*(u + 1)**2
Let n(y) be the first derivative of y**4/14 - 2*y**3/21 + 33. Suppose n(d) = 0. Calculate d.
0, 1
Let s be (-6)/21 + (-1393)/(-245). Solve -s*c**5 + 72/5*c**4 + 12/5*c + 24/5 - 3/5*c**3 - 78/5*c**2 = 0.
-2/3, 1, 2
Let z = 0 - 0. Let q be (0/(-1) + z)/1. Factor 0*h - 1/4*h**5 + 1/2*h**4 + q*h**2 + 0 - 1/4*h**3.
-h**3*(h - 1)**2/4
Factor 1/2*q**3 + 1/2 - 1/2*q**4 + 2*q**2 - 1/4*q**5 + 7/4*q.
-(q - 2)*(q + 1)**4/4
Let j = -338/11 + 3633/110. Let n(t) be the second derivative of 0 + 9/2*t**4 + 2*t**2 + 13/3*t**3 + 7/15*t**6 + j*t**5 - 2*t. Factor n(d).
2*(d + 1)**3*(7*d + 2)
Suppose 2*z - 4*y + 16 = 0, 2*z + 21 = 2*y + 3*y. Factor 0 + 0*x + x**3 - 1/4*x**z.
x**2*(4*x - 1)/4
Let c be 0*-2*(-3)/(-18). Let z(p) be the third derivative of 0*p + c - p**2 + 1/12*p**4 + 1/60*p**5 + 1/6*p**3. Let z(i) = 0. What is i?
-1
Find i such that 0 + 8/13*i + 10/13*i**3 - 16/13*i**2 - 2/13*i**4 = 0.
0, 1, 2
Factor -18/7*x + 0 - 2/7*x**2.
-2*x*(x + 9)/7
Let x(u) be the third derivative of -u**8/672 + u**7/120 - 3*u**6/160 + u**5/48 - u**4/96 + 3*u**2. Let x(b) = 0. What is b?
0, 1/2, 1
Factor -3/4*k**5 + 3/2*k**3 - 3/4*k + 3/4 - 3/2*k**2 + 3/4*k**4.
-3*(k - 1)**3*(k + 1)**2/4
Suppose 1/4 - 5/2*r**3 + 5/2*r**2 - 5/4*r - 1/4*r**5 + 5/4*r**4 = 0. Calculate r.
1
Suppose -4/7 - 6/7*l - 2/7*l**2 = 0. What is l?
-2, -1
Determine t so that -3/2 + 2*t - 1/2*t**2 = 0.
1, 3
Let d(v) = v**2 + 8*v - 8. Let z be d(-9). Let u = 3 - z. Determine c so that -4*c**3 + 5*c**u + 0*c + 2*c**3 - 4*c - 4 + 2*c**2 = 0.
-1/2, 2
Let y = -815/2 - -409. Factor y*v - 3/4*v**2 - 3/4.
-3*(v - 1)**2/4
Let k(c) be the first derivative of -3*c**5/5 + c**4/6 - 6*c + 4. Let m(b) be the first derivative of k(b). Factor m(p).
-2*p**2*(6*p - 1)
Suppose -2*r - 10 = 3*x, -x + 2 = -r - 3. Suppose x = -2*c + 2 + 2. Determine q, given that -2/7*q**c - 2/7*q + 4/7 = 0.
-2, 1
Let z be (-112)/196*(-2)/(40/14). Factor -3/5*k**4 - z*k**3 + 2/5*k + 0 + 3/5*k**2.
-k*(k - 1)*(k + 1)*(3*k + 2)/5
Let 2 - 2*g**4 - g**3 + 11*g**3 + 14*g - 6 - 70*g**2 + 52*g**2 = 0. Calculate g.
1, 2
Let y(c) = -c - 3. Let o be y(-7). Find a such that o*a**4 + a**4 - 2*a**5 - 2*a**4 - 2*a + a**3 + 3*a**5 - 3*a**2 = 0.
-2, -1, 0, 1
Let w be ((-12)/15)/(6/(-15)). Let h(k) be the first derivative of 1/2*k**w + 1/12*k**3 + 1 + k. Suppose h(l) = 0. What is l?
-2
Factor 3 + 0*h**3 - 1 - 4*h**2 + 0*h**3 + 2*h**4.
2*(h - 1)**2*(h + 1)**2
Let s(c) = -c**5 + c**4 + c**2 - c. Let l(o) = -4*o**5 + o**4 - o**3 + 3*o**2 - 3*o. Let i(n) = 4*l(n) - 12*s(n). Factor i(v).
-4*v**3*(v + 1)**2
Suppose -7*r = -5*r - 6. Suppose 4*a = 20, h - 23 = -7*a + r*a. Factor 0 + 1/2*w**5 + 0*w - 1/2*w**2 + 1/2*w**4 - 1/2*w**h.
w**2*(w - 1)*(w + 1)**2/2
Let f = -447/16 + 28. Let w(c) be the first derivative of 0*c - 1/20*c**5 + 1/12*c**3 + 0*c**2 - f*c**4 + 1/24*c**6 - 4. Let w(g) = 0. What is g?
