g(k) = k**3 - 7*k**2 + 10*k - 21. Let l be g(6). Factor -10/9*w**l + 0 - 4/9*w**2 + 0*w - 2/3*w**4.
-2*w**2*(w + 1)*(3*w + 2)/9
Let c(u) = -u**5 + u**3 + u**2 - u - 1. Let y(m) = 11*m**5 - 16*m**3 - 6*m**2 + 11*m + 6. Let f(p) = 6*c(p) + y(p). Factor f(h).
5*h*(h - 1)**2*(h + 1)**2
Let w be 1*1/(-3)*44/(-55). Let a(b) be the first derivative of -3/10*b**6 - 3 - 12/25*b**5 - 1/10*b**2 + w*b**3 + 1/10*b**4 + 0*b. Factor a(s).
-s*(s + 1)**2*(3*s - 1)**2/5
Let c(h) = 2*h + 1. Let q be c(-2). Let p(w) = -2*w**2 - w - 3. Let z(k) = -k - 1. Let t(d) = q*z(d) + p(d). Let t(y) = 0. What is y?
0, 1
Let j(b) be the third derivative of b**5/30 - b**4/4 + 2*b**3/3 + 9*b**2. Factor j(h).
2*(h - 2)*(h - 1)
Let j(k) be the third derivative of -16*k**7/1365 + 14*k**6/195 - 19*k**5/130 + 19*k**4/156 - 2*k**3/39 + k**2. Suppose j(v) = 0. What is v?
1/4, 1, 2
Let x be (1 - -5)*(-2)/(-4). Factor -1 - 2*k**2 - 7 - x*k + 8*k**3 + 2*k**4 - 5*k + 8*k**2.
2*(k - 1)*(k + 1)*(k + 2)**2
Let z(b) = b**3 - 7*b**2 - b - 5. Let m be z(7). Let y be (m/(-15))/((-6)/(-5)). Factor 2/3*a + y*a**3 + 4/3*a**2 + 0.
2*a*(a + 1)**2/3
Factor 10*x**2 - 5*x + x + 5*x**3 - 11*x.
5*x*(x - 1)*(x + 3)
Let n = 135/22 - 62/11. What is k in 1 + n*k - 1/2*k**2 = 0?
-1, 2
Let u = -12 + 12. Suppose 0 = -u*o - o. Factor o*p + 0 + 0*p**3 - 1/4*p**5 + 3/4*p**4 - p**2.
-p**2*(p - 2)**2*(p + 1)/4
Suppose 0 = 3*j - j - 10. Factor 2*l**2 + j*l**3 + 3*l**3 - 4*l**3 + 2*l**4.
2*l**2*(l + 1)**2
Let r be (-18)/(-9) + (1 - 3). Factor 8*w**4 - 2*w**4 - 3*w**3 + 7 - 3*w - 1 - 18*w**2 + r*w**4.
3*(w - 2)*(w + 1)**2*(2*w - 1)
Let j(i) = -i**3 + 8*i**2 + 6*i + 31. Let z be j(9). Let m(s) be the second derivative of 1/36*s**z + 0 + s + 1/3*s**3 + 3/2*s**2. Factor m(p).
(p + 3)**2/3
Let v(i) be the first derivative of -i**3/3 + 6*i**2 - 36*i - 56. Solve v(h) = 0 for h.
6
Let f = 4 + 0. Suppose f*r = r + 9. Determine g so that 0*g**4 - g**4 + 4*g**2 - 6*g**4 - 12*g**r = 0.
-2, 0, 2/7
Let a(i) be the second derivative of -i**5/20 + 9*i**4/32 - i**3/4 + 5*i**2 + 7*i. Let v(z) be the first derivative of a(z). Factor v(u).
-3*(u - 2)*(4*u - 1)/4
Determine q so that -1/2 + 2*q**3 + 2*q - 3*q**2 - 1/2*q**4 = 0.
