t h(a) = 8*a**4 + 72*a**3 + 216*a**2 + 216*a + 17. Let d(u) = -u**4 - 9*u**3 - 27*u**2 - 27*u - 2. Let w(y) = 51*d(y) + 6*h(y). Let w(l) = 0. Calculate l.
-3, 0
Let l(k) = -4*k**5 - 4*k**4 + 8*k**3. Let w(j) = -4*j**5 - 3*j**4 + 8*j**3 - j. Let u(y) = 3*l(y) - 4*w(y). Factor u(c).
4*c*(c - 1)**2*(c + 1)**2
Let g(r) = -4*r**3 - 3*r**2 - 3*r. Let b(o) = -o**3 - o**2 - o. Let m(q) = -3*b(q) + g(q). Factor m(f).
-f**3
Let u(d) = 7*d**2 + 8*d + 6. Let r(l) = 4*l**2 + 4*l + 3. Let f be 2 - 4 - (-2 - -3). Let g(b) = f*u(b) + 5*r(b). Factor g(c).
-(c + 1)*(c + 3)
Let z(i) be the third derivative of i**6/40 + i**5/10 + i**4/8 - 2*i**2. Let z(u) = 0. What is u?
-1, 0
Let a(g) be the first derivative of 7*g**3/6 - g**2/2 + 21. Factor a(m).
m*(7*m - 2)/2
Let l(y) = -5*y**3 - 2*y**2 - y - 4. Let w(x) be the first derivative of x**4/4 + x + 2. Let g(m) = -l(m) - 4*w(m). Find b such that g(b) = 0.
-1, 0
Let l(n) be the third derivative of -4*n**2 - 1/80*n**6 + 0*n**3 + 0 + 1/24*n**5 + 1/24*n**4 + 0*n. Factor l(f).
-f*(f - 2)*(3*f + 1)/2
Factor b + 1/3*b**2 + 2/3.
(b + 1)*(b + 2)/3
Let a(z) be the second derivative of -z**6/1080 - z**5/180 - z**4/72 + z**3/2 + 3*z. Let k(c) be the second derivative of a(c). Factor k(l).
-(l + 1)**2/3
Factor 4*v**3 + 6*v**4 + 11 - 20*v**2 - 2*v**4 - 11 + 12*v.
4*v*(v - 1)**2*(v + 3)
Let d be 4 - (-5)/(-9 + 4). Let r(a) be the third derivative of 0 + 0*a + 0*a**d - a**2 - 1/60*a**4 - 1/150*a**5. What is b in r(b) = 0?
-1, 0
Let b(d) be the second derivative of d**5/4 - 5*d**4/12 - 5*d**3/6 + 5*d**2/2 - 2*d. Factor b(n).
5*(n - 1)**2*(n + 1)
Let a(n) be the third derivative of 0 + 0*n - 2*n**2 - 1/21*n**3 - 1/420*n**6 - 1/70*n**5 - 1/28*n**4. Suppose a(o) = 0. What is o?
-1
Let w(o) be the second derivative of o**7/42 + o**6/15 - 3*o**5/20 - o**4/3 + 2*o**3/3 + 16*o. Factor w(y).
y*(y - 1)**2*(y + 2)**2
Let w(k) = -3*k**2 + 21*k + 6. Let v(y) = 1. Let o(c) = -6*v(c) + w(c). Factor o(r).
-3*r*(r - 7)
Suppose 4*h = 2*h + 8, 5*y + h = 39. Factor -y + 9 + 14 + 48*r + 3*r**3 + 5*r**3 + 36*r**2.
4*(r + 2)**2*(2*r + 1)
Let v be 0/(-4 + -2 + 4). Factor 5*m**2 + v*m - m**2 + 8*m + 4.
4*(m + 1)**2
Let u(j) be the first derivative of 3 - 2/27*j**3 + 4/9*j**2 - 8/9*j. Determine n so that u(n) = 0.
2
What is o in 2/11*o**4 - 2/11*o**2 - 2/11*o**3 + 2/11*o**5 + 0 + 0*o = 0?
-1, 0, 1
Let m(u) be the second derivative of 2*u**7/147 - 6*u**6/35 + 24*u**5/35 - 16*u**4/21 + 18*u. Factor m(p).
4*p**2*(p - 4)**2*(p - 1)/7
Suppose 6 + 21 = -3*y. Let x be 2/4 + y/(-6). Factor 2/5*c**x - 2/5 + 0*c.
2*(c - 1)*(c + 1)/5
Let w be 4/(-3)*(-4014)/96. Let b = -55 + w. Solve b*v - v**5 + 1/2 + 3*v**4 - 5/4*v**3 - 2*v**2 = 0.
