0. Calculate l.
1, 5
Let s(g) be the third derivative of g**5/300 + 13*g**4/120 - 34*g**3/15 - 259*g**2. Suppose s(v) = 0. What is v?
-17, 4
Suppose 0 = 5*y - 2*h - 6, -2*y + 3*h - 2 = 0. Let q = 6 + y. Let 2 - 5*m - 187*m**2 + 182*m**2 + q = 0. Calculate m.
-2, 1
Factor -32/7*m**3 + 80/7*m - 44/7*m**2 + 0 - 4/7*m**4.
-4*m*(m - 1)*(m + 4)*(m + 5)/7
Factor 258002*a**4 + 20*a**2 - 34*a**3 - 257997*a**4 + 9*a**3.
5*a**2*(a - 4)*(a - 1)
Let g = 69 - 18. Let x = g + 4. Factor 51*q**3 - x*q**3 - 4*q**2 + 7*q**5 - 3*q**5 + 4*q**4.
4*q**2*(q - 1)*(q + 1)**2
Let u = -16 - -20. Solve -n**u + 4*n**3 + 0*n - 3*n**2 + 2*n**2 + 3 - 4*n - n**2 = 0 for n.
-1, 1, 3
Let i = 39 + -36. Determine b so that 0*b + 2*b**2 - 2*b - 7 + i = 0.
-1, 2
Let f(p) be the third derivative of p**6/60 - 17*p**5/15 + 21*p**4 + 216*p**3 - 12*p**2 + 3*p. Let f(g) = 0. What is g?
-2, 18
Solve 3/2*l**3 + 138*l**2 - 282*l + 0 = 0.
-94, 0, 2
Let h = 237 - 235. Let d(y) be the second derivative of -1/10*y**6 + 0 + 0*y**h + 0*y**5 + 0*y**3 + 3*y + 0*y**4. Solve d(l) = 0.
0
Let z(t) be the third derivative of 2 + 1/7*t**7 + 5/336*t**8 + 1/2*t**6 + 5/8*t**4 + 4*t**2 + 0*t**3 + 0*t + 5/6*t**5. Determine m so that z(m) = 0.
-3, -1, 0
Let n = -131 + 128. Let y(l) = l**3 + 4*l**2 + 8*l + 15. Let f be y(n). Factor -3/5*s + f + 3/5*s**2.
3*s*(s - 1)/5
Suppose 4*g = -g. Let a = 3 - g. What is f in 0*f + a*f + 3*f - 4*f**2 + 7*f**2 = 0?
-2, 0
Let w(u) be the second derivative of 3*u**7/7 + 2*u**6 + 37*u**5/10 + 10*u**4/3 + 4*u**3/3 - 116*u. Determine x, given that w(x) = 0.
-1, -2/3, 0
Let a = -16024/3 - -5342. Solve 0 - 2/3*b + a*b**2 = 0.
0, 1
Let h(r) be the first derivative of 13*r**3/21 + 29*r**2/14 + 6*r/7 - 316. Factor h(i).
(i + 2)*(13*i + 3)/7
Let g be 438/803*(-11)/(-2). Factor 0 + 0*c**2 + 3/2*c**g - 3/2*c.
3*c*(c - 1)*(c + 1)/2
Let f(k) be the first derivative of k**5 - 35*k**4/4 + 25*k**3 - 65*k**2/2 + 20*k - 148. Find h such that f(h) = 0.
1, 4
Let u = 35 + -25. Let q be ((-45)/9)/(u/(-4)). Factor 3*r + r + r**2 - 3*r**q + 4*r**2.
2*r*(r + 2)
Let g(t) = -8*t + 4. Let r be g(-4). Let v be 8/r + (-25)/(-9). Factor 26*l**v - 24*l**3 - 3*l**5 + l**5.
-2*l**3*(l - 1)*(l + 1)
Determine r so that -243 - 110*r**3 + 114*r**3 + 320*r + 76*r**2 - 157 = 0.