-1, 0, 1
Let l(m) be the first derivative of -m**6/15 + 16*m**5/25 - 3*m**4/5 - 16*m**3/15 + 7*m**2/5 - 3. Determine h, given that l(h) = 0.
-1, 0, 1, 7
Let w = 35 + -35. Let t(o) be the second derivative of -1/48*o**4 - 1/2*o**2 + w + 1/6*o**3 + 3*o. Let t(p) = 0. What is p?
2
Let q be (12/(-16))/((-6)/16). Factor -q*m**2 - 4*m**3 + 12*m**2 + 16*m - 32 + 14*m**2 - 4*m**4.
-4*(m - 2)*(m - 1)*(m + 2)**2
Let v be (-8)/6*30/(-20). Let m(p) = p**3 - 4*p**2 + p. Let g be m(4). Factor -3*w**4 + w**2 - w**3 + v*w**3 + w**g.
-w**2*(w - 1)*(2*w + 1)
Let c(i) be the second derivative of i**4/4 + 2*i**3 + i. Find d such that c(d) = 0.
-4, 0
Let i(p) be the second derivative of -p**6/40 + p**4/8 - 3*p**2/8 - 5*p. Factor i(v).
-3*(v - 1)**2*(v + 1)**2/4
Let v(c) be the first derivative of -c**3/18 - c**2/4 + 1. Factor v(f).
-f*(f + 3)/6
Let g be -3 - (-55)/15 - (6 - 6). Find x, given that g - 2/3*x - 2/3*x**2 + 2/3*x**3 = 0.
-1, 1
Suppose r - 3 = -1. Suppose 2*p + 4*p**3 + r*p + 0*p**3 - 8*p**2 = 0. What is p?
0, 1
Suppose 3*y = 2*k - 11, 0*k - 5*k = 3*y - 38. Let n = -10 + k. Let h(d) = -8*d**2 + d. Let w(b) = -7*b**2. Let c(l) = n*w(l) + 2*h(l). Factor c(a).
a*(5*a + 2)
Let x = -2 + 2. Factor 0 + 0*f - 2/7*f**2 + 2/7*f**4 + x*f**3.
2*f**2*(f - 1)*(f + 1)/7
Let w = -4 + 6. Factor 1 + 1 - w*i**2 + 0.
-2*(i - 1)*(i + 1)
Let h(a) be the second derivative of a**4/28 + a**3/14 + 3*a. Suppose h(t) = 0. What is t?
-1, 0
Find u such that 5*u**4 - 15*u**3 - 167*u - 8 + 182*u - 2 + 5*u**2 = 0.
-1, 1, 2
Suppose -4*c + 15 = -3*g - 8, 5*c + 10 = -4*g. Factor -1 - s**5 + 0*s**2 - s + 2*s**3 + 3*s**2 - s**c + 0*s**4 - s**4.
-(s - 1)**2*(s + 1)**3
Factor -87*n**4 + 4 - n**3 + 83*n**4 - 2*n**3 - 5*n**3 + 8*n.
-4*(n - 1)*(n + 1)**3
Let v = 3 + -5. Let p = v + 4. Find y such that 2*y**2 - 4*y + 3*y**p + 4 - 4*y**2 = 0.
2
Factor 1/7*n**4 + 0 + 0*n + 0*n**2 + 1/7*n**3.
n**3*(n + 1)/7
Suppose -5*w = 2*z - 10, 0 = 5*w + 4*z - 7 - 3. Suppose 5*d - 3*d = 0. Find n, given that d + 3/2*n**w - 1/2*n = 0.
0, 1/3
What is u in -6*u - 8*u - 4*u**2 + 3*u - u = 0?
-3, 0
Let v(w) = 8*w**2 + 2*w + 2. Let q be v(-1). Suppose -q*x = -x. Factor 0*u + 2/3*u**2 + x.
2*u**2/3
Let v(a) be the third derivative of a**8/840 - a**7/175 + a**6/100 - a**5/150 - 34*a**2. Let v(i) = 0. Calculate i.
0, 1
Suppose 4*m - 16 + 0 = 0. Suppose -m*h + h = 0. Factor h + 2*q**4 + 0.
2*q**4
Suppose 0 = -x + 4*x - 15. Factor -12*c**2 - 18*c**3 - 2*c - 3*c**x + 2*c - c - 12*c**4 - 2*c.
-3*c*(c + 1)**4
Let h = 2/81 + -4297/162. Let y = h - -27. Factor y*d + 0 - d**2.
-d*(2*d - 1)/2
Let i(h) be the third derivative of h**8/112 + h**7/70 - 5*h**2. Determine m, given that i(m) = 0.