-1/2, 1, 2
Let b(h) = 9*h - 36. Let k be b(4). Let f(r) be the second derivative of -1/18*r**4 + 0*r**2 + k + 1/45*r**6 - 1/9*r**3 + 1/30*r**5 - 3*r. Factor f(c).
2*c*(c - 1)*(c + 1)**2/3
Let m = -32 - -37. Let y(c) be the second derivative of 0*c**3 - c + 0*c**2 - 1/135*c**6 + 0 + 1/189*c**7 + 1/54*c**4 - 1/90*c**m. Factor y(u).
2*u**2*(u - 1)**2*(u + 1)/9
Let l be ((-4 - -12)/(-4) + 2)/(-2). Factor l - 1/3*o**2 - 1/3*o**3 + 0*o.
-o**2*(o + 1)/3
Let f(d) be the first derivative of -d**6/900 + d**5/50 - 3*d**4/20 + 5*d**3/3 - 6. Let t(h) be the third derivative of f(h). Factor t(z).
-2*(z - 3)**2/5
Let m(l) be the third derivative of 1/3*l**3 + 0 + 2/15*l**5 + 1/3*l**4 + 0*l + 9*l**2. Factor m(n).
2*(2*n + 1)**2
Let y(c) be the first derivative of -c**4 + 16*c**3/3 - 10*c**2 + 8*c + 14. Factor y(v).
-4*(v - 2)*(v - 1)**2
Suppose 0 = q + q - 4. Factor -8/5*r**2 + q*r - 4/5 + 2/5*r**3.
2*(r - 2)*(r - 1)**2/5
Suppose 3*g - 3 - 75 = 0. Suppose 8*r - 22 = -d + 3*r, 3*d = -5*r + g. Factor 4/7*u - 2/7*u**d - 2/7.
-2*(u - 1)**2/7
Let n(f) be the third derivative of f**7/105 - f**6/30 - f**5/10 + f**4/3 + 4*f**3/3 + 30*f**2. Solve n(w) = 0.
-1, 2
Let i(u) be the second derivative of -1/10*u**5 + u + 0 - 1/3*u**4 - 4/9*u**3 + 0*u**2 - 1/90*u**6. Let i(y) = 0. Calculate y.
-2, 0
Let c = -5 - -10. Let f = 100 + -97. Determine s so that 0 - 12/5*s**f - 2/5*s**c + 8/5*s**4 + 8/5*s**2 - 2/5*s = 0.
0, 1
Let t be (3/9 - (-64)/(-12))/(-1). Solve -2/7*o + 2/7 - 4/7*o**2 + 4/7*o**3 + 2/7*o**4 - 2/7*o**t = 0 for o.
-1, 1
Let f(s) be the first derivative of -s**8/5040 + s**6/540 - s**4/72 - 4*s**3/3 + 4. Let o(q) be the third derivative of f(q). Solve o(v) = 0 for v.
-1, 1
Let j(m) = m**3 - 2*m + 1. Let d be j(1). Let t(h) be the second derivative of 4/7*h**2 + 1/42*h**4 + d - 4/21*h**3 - 3*h. Suppose t(w) = 0. Calculate w.
2
Let l(r) = 8*r**4 - 6*r**3 - 2*r**2 + 6*r. Let c(w) = -9*w**4 + 7*w**3 + 2*w**2 - 7*w. Let y(i) = -6*c(i) - 7*l(i). Factor y(s).
-2*s**2*(s - 1)*(s + 1)
Let c = 1/10 - -3/20. Let p(z) be the first derivative of -2 - 1/4*z**2 + c*z + 1/12*z**3. Find a such that p(a) = 0.
1
Let r(u) be the first derivative of -u**5 - 15*u**4 - 80*u**3 - 160*u**2 - 6. Factor r(g).
-5*g*(g + 4)**3
Factor 1/4*z**3 + 3/4*z + 5/4*z**2 - 9/4.
(z - 1)*(z + 3)**2/4
Let i(s) be the third derivative of s**7/630 + s**6/90 - s**4/8 + s**2. Let y(d) be the second derivative of i(d). Factor y(w).
4*w*(w + 2)
Find l such that -1/10*l**3 + 0*l**2 + 1/5 + 3/10*l = 0.
-1, 2
Let b = -58097/50 + 1162. Let l = 121/350 - b. Factor 4/7*q**2 - 2/7 + 0*q + 0*q**3 - l*q**4.
-2*(q - 1)**2*(q + 1)**2/7
Factor -3*c**4 + 10*c**3 - 2*c**3 - 2*c**3 - 3*c**5.
-3*c**3*(c - 1)*(c + 2)
Suppose 1/9*i**2 + 0 - 1/9*i**3 + 0*i = 0. Calculate i.
