**2 + 4*t**4 - 5*t**2.
-2*t**2*(t + 1)*(7*t + 2)
Let x be (-2)/(-1) - (0 + -2). Factor 16*n**2 + 9*n**3 - 17*n**3 + 28*n + 4*n - 4*n**x.
-4*n*(n - 2)*(n + 2)**2
Let m(r) be the second derivative of -r**4/6 + r**3/3 + 2*r. Find a such that m(a) = 0.
0, 1
Let m = 79 - 77. Suppose 8/3*o - 4/3*o**m - 16/9 + 2/9*o**3 = 0. Calculate o.
2
Factor -2/9*t**2 + 20/9*t + 0.
-2*t*(t - 10)/9
Let t(m) be the second derivative of -m**7/105 - m**6/150 - 4*m. Suppose t(j) = 0. What is j?
-1/2, 0
Let w(o) = -6*o**4 - 9*o**3 - 6*o**2 + 3*o + 6. Let i(q) = -6*q**4 - 8*q**3 - 5*q**2 + 4*q + 7. Let n(v) = 6*i(v) - 7*w(v). Factor n(y).
3*y*(y + 1)**2*(2*y + 1)
Let d(s) = -3*s - 4. Let k be d(-3). Let c(h) be the third derivative of -h**2 + 1/60*h**4 + 0 + 1/300*h**6 - 1/75*h**k + 0*h**3 + 0*h. Factor c(b).
2*b*(b - 1)**2/5
Let l be 0/(-1 + -2 + 4). Factor 0*m + l*m**4 + 0 + 2/5*m**3 + 0*m**2 - 2/5*m**5.
-2*m**3*(m - 1)*(m + 1)/5
Let r(z) = 2*z**2 - 5*z. Let p be r(6). Factor -54*b**2 + 2*b**4 - 4*b**4 + p + b**4 - 123 + 108*b + 12*b**3.
-(b - 3)**4
Let d = -191/21 - -87/7. Solve 8/3*c - d*c**2 - 2/3 + 4/3*c**3 = 0.
1/2, 1
Suppose 0*x - 2*x - 6 = 0. Let c(h) = 7*h**2 - 6*h. Let f(b) = 6*b**2 - 6*b. Let i(a) = x*c(a) + 4*f(a). Let i(z) = 0. Calculate z.
0, 2
Let i(s) be the second derivative of -2/13*s**2 - 1/39*s**3 + 3*s + 1/26*s**4 + 0. Factor i(r).
2*(r - 1)*(3*r + 2)/13
Let k(m) = m**2 - 10*m + 20. Let d be k(8). Let y(i) be the third derivative of 1/84*i**d + 0*i - 1/420*i**6 + 0 + 0*i**5 + 0*i**3 - 3*i**2. Factor y(h).
-2*h*(h - 1)*(h + 1)/7
Let z be 0 + (-29)/(-9) + 4/(-18). Let 2/9*j**2 - 2/9*j**4 - 4/9*j**z + 0*j + 0 + 4/9*j**5 = 0. What is j?
-1, 0, 1/2, 1
Let g(q) be the first derivative of q**5/80 - q**4/16 - 2*q**2 + 9. Let t(r) be the second derivative of g(r). Factor t(k).
3*k*(k - 2)/4
Let t(q) be the first derivative of 2*q**5/65 + 3*q**4/26 + 2*q**3/13 + q**2/13 + 5. Factor t(c).
2*c*(c + 1)**3/13
Let k(h) = -h**2 - h - 1. Let i(j) be the first derivative of -j**3/3 - 9*j**2/2 - 6*j - 4. Let y(l) = -i(l) + 4*k(l). Factor y(q).
-(q - 2)*(3*q + 1)
Suppose -3*p - 6 = -30. Solve -4*f**2 + 2/3*f**3 - 16/3 + p*f = 0.
2
Suppose 8*p = 7*p. Determine s so that 0 + 2/3*s**5 - 4/3*s**2 + 10/3*s**3 + p*s - 8/3*s**4 = 0.
0, 1, 2
Let t(u) be the second derivative of -u**8/336 + u**7/840 + u**6/360 - u**4/12 - 2*u. Let f(i) be the third derivative of t(i). Factor f(m).
-m*(4*m + 1)*(5*m - 2)
Factor -4*x + 24*x**3 - 4*x**2 - 20*x**3 + 2*x**2 + 2*x**4.
2*x*(x - 1)*(x + 1)*(x + 2)
Let m(g) = -10*g**4 - 2*g**3 + 24*g**2 + 20*g + 7. Let z(s) = s**4 - s**2 - 1. Let q(o) = -m(o) - 3*z(o). Find j, given that q(j) = 0.
-1, -2/7, 2
Suppose -4*j - 2*n = -35 + 11, 2*j - 3*n - 12 = 0. Let l = 8 - j. Factor -8*u - 2*u - u**3 + l*u - 5*u**2 - 4.
