3 - 2*y**3/9 + 2*y**2/3 + 2*y/3 + 7. Determine c so that w(c) = 0.
-1, -1/2, 1
Let w(h) = -h**2 + 9*h - 5. Let g(s) = s. Let r(v) = 14*v + 2. Let m(k) = -36*g(k) + 2*r(k). Let u(f) = -3*m(f) - 4*w(f). Solve u(p) = 0.
1, 2
Let 18*z**3 - 29*z**3 + 24*z**2 + 20*z + 15*z**3 = 0. Calculate z.
-5, -1, 0
Let a(h) be the third derivative of -h**6/300 + 7*h**5/150 - 5*h**2. Factor a(f).
-2*f**2*(f - 7)/5
Suppose 0 = 2*a - 13 + 7. Factor 4*s**4 - 3*s**a - s**3 - 31*s + 31*s.
4*s**3*(s - 1)
Let i(c) = c**2 - 5*c + 3. Let y be i(5). Determine h, given that y*h**3 + 6*h**4 + h**4 - 4*h**4 = 0.
-1, 0
Let l(v) = -3*v**4 - 3*v**3 + 7*v**2 - v. Let y(n) = -5*n**4 - 6*n**3 + 13*n**2 - 2*n. Let i(q) = 7*l(q) - 4*y(q). Determine k, given that i(k) = 0.
0, 1
Let y(c) = -11*c**2 - 2*c + 4. Let q(v) = -21*v**2 - 3*v + 7. Let n(g) = -4*q(g) + 7*y(g). Determine p so that n(p) = 0.
0, 2/7
Let q(z) be the first derivative of 0*z + 1/15*z**5 + 0*z**2 + 1/12*z**4 - 1/18*z**6 + 1 - 1/9*z**3. Let q(o) = 0. Calculate o.
-1, 0, 1
Solve -7*t**2 - 2*t**3 + 26*t**2 - 17*t**2 = 0 for t.
0, 1
Solve 2/11 + 27/11*b**4 + 7/11*b - 27/11*b**3 - 9/11*b**2 = 0 for b.
-1/3, 2/3, 1
Let w be (-2)/((-1)/(3 + -1)). Let u = 10 + w. Determine o, given that 0 + 16*o**2 - 98/3*o**4 - u*o**3 - 8/3*o = 0.
-1, 0, 2/7
Let n(v) = v**5 + v**4 - v**3 - v. Let z(g) = -8*g**5 - 24*g**4 - 26*g**3 - 13*g**2 - g. Let o = 7 - 9. Let x(d) = o*n(d) - 2*z(d). Factor x(f).
2*f*(f + 1)**3*(7*f + 2)
Determine w, given that 0*w - 2/3 + 1/6*w**2 = 0.
-2, 2
Let b(o) be the third derivative of -o**5/60 - o**4/8 + 2*o**3/3 + 17*o**2. What is f in b(f) = 0?
-4, 1
Let g(y) = -y**4 - 5*y**3 + 3*y**2 + 5*y + 2. Let i(s) = -6*s**3 + 3*s**2 + 6*s + 3. Let k(f) = 3*g(f) - 2*i(f). Factor k(m).
-3*m*(m - 1)*(m + 1)**2
Let v(j) be the first derivative of -j**5/5 + j**4/4 - 27. Factor v(p).
-p**3*(p - 1)
Let i = 14 + -7. Suppose -1 - i*s**4 - 3*s**5 + 3*s**5 - 3*s**3 + 8*s**2 + s**3 - 2*s + 4*s**5 = 0. What is s?
-1, -1/4, 1
Let m(v) = -v**2 + 7*v - 1. Let s be m(6). Suppose 5*r + 5*f + 0*f - s = 0, -3*f - 7 = -2*r. What is q in 3*q - 3*q - 4*q**4 - q - 4*q**r - q**5 - 6*q**3 = 0?
-1, 0
Suppose -4*s + 44 - 11 = 3*f, -2*s + 9 = -f. Let h be (2/(-5))/(s/(-30)). Factor h*d**2 + 7 + 0*d + 2*d - 7.
2*d*(d + 1)
Suppose 0 = -2*z - 3*n - 3 - 12, 0 = 5*z - 4*n - 20. Determine b so that 4/3 + z*b**2 - 2*b + 2/3*b**3 = 0.
-2, 1
Solve -2/3*s - 1/3*s**4 + 2/3*s**3 + 0 + 1/3*s**2 = 0.
-1, 0, 1, 2
Let h(y) = y**3 + 9*y**2 + 8*y + 3. Let r be h(-8). Let t = 3 - r. Factor 1/3*q**3 + t + 0*q**2 + 0*q.
q**3/3
Let l(v) = -v**3 + 3*v**2 + 6*v - 8. Let o be l(4). Factor 1/3*n**4 - 1/6*n**5 + o - 2/3*n + 1/2*n**3 - 2/3*n**2.