1
Let s = 138 + -136. Find v such that -2/9*v**s - 2/9 - 4/9*v = 0.
-1
Let y(o) = -4*o**2 + 17*o. Let v(w) = 20*w**2 - 84*w. Let q(u) = -5*v(u) - 24*y(u). Factor q(c).
-4*c*(c - 3)
Let z(r) be the second derivative of -r**6/70 + 3*r**5/70 + r**4/28 - r**3/7 + 11*r. Suppose z(s) = 0. What is s?
-1, 0, 1, 2
Let i = -103 - -107. Solve 0*b - 2/3*b**i + 0*b**3 - 2/3 + 4/3*b**2 = 0.
-1, 1
Let v(j) = -10*j - 3. Let b be v(1). Let x = 13 + b. Factor x*o + 0*o**3 - 2/3*o**4 + 0 + 2/3*o**2.
-2*o**2*(o - 1)*(o + 1)/3
Let v be 2/4*3/13. Let u = v - -7/52. Suppose -3/4*w - u*w**2 - 1/2 = 0. What is w?
-2, -1
Let u(a) be the third derivative of 0*a**3 + 4*a**2 + 0 + 0*a + 0*a**4 + 0*a**5 - 1/420*a**7 - 1/240*a**6. Let u(b) = 0. What is b?
-1, 0
Let n be (2/(-5))/((-21)/45). Let c be ((-2)/(-14))/(-4*5/(-80)). Determine h, given that -c + n*h + 10/7*h**2 = 0.
-1, 2/5
Let c(b) be the first derivative of 0*b - 2/5*b**2 + 3 + 2/15*b**3. Factor c(v).
2*v*(v - 2)/5
Suppose 0 = 2*a - 0*a. Find g, given that 0*g**2 + 0 + 2/3*g**4 + a*g + 0*g**3 + 2/3*g**5 = 0.
-1, 0
Suppose 5*g + n - 1 = 15, -3*n - 12 = 0. Let r(b) be the first derivative of -4*b - 2 - 4/3*b**3 + 7*b**2 - 3/2*b**g. Determine k so that r(k) = 0.
-2, 1/3, 1
Suppose 5*z - 4*z = 5*h - 29, -5*z = -2*h + 30. Let m be -4 + h - 2/(-10). Solve 0 + 2/5*d**5 + 6/5*d**3 + 0*d + 2/5*d**2 + m*d**4 = 0.
-1, 0
Solve -2/11*h + 1/11*h**4 + 2/11*h**3 - 1/11 + 0*h**2 = 0.
-1, 1
Let g be (160/(-144))/((-16)/30). Let t(o) be the second derivative of 0 - o + 2*o**2 + 8/3*o**3 + g*o**4 + 7/30*o**6 + 19/20*o**5 + 1/42*o**7. Factor t(c).
(c + 1)**3*(c + 2)**2
What is n in 20/3*n + 16/3*n**3 + 32/3*n**2 + 4/3 = 0?
-1, -1/2
What is d in 8/5*d**2 + 2/5*d**3 + 2*d + 4/5 = 0?
-2, -1
Let x(s) be the first derivative of -s**6/135 - 2*s**5/45 - 2*s**4/27 + 8*s + 10. Let j(q) be the first derivative of x(q). Suppose j(r) = 0. What is r?
-2, 0
Let u(j) be the second derivative of -j**4/108 + 4*j**3/27 - 8*j**2/9 + 25*j. Factor u(r).
-(r - 4)**2/9
Let k(p) be the third derivative of p**6/60 + p**5/30 - p**4/12 - p**3/3 + p**2. Factor k(u).
2*(u - 1)*(u + 1)**2
Let d(s) be the third derivative of 0*s - 1/120*s**5 + 0 + 1/6*s**3 - 1/48*s**4 - s**2. Let d(r) = 0. Calculate r.
-2, 1
Let f(p) be the first derivative of -p**4/3 + 2*p**2 + 8*p/3 - 7. Find o such that f(o) = 0.