-(u + 1)*(u + 2)**2
Suppose -s = a + 4*s + 10, 4*a = -2*s - 4. Suppose -4*i + 6*i = a. Let 1/4*y**4 + 0*y + 0*y**3 + 0*y**2 + i = 0. What is y?
0
What is f in 18/5*f**4 + 24/5*f**2 + 0 - 3/5*f**5 + 0*f - 36/5*f**3 = 0?
0, 2
Suppose 2*v = -2*b + 3*b, -3*v = 3*b. Suppose b + 0*f**2 + 1/2*f**3 - 1/2*f = 0. What is f?
-1, 0, 1
Let k = -3498596/18249 - -2/18249. Let h = 192 + k. Factor 0 - h*o - 2/7*o**2.
-2*o*(o + 1)/7
Suppose h + 18 - 30 = 0. Let t be h/(-252) - (-1)/3. Determine z so that 0*z - t*z**2 + 0 - 2/7*z**3 + 2/7*z**5 + 2/7*z**4 = 0.
-1, 0, 1
Let -5*h**4 + 4*h**3 + 2*h**5 - h**2 + 3*h**2 - 3*h**2 = 0. What is h?
0, 1/2, 1
Let p(b) = b**2 + 12*b + 34. Let y be p(-8). Solve -1 + 1/2*c**y - 1/2*c = 0.
-1, 2
Let i(z) be the second derivative of 1/14*z**7 + 1/3*z**4 - 1/6*z**6 + 0*z**2 + 0*z**3 - 1/5*z**5 + 0 - 4*z. Factor i(n).
n**2*(n - 2)*(n + 1)*(3*n - 2)
Let m(j) = -9*j**3 - 6*j**2 - j - 11. Let q(s) = -s**2 + 10*s + 6. Let p be q(8). Let x(l) = -1. Let u(r) = p*x(r) - 2*m(r). What is f in u(f) = 0?
-1/3, 0
Suppose -6*t + 10*t = 12. Factor 8*h**2 - 32*h**2 - 2*h**4 - 5*h**t - 16*h - 7*h**3.
-2*h*(h + 2)**3
Let z(x) be the third derivative of x**6/900 + x**5/90 + 2*x**4/45 + 4*x**3/45 - 5*x**2. Factor z(w).
2*(w + 1)*(w + 2)**2/15
Let n(l) be the first derivative of -2/13*l**2 + 0*l - 2/65*l**5 + 2/39*l**3 + 3 + 1/13*l**4. Let n(y) = 0. Calculate y.
-1, 0, 1, 2
Suppose -2*l = -5*o + 10, 3*l = 4*o + 8*l - 8. Suppose 3 - 2 = -o*r - 3*n, -23 = -5*r + n. Solve 75/2*y**2 - 2 - 133/2*y**3 + r*y - 98*y**4 = 0.
-1, -1/4, 2/7
Let h(a) = -33*a. Let x be h(1). Let o be (-17)/x + 8/(-44). Factor -2/3*r**3 + 0*r + 1/3*r**2 + 0 + o*r**4.
r**2*(r - 1)**2/3
Let i be 24/20*(-40)/(-6). Let m(r) = -6*r**2 - 24*r - 16. Let v(h) = 4*h**2 + 16*h + 11. Let l(s) = i*v(s) + 5*m(s). Factor l(k).
2*(k + 2)**2
Let v = -2239/13 + 173. Solve 16/13*h**2 - 8/13*h - v*h**3 + 2/13*h**4 + 0 = 0 for h.
0, 1, 2
Let x(m) be the third derivative of -2*m**7/105 + m**5/15 - 12*m**2. Suppose x(l) = 0. What is l?
-1, 0, 1
Factor -48/7*c**2 + 0 - 16/7*c - 36/7*c**3.
-4*c*(3*c + 2)**2/7
Let a(x) = -2*x**2. Suppose -i = -3*i - 8. Let b = -2 - i. Let t(c) = c**2 + 4*c - 4. Let d(y) = b*a(y) - 2*t(y). Let d(m) = 0. What is m?
-2, 2/3
Suppose -4*r + r = -4*b - 20, 5*r - 14 = -3*b. Suppose 0*l**2 - 4/3*l**3 + 0*l + 0 + 4/3*l**r = 0. Calculate l.
0, 1
Let b be 32/18 - (-6)/27. Let w(m) = 0*m + 5*m**b + 13 - 4 + 7*m. Let z(k) = 3*k**2 + 4*k + 5. Let i(y) = 4*w(y) - 7*z(y). Solve i(u) = 0.
-1, 1
Let a = -178 - -363/2. Factor -k**3 + 0 + a*k**4 + 0*k**2 + 0*k.
k**3*(7*k - 2)/2
Factor -10*a**2 - 15*a - 6 + 10 - 9.
-5*(a + 1)*(2*a + 1)
Suppose 4*z = r - 17 - 42, 2*r = -z - 8. Let k be 12/24 - 5/z. Factor k*w**2 + 2/7 + 6/7*w + 2/7*w**3.