-n*(n - 2)**2*(n + 1)**2/6
Suppose -m = -4*t - 18, -8*t - 12 = -5*t. Factor 3/4*j**4 + 9/4*j**3 + 0 + 9/4*j**m + 3/4*j.
3*j*(j + 1)**3/4
Factor 0*u**4 + u**3 - 1/2*u**5 + 0*u**2 + 0 - 1/2*u.
-u*(u - 1)**2*(u + 1)**2/2
Let m(j) be the second derivative of 0*j**2 - 3/40*j**5 + 0 - 1/24*j**4 - 1/84*j**7 + 2*j - 1/20*j**6 + 0*j**3. Determine q so that m(q) = 0.
-1, 0
Suppose -4*c + 3*i = -2 - 1, -3*c = -i - 1. Factor c*a - a + a**3 + 3*a**2 + 2*a - a**2.
a*(a + 1)**2
Determine z, given that -12/11*z + 0 + 2/11*z**2 + 2/11*z**3 = 0.
-3, 0, 2
Let c(b) be the third derivative of 0*b**5 - 1/75*b**6 + 0*b**4 - 2/175*b**7 - 9*b**2 + 0*b + 0 + 0*b**3 + 1/84*b**8. Determine o, given that c(o) = 0.
-2/5, 0, 1
Suppose -2*z - 3*q + 21 = 0, 4*z - 59 = -5*q - 22. Let o(i) be the second derivative of 1/24*i**4 + 0 + 0*i**z - 1/40*i**5 + 0*i**2 - 3*i. Factor o(g).
-g**2*(g - 1)/2
Suppose p - 9 = -2*p, 4*p + 3 = 5*r. Factor 24 - 3*j**3 - 24 + r*j**5.
3*j**3*(j - 1)*(j + 1)
Let x(l) be the second derivative of 7*l**6/90 - l**5/60 + 34*l + 2. Factor x(m).
m**3*(7*m - 1)/3
Factor s**4 - 2*s**4 + s**3 + 0*s**3.
-s**3*(s - 1)
Let a(l) be the third derivative of l**7/1470 - l**6/280 + l**5/140 - l**4/168 - 5*l**2. What is z in a(z) = 0?
0, 1
Let m(h) be the third derivative of 0 + 0*h + h**2 - 1/6*h**3. Let k(n) = -2*n**2 + 2*n + 9. Let x(i) = -k(i) - 5*m(i). Let x(a) = 0. What is a?
-1, 2
Factor 7/3 - 31/3*i**2 + 20/3*i + 4/3*i**3.
(i - 7)*(i - 1)*(4*i + 1)/3
Determine p so that -27/2*p**5 - 36*p + 123/2*p**3 + 153/2*p**2 - 117/2*p**4 - 30 = 0.
-5, -2/3, 1
Let q**5 + 149*q**2 + 5*q**4 + 5*q**3 - 6*q**5 - 154*q**2 = 0. What is q?
-1, 0, 1
Let f(l) be the first derivative of -l**6/3 + 2*l**5/5 + l**4 - 7. Let f(k) = 0. Calculate k.
-1, 0, 2
Let c(k) = -k**2 + 6*k. Let b be c(5). Suppose -20 = -b*g + 20. Factor 0*j**3 - g*j + 1 - 5 + j**2 - 6*j**2 - j**3.
-(j + 1)*(j + 2)**2
Let y(f) = f**2 + 5*f + 6. Let m be y(-1). Factor 1/4*d**3 + m + 3/2*d**2 + 3*d.
(d + 2)**3/4
Let b be 216/60*6/27. Factor -b*u + 1/5*u**2 + 4/5.
(u - 2)**2/5
Let o(z) = 10*z**3 - z**2 - z + 1. Let r be o(1). Solve r*c - 8*c - 13*c + 3*c**2 = 0.
0, 4
Let b(i) be the first derivative of -5*i**6/6 + 15*i**4/2 - 40*i**3/3 + 15*i**2/2 - 22. Solve b(h) = 0.
-3, 0, 1
Let v be (-180)/(-81) + (-2)/3. Suppose 26/9*g**2 + 46/9*g**4 + 0 + v*g**5 + 6*g**3 + 4/9*g = 0. Calculate g.
-1, -2/7, 0
Let d be 12 + -10 - (-1)/1. Solve 2/9*g**4 - 2/9*g - 2/9*g**2 + 0 + 2/9*g**d = 0.
-1, 0, 1
Find y, given that -12*y**4 - 8*y + 14*y**4 + 16*y**2 - 10*y**3 + 0*y**4 = 0.
0, 1, 2
Let -1/3*k - 4/3 + 5/3*k**2 = 0. What is k?
-4/5, 1
Let i(j) = 6*j**2 - 80*j + 224. Let h(o) = 4*o**2 - 53*o + 149. Let y(f) = 8*h(f) - 5*i(f). Solve y(g) = 0.