-10, 1
Find r, given that -318*r**2 - 324*r**4 + 3*r**5 + 864*r**3 + 0 + 0 + 289*r**3 - 514*r**3 = 0.
0, 1, 106
Factor 1/3*q**2 - 8/3*q - 3.
(q - 9)*(q + 1)/3
Let j be 9/70 - (-17)/(-136). Let p(f) be the third derivative of 1/7*f**3 + 1/56*f**4 + 0*f - 1/70*f**5 + 9*f**2 + 0 - j*f**6. Factor p(q).
-3*(q - 1)*(q + 1)*(q + 2)/7
Let s be (3 + (-7)/2)*(-9)/(-27)*-32. Suppose 24 + 4/3*n**3 - 4*n - s*n**2 = 0. Calculate n.
-2, 3
Let n(l) be the second derivative of -1/15*l**4 + 0 - 8/15*l**3 + 15*l + 8/5*l**2 + 1/25*l**5. Factor n(a).
4*(a - 2)*(a - 1)*(a + 2)/5
Let d = 9 - 7. Solve b + 2 - 4*b**2 + b**d + 2*b**2 = 0 for b.
-1, 2
Let c be 9 - 4 - ((-11 - -22) + -9). Factor -16/15*f**c - 44/15*f**2 - 16/5*f - 6/5 - 2/15*f**4.
-2*(f + 1)**2*(f + 3)**2/15
Let t(i) = -i**3 - 14*i**2 - 14*i + 14. Let s be t(-13). Let g = s - 22. Factor -g*o**3 + 4*o**2 - 2*o**2 + 2*o**2 - 2*o + 3*o**2.
-o*(o - 1)*(5*o - 2)
Factor 9/2*g**3 - 14*g - 3/4*g**2 - 9 + 1/4*g**4.
(g - 2)*(g + 1)**2*(g + 18)/4
Let o be (-3 - 6)*9/(1890/(-20)). Factor o*l + 0 + 2/7*l**2.
2*l*(l + 3)/7
Let f(a) be the second derivative of a**9/9072 + a**8/1680 + a**7/1260 + 4*a**3 - 4*a. Let h(q) be the second derivative of f(q). Let h(c) = 0. What is c?
-2, -1, 0
Let f = 6385 + -6383. Factor 2/5*d**f + 0 + 2/5*d.
2*d*(d + 1)/5
Let g(i) be the third derivative of i**7/735 - i**6/70 - i**5/30 + 3*i**2 + 2. Let g(u) = 0. What is u?
-1, 0, 7
Let k(x) be the second derivative of -x**5/12 + 5*x**4/4 - 25*x**3/6 + 5*x**2 - 34*x. Let w(i) be the first derivative of k(i). Suppose w(t) = 0. What is t?
1, 5
Factor -12*z + 3*z**4 - 2*z**4 + 4 + 11*z**2 + 5 + 4*z**3 - 13*z**2.
(z - 1)**2*(z + 3)**2
Let p(i) = -i**4 - i**3 - i**2 - 1. Let a(l) = -28*l**4 - 16*l**3 - 24*l**2 - 24. Let b(s) = a(s) - 24*p(s). Factor b(r).
-4*r**3*(r - 2)
Let y(t) be the first derivative of -1/7*t**2 - 1 + 0*t - 1/14*t**4 + 4/21*t**3. Factor y(h).
-2*h*(h - 1)**2/7
What is u in 1/3*u**2 - 13/3 - 4*u = 0?
-1, 13
Suppose q + 4*a + 1 + 12 = 0, 2*a = -5*q + 7. Let g be 4/16*14 - (-3)/(-6). Factor -g*r + 0*r**3 + 18*r + 3*r + 2*r**q + 12*r**2.
2*r*(r + 3)**2
Let r(h) = h**5 + h**3 - h + 1. Let z(o) = o**4 + 6 + 4*o**3 - 6*o - 3*o**4 + o**2 + 3*o**5 + 7*o**5 + 3*o**2. Let t(c) = -8*r(c) + z(c). What is s in t(s) = 0?