2*(w + 1)**3/7
Let f(n) = 3*n**3 - 2*n**2 + n. Let s(j) = 25*j**3 - 16*j**2 + 8*j. Let q(b) = 51*f(b) - 6*s(b). Let q(w) = 0. What is w?
0, 1
Let i(h) = h**3 + 14*h**2 + 12*h - 11. Let j be i(-13). Let a(f) be the first derivative of 3 - 4*f**j - 2*f - 7/6*f**3. Factor a(u).
-(u + 2)*(7*u + 2)/2
Let a = 51/2 + -25. Factor a*q - 1/2*q**2 + 0.
-q*(q - 1)/2
Factor -2/3*k + 2/3*k**3 - 1/3*k**2 + 1/3*k**4 + 0.
k*(k - 1)*(k + 1)*(k + 2)/3
Let b(w) = w**3 + w**2 + w - 1. Let y be b(1). Solve 0*n - 6*n**3 - 2*n**y + 4*n**3 + 4*n = 0.
-2, 0, 1
Factor 0 - 1/4*v + 1/4*v**2.
v*(v - 1)/4
Suppose 14*m + 412 = 16*m. Find l such that 206 - l**2 + 2*l - l**2 - m = 0.
0, 1
Let f(w) be the second derivative of -1/20*w**5 + 0 - 1/12*w**4 + 0*w**3 + 0*w**2 + w. Factor f(c).
-c**2*(c + 1)
Suppose 0 = m - 5*o - 24, 6*m + 4 = 4*m - 3*o. Let s(a) be the second derivative of -7/9*a**3 - 2*a + 2/3*a**2 + 0 + 5/18*a**m. Suppose s(f) = 0. Calculate f.
2/5, 1
Factor -1/8*h**5 - 1/4*h + 7/8*h**2 - 9/8*h**3 + 5/8*h**4 + 0.
-h*(h - 2)*(h - 1)**3/8
Let x = -88 - -139. Let t(u) = 8*u**2 - 8*u + 17. Let z(y) = y**2 - y + 2. Let g(k) = x*z(k) - 6*t(k). Determine s so that g(s) = 0.
0, 1
Find a, given that 5*a**2 - 40*a - 60 - 33*a**3 + 70*a**3 - 32*a**3 = 0.
-2, 3
Let a = -9 - -9. Let k(o) be the second derivative of a + 0*o**2 + 2*o + 0*o**4 + 1/70*o**5 + 0*o**3. Find i such that k(i) = 0.
0
Suppose 0 = -3*b - 3*j + 3, -2*b = 5*j + 5 - 1. Solve 2*q + 16/7*q**4 - 8/7*q**b - 6/7*q**5 - 4/7 - 12/7*q**2 = 0 for q.
-1, 2/3, 1
Suppose 0 = 3*b + 2*b - 10. Let q be (b/8)/(-3 - -4). Factor 1/2*s - q - 1/4*s**2.
-(s - 1)**2/4
Let a(f) be the first derivative of -f**6/2 + 3*f**5/5 + 3*f**4/2 - 2*f**3 - 3*f**2/2 + 3*f - 1. What is k in a(k) = 0?
-1, 1
Suppose -8/5*z + 6/5*z**2 - 8/5 + 2/5*z**4 + 8/5*z**3 = 0. Calculate z.
-2, -1, 1
Let c(u) be the third derivative of -u**9/8640 + 19*u**8/20160 - u**7/630 - u**6/180 - u**5/30 - 3*u**2. Let b(p) be the third derivative of c(p). Factor b(g).
-(g - 2)*(g - 1)*(7*g + 2)
Let m(t) = 6*t**2 - 9*t - 1. Let v(n) = -n**2 - n + 1. Let r(w) = -m(w) - v(w). Factor r(b).
-5*b*(b - 2)
Find j, given that -8/5 + 2/5*j + 1/5*j**2 = 0.
-4, 2
Let z(c) be the third derivative of -c**8/2520 + c**7/420 - c**6/180 + c**5/180 + c**3/6 - 3*c**2. Let h(s) be the first derivative of z(s). Factor h(b).
-2*b*(b - 1)**3/3
Let r = 5/13 + -2/39. Suppose -8 = 5*t - 2*k - 2*k, -3*k = -t - 6. Let 1/6*m**2 + 1/6*m**4 + 0 + r*m**3 + t*m = 0. What is m?
-1, 0
Let l = -6 + 8. Suppose l*g - 7*g = 0. Solve 6/5*a**2 + g - 4/5*a + 6/5*a**5 + 6/5*a**3 - 14/5*a**4 = 0.
-2/3, 0, 1
Suppose 0*f + 4 = 4*f. Let a(q) be the first derivative of -f + 0*q - 5/2*q**6 - 9/4*q**4 - 111/20*q**5 + 7/4*q**3 