6
Let k be 16/(-4) - (-2 + -2). Let y(d) be the third derivative of k*d - 5/132*d**4 - 2/33*d**3 - 1/660*d**6 - 2/165*d**5 + 0 + d**2. Solve y(z) = 0 for z.
-2, -1
Let v(a) be the first derivative of -2*a**5/55 + a**4/22 + 2*a**3/33 - a**2/11 + 42. Let v(n) = 0. Calculate n.
-1, 0, 1
Suppose -3*i + 5*g = 3*g, 0 = 2*i - 5*g. Suppose i = -v + 2*v. Factor 1/2*b**2 + 0 + 1/4*b**5 - 1/4*b - 1/2*b**4 + v*b**3.
b*(b - 1)**3*(b + 1)/4
Let k = -2 + 3. Let u = -1 + k. Find l, given that u*l + 2*l**2 + l - 2*l - l**3 = 0.
0, 1
Let p be (-11)/(-2) - 2/4. Let o(z) = -3 + 3*z**2 + 0*z - 4*z - p. Let l(i) = 2*i**2 - 4*i - 7. Let g(f) = -4*l(f) + 3*o(f). Factor g(c).
(c + 2)**2
Let a = 64 - 255/4. Factor -a + 1/2*c - 1/4*c**2.
-(c - 1)**2/4
Suppose -18 = -4*a - 2. Factor 2*k**a - k**4 + 3*k - 3*k**3 + k.
k*(k - 2)**2*(k + 1)
Let l = 1 + 5. Let v be ((-8)/l)/((-4)/6). Factor -8/9 - 8/3*d + 14/9*d**v.
2*(d - 2)*(7*d + 2)/9
Suppose 0 = 5*u - 5. Let s(r) = 1 + 0 - 1 + r**2. Let z(b) = b**2. Let i(t) = u*z(t) - 2*s(t). Let i(k) = 0. Calculate k.
0
Let z(a) = 2*a**3 - 10*a**2 + 8*a + 20. Let q(n) = -4*n**3 + 20*n**2 - 17*n - 41. Let m(r) = 4*q(r) + 10*z(r). Factor m(h).
4*(h - 3)**2*(h + 1)
Let g(a) be the third derivative of 0*a**5 + 0*a**3 + 0*a + 0 + 1/96*a**4 - 1/480*a**6 - 3*a**2. Factor g(y).
-y*(y - 1)*(y + 1)/4
Let t be (1 - 2)*11/(-55). Factor 2/5*z**2 + 0*z**3 + 0*z - t*z**4 - 1/5.
-(z - 1)**2*(z + 1)**2/5
Let d(q) be the first derivative of 3/8*q**2 - 1/12*q**3 - 1 - 1/2*q. Let d(b) = 0. What is b?
1, 2
Let d be 1*12/15*5. Let n(s) be the third derivative of 0*s**5 + 0*s + 0*s**3 - 2*s**2 + 0 - 1/84*s**d + 1/420*s**6. What is f in n(f) = 0?
-1, 0, 1
Let v(l) be the second derivative of -l**8/13440 + l**7/5040 + l**6/720 - l**4/6 + l. Let w(y) be the third derivative of v(y). Factor w(a).
-a*(a - 2)*(a + 1)/2
Let o = 3 - 3. Suppose -m + o*m - 3*w = 0, m = 2*w. What is l in 0*l**4 + m - 2/3*l + 0*l**2 + 4/3*l**3 - 2/3*l**5 = 0?
-1, 0, 1
Factor 2916*n**3 - 32 - 801*n**2 + 118*n + 314*n - 1143*n**2.
4*(9*n - 2)**3
Let n(r) be the first derivative of 8*r**3/9 - 4*r**2 + 6*r - 3. Factor n(b).
2*(2*b - 3)**2/3
Let t(r) be the third derivative of r**6/280 + r**5/35 + 3*r**4/56 - 33*r**2. Solve t(c) = 0 for c.
-3, -1, 0
Let k(c) = c**2 + 8*c + 10. Let q be k(-7). Factor -b**q + 0*b**2 + 0*b**2.
-b**3
Let y(q) be the second derivative of -3/20*q**5 - 19/18*q**3 + 0 - 3*q - 1/2*q**2 - 11/12*q**4. Factor y(o).
-(o + 3)*(3*o + 1)**2/3
Let f(n) = 7*n**2 + 7*n + 2. Let g(i) = 10*i**2 + 10*i + 3. Let w(z) = -7*f(z) + 5*g(z). Let u be w(-2). Factor u*h**2 + 3*h - h**2 - 2*h + h.
2*h*(h + 1)
Let h(o) be the first derivative of 2*o**5/9 + o**4/18 - 10*o**3/27 - o**2/9 + 6. Suppose h(b) = 0. Calculate b.
-1, -1/5, 0, 1
Let k = 49/9 - 677/126. Let m(z) be the second derivative of -5/21*z**3 + 0 - k*z**4 - 2/7