-1, 0
Let d = -673 - -4712/7. Factor 0 + 0*s + 1/7*s**2 + d*s**3.
s**2*(s + 1)/7
Factor -3/5*g**2 + 1/5*g**3 - 1/5*g + 3/5.
(g - 3)*(g - 1)*(g + 1)/5
Suppose 4*w + 3*c - 5 = 0, 3*w + 2*c - 2 = 3. Find y, given that 192 - y**3 - y**3 + 36*y**2 + 144*y + w*y**3 = 0.
-4
What is l in -1/8*l**4 + 0 - 1/2*l + 1/8*l**5 - 9/8*l**3 - 11/8*l**2 = 0?
-1, 0, 4
Factor -52/7*m**2 - 4/7*m**4 - 16/7 - 24/7*m**3 - 48/7*m.
-4*(m + 1)**2*(m + 2)**2/7
Let s(c) be the first derivative of -4*c**3 + 7*c**2 - 2*c**4 - c**6 - 4*c - 1 + 16/5*c**5. Find g, given that s(g) = 0.
-1, 2/3, 1
Let i be -12 - 3*(-1)/1. Let n be ((-3)/i)/((-3)/(-18)). Suppose -q**n - 1/3*q**4 - 1/3*q + 0 - q**3 = 0. What is q?
-1, 0
Let h(j) be the second derivative of j**7/21 - j**6/15 - j**5/10 + j**4/6 - 6*j. Factor h(q).
2*q**2*(q - 1)**2*(q + 1)
Let x = -2/429 - -3814/143. Factor 0*w**4 + 160/3*w**3 + x*w**2 - 256/3*w**5 + 1/3 + 5*w.
-(w - 1)*(4*w + 1)**4/3
Let z = -9 - -11. Suppose -3/2*i**z - 9/2*i - 3 = 0. What is i?
-2, -1
Let a(w) = -w**2 - 2*w - 1. Let p be a(-3). Let h = p + 6. Let 4/5*n**3 - 2/5*n + 0 + 2/5*n**h = 0. What is n?
-1, 0, 1/2
Suppose -t + 5 = 4*t, 0 = 2*o - 3*t + 17. Let u(h) = -h**2 - 6*h + 9. Let b be u(o). Factor 0*j**2 + 2*j**2 + j**4 - 3*j**b.
j**2*(j - 1)*(j + 1)
Let d be ((-4)/(-15))/(-9*6/(-45)). Find h such that 2/9 + d*h**2 - 4/9*h = 0.
1
Let z be (-12)/60 + (-34)/(-70). Factor -z*m + 8/7*m**3 + 6/7*m**2 + 0.
2*m*(m + 1)*(4*m - 1)/7
Let h be (0 + 9)/(6/2). Factor -12*c + 3*c**2 + 4 - 8*c**3 + 9*c**2 + 4*c**h.
-4*(c - 1)**3
Let w(a) be the first derivative of -13/9*a**3 - 1/6*a**2 + 1/3*a + 1 + 25/12*a**4 - 4/5*a**5. Determine q, given that w(q) = 0.
-1/4, 1/3, 1
Let c(j) = -2*j + 5. Let n be c(3). Let x be (n/5)/((-16)/20). Determine m so that -x*m**4 + 1/2*m**3 + 0 - 1/4*m**5 + 0*m + 0*m**2 = 0.
-2, 0, 1
Let c(a) be the first derivative of a**3/18 - a**2/6 + a/6 + 17. Let c(z) = 0. What is z?
1
Let o be (6 - 6) + 22/6 - 3. Let g(j) be the first derivative of 1/2*j**2 + 0*j - o*j**3 + 1/4*j**4 + 3. Find f, given that g(f) = 0.
0, 1
Let d(j) = -j**3 + 2*j**2 + 3*j + 4. Let c be d(3). Let x(h) be the first derivative of 1/12*h**c - 1/6*h**2 - 1 + 0*h + 0*h**3. Suppose x(a) = 0. Calculate a.
-1, 0, 1
Suppose -5*w + 3*s + 11 = 4, 4*s - 4 = 0. Factor 0*r**w + 0*r - 1/5*r**3 + 0.
-r**3/5
Let w be 1/(-1) + 91/35. Solve -12/5*c - 6/5*c**2 - 1/5*c**3 - w = 0.
-2
Suppose 3*x + 3 - 6 = 2*i, 3*x - 12 = -i. Let u be 3*(i/1 + -2). Factor -k - 3*k**3 - 2*k - 5*k**2 - k + 5*k**4 + 4*k**5 + u*k.
k*(k - 1)*(k + 1)**2*(4*k + 1)
Let t(q) = -2*q**2 - 6*q. Let a(f) = 4*f**2 + 13*f - 1. Let r(m) = 2*a(m) + 5*t(m). Factor r(n).
-2*(n + 1)**2
Let p = 178 - 175. Let l be (-1 - -6) + 2/(-2). Determine x so 