0, 1
Suppose 0 = -16*u + 8*u. Factor 1/4*n**5 + 0*n + u*n**2 + 0*n**3 + 0 - 1/4*n**4.
n**4*(n - 1)/4
Suppose -2*g = -4*g + a + 8, g - 4*a - 18 = 0. Determine q, given that -2*q**3 - 3*q + 5*q + 4*q**2 + 3*q**3 - q**g = 0.
-2, -1, 0
Let g(s) be the third derivative of -1/60*s**5 + 0 + 0*s + 0*s**3 + s**2 - 1/120*s**6 + 0*s**4. Let g(t) = 0. What is t?
-1, 0
Factor 196*g**3 - 76*g - 170*g**2 - 306*g**2 - 244*g - 48.
4*(g - 3)*(7*g + 2)**2
Factor -3/8*h + 3/8*h**2 + 0.
3*h*(h - 1)/8
Factor -1/5*j**4 - 1/5*j + 0 + 1/5*j**3 + 1/5*j**2.
-j*(j - 1)**2*(j + 1)/5
Suppose -5*k + 105 = -3*d, -5*d - 74 = -2*k - 13. Let b be 1 - (k/8)/9. Find f, given that -f**2 + b*f**3 + 0 - f = 0.
-2/3, 0, 2
Find z, given that 162*z - 108 + 19/2*z**3 - 1/2*z**4 - 63*z**2 = 0.
1, 6
Let k(r) be the third derivative of r**7/105 + r**6/60 - 2*r**5/15 - r**4/3 - 29*r**2. Factor k(a).
2*a*(a - 2)*(a + 1)*(a + 2)
Factor -1/4*a**2 + 1/2*a + 3/4.
-(a - 3)*(a + 1)/4
Let u = 42 - 2. Let 5*l + 60*l**3 + 3 + 25*l**2 + 74*l**2 + u*l + 3 = 0. Calculate l.
-1, -2/5, -1/4
Let i(j) be the first derivative of -j**7/2520 - j**6/1080 + j**5/72 - j**4/24 + j**3/3 + 1. Let u(n) be the third derivative of i(n). Factor u(x).
-(x - 1)**2*(x + 3)/3
Let v be 7/((-49)/(-2))*1. Let w be 7 - (-5)/((-5)/4). Factor -2/7*g**4 + 0 + 2/7*g**2 + v*g - 2/7*g**w.
-2*g*(g - 1)*(g + 1)**2/7
Let s(z) = z + 9. Let j(l) = l + 8. Let v(y) = -4*j(y) + 3*s(y). Let n be v(-5). Factor n + 2/3*b**4 - 2/3*b**2 + 0*b**3 + 0*b.
2*b**2*(b - 1)*(b + 1)/3
Let c(o) be the third derivative of 0*o + o**2 + 1/60*o**5 - 1/420*o**7 - 2/3*o**3 + 0*o**6 + 0 + 0*o**4. Let g(n) be the first derivative of c(n). Factor g(b).
-2*b*(b - 1)*(b + 1)
Let m(y) be the first derivative of y**4/4 + y**3 - 4. Solve m(z) = 0.
-3, 0
Let q = 9/140 + 1/28. Let r(v) be the first derivative of -1/2*v**2 + 0*v**3 - q*v**5 + 1/4*v**4 + 1 + 1/2*v. What is a in r(a) = 0?
-1, 1
Let z = -1 + 1. Let r be (0/1)/(z - -1). What is y in 0*y**2 + r*y + 0 - 1/2*y**5 - y**4 - 1/2*y**3 = 0?
-1, 0
Let t(f) be the third derivative of f**5/510 - f**4/68 + 4*f**2. Factor t(w).
2*w*(w - 3)/17
Let u = 175/4 + -43. Solve 3/4*d + 1/4*d**3 + 1/4 + u*d**2 = 0 for d.
-1
Let v = -2 - -5. Solve u**4 + 0*u**4 + 2*u**4 + u**2 + 2*u**v + u**3 + u**5 = 0.
-1, 0
Factor 55*r**3 - 3*r**2 + 9*r**4 - 49*r**3 + 4*r**5 + 4*r**2.
r**2*(r + 1)**2*(4*r + 1)
Let m = 13 - 11. Find u, given that -10*u + 14*u**m - 7*u**2 - u**2 - 2*u**4 + 2*u**3 + 4 = 0.
-2, 1
Suppose 2*s = -s + 210. Let -70 - 9*h - 6*h**2 + s - h**3 = 0. What is h?
-3, 0
Let c(r) = -r**3 - r**2 + r. Let b(f) be the second derivative of -f**2/2 + f. Let s(m) = -b(m) + c(m). Suppose s(u) = 0. Calculate u.
-1, 1
Let h(v) = -v + 9. Let c be h(7). Factor 7*x**c - x**4 - 15*x**2 - 4*x + 4*x**3 + 2 + 7*x**4.
2*(x - 1)*(x + 1)**2*(3*x - 1)
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