-1, 1
Let i(z) be the third derivative of -25*z**7/7 - 55*z**6/8 - 21*z**5/4 - 17*z**4/8 - z**3/2 + 9*z**2. Determine c, given that i(c) = 0.
-1/2, -1/5
Suppose -42 = -4*n - 0*n - 2*i, 4*i = -5*n + 57. Let x = n - 7. Solve -5*j**2 + 15*j - 5 - 2*j**x + j**3 - 3 - 1 = 0.
1, 3
Let j be 2/6 + (-71)/(-3). Let x be (2*(-4)/j)/((-1)/9). Suppose 3/8*r**5 - 3/8*r**2 + 0*r - 3/8*r**x + 3/8*r**4 + 0 = 0. Calculate r.
-1, 0, 1
Let l(w) be the third derivative of -w**7/1050 - 7*w**6/600 + w**5/100 + 23*w**4/120 + 7*w**3/15 + 38*w**2. Factor l(a).
-(a - 2)*(a + 1)**2*(a + 7)/5
Let y = 222 + -219. Let m(p) be the first derivative of -6 - 4/9*p - 2/9*p**y - 5/9*p**2. Suppose m(h) = 0. What is h?
-1, -2/3
Factor -9/5 - 1/5*n**5 - 33/5*n - 6*n**3 - 46/5*n**2 - 9/5*n**4.
-(n + 1)**3*(n + 3)**2/5
Suppose -5*c = -15 + 15. Let s(t) be the third derivative of 0*t + 1/210*t**7 + 1/120*t**6 + 0 + 0*t**3 + 0*t**4 + 2*t**2 + c*t**5. Factor s(x).
x**3*(x + 1)
Let h(v) = -3*v**3 - 27*v**2 + 5*v - 5. Let b(r) = -2*r**3 - 14*r**2 + 3*r - 3. Let z(j) = 10*b(j) - 6*h(j). Factor z(n).
-2*n**2*(n - 11)
Let t(x) = -x**3 - x**2 - 1. Let d(r) = -20*r**3 - 15*r**2 - 47*r**2 + 35*r**2 - 60*r - 18*r**2 - 55. Let u(l) = -d(l) + 15*t(l). Factor u(a).
5*(a + 2)**3
Factor 1/4*t**2 + 0 - 5/4*t**3 - 1/4*t**4 + 5/4*t.
-t*(t - 1)*(t + 1)*(t + 5)/4
Let l(b) be the first derivative of b**7/28 - b**6/10 + b**4/4 - b**3/4 - b + 8. Let p(s) be the first derivative of l(s). What is k in p(k) = 0?
-1, 0, 1
Let u = 18757/36 + -521. Let q(j) be the third derivative of u*j**3 - 1/48*j**4 + j**2 + 0*j + 1/120*j**5 - 1/720*j**6 + 0. Determine l, given that q(l) = 0.
1
Let a(t) = -t**3 + t**2 + 3*t. Let n(h) = -32*h**3 - 76*h**2 - 55*h - 8. Let g(l) = 3*a(l) + n(l). Determine p, given that g(p) = 0.
-1, -4/5, -2/7
Let i(q) be the second derivative of -5*q**6/72 + q**5/12 + 5*q**4/8 + 11*q**3/6 - q. Let v(m) be the second derivative of i(m). Factor v(c).
-5*(c - 1)*(5*c + 3)
Let s = -72011/455 - -370/91. Let c = s + 155. Factor -2/5*n + c - 2/5*n**2.
-2*(n - 1)*(n + 2)/5
Let z be (0/(0 - -3))/(-8 - -6). Suppose u + 0 = 4. Find l, given that 8/3*l**3 + 4/3*l**u + 0 + z*l**2 + 0*l = 0.
-2, 0
Suppose 42 - 80 = -19*p. Let s(k) be the third derivative of 0*k**3 - 11*k**p + 0*k**5 + 0 + 1/420*k**8 + 0*k**6 + 0*k**7 + 0*k