-1, 2
Let t(q) = -2*q**4 + q**3 + 3*q**2 + 5*q + 2. Let s(c) = 5*c**4 - 3*c**3 - 7*c**2 - 11*c - 5. Let o(m) = 6*s(m) + 14*t(m). Solve o(f) = 0 for f.
-1, 1
Let z(f) = -f**4 + 2*f**3 + 3*f**2 - 2. Let u(w) = -w**3 - w**2 + 1. Let j(h) = -h**3 - 4*h**2 + 2*h + 6. Let k be j(-4). Let n(q) = k*u(q) - z(q). Factor n(a).
a**2*(a - 1)*(a + 1)
Let v(l) be the third derivative of l**8/40320 - l**5/30 - 4*l**2. Let r(y) be the third derivative of v(y). Factor r(d).
d**2/2
Let u(v) be the second derivative of v**7/42 + v**6/15 + v**5/20 + 9*v. Factor u(k).
k**3*(k + 1)**2
Let s(o) = -10*o**3 - 14*o**2 + 10*o + 32. Let t(n) = -11*n**3 - 15*n**2 + 9*n + 32. Let b(z) = 7*s(z) - 6*t(z). Find a, given that b(a) = 0.
-2, 2
Let r(o) = -3*o - 15. Let n(s) = 2*s + 8. Let t(i) = 5*n(i) + 3*r(i). Let a be t(8). Solve g + 2*g**4 - 2*g**2 + 6*g**2 + 7*g**a - 2*g**3 = 0.
-1, -1/2, 0
Let o = -165 + 165. Let w(p) be the third derivative of 1/168*p**8 - 1/4*p**4 - 1/15*p**5 - 1/3*p**3 - 3*p**2 + 1/30*p**6 + o*p + 0 + 1/35*p**7. Factor w(m).
2*(m - 1)*(m + 1)**4
Let z(j) be the first derivative of -j**4/6 - 2*j**3 - 9*j**2 - 18*j + 7. Factor z(f).
-2*(f + 3)**3/3
Let x(j) be the third derivative of -j**8/6720 + j**7/1120 - j**6/720 + j**3/3 - j**2. Let n(f) be the first derivative of x(f). Determine m so that n(m) = 0.
0, 1, 2
Let l = 20 - 20. Let q(y) be the first derivative of 2 - 4/3*y**3 + 0*y + l*y**2 + 5/3*y**6 + 4/5*y**5 - 5/2*y**4. Find z such that q(z) = 0.
-1, -2/5, 0, 1
Let p(r) = 10*r**4 - 14*r**3 - 16*r**2 - 10*r + 6. Let f(t) = -28*t**4 + 41*t**3 + 47*t**2 + 29*t - 17. Let j(w) = 6*f(w) + 17*p(w). Factor j(h).
2*h*(h + 1)**2*(h + 2)
Let k(x) be the second derivative of x**3/6 + 9*x**2/2 + 4*x. Let j be k(-7). Determine d so that -j*d**2 + 0 + 4/5*d + 6/5*d**3 = 0.
0, 2/3, 1
Suppose 1/4*o**3 + 0 + 0*o - 1/4*o**2 = 0. Calculate o.
0, 1
Factor 16/7 + 4/7*l**2 + 20/7*l.
4*(l + 1)*(l + 4)/7
Let b(i) be the second derivative of -5*i**4/48 - 5*i**3/24 + 5*i**2/4 - 2*i. Factor b(r).
-5*(r - 1)*(r + 2)/4
Let r(l) be the first derivative of -l**8/2520 - l**7/1260 + l**3/3 + 3. Let c(a) be the third derivative of r(a). Factor c(v).
-2*v**3*(v + 1)/3
Let i(s) be the third derivative of s**8/672 + s**7/420 - s**6/60 - s**5/30 - 12*s**2. Factor i(x).
x**2*(x - 2)*(x + 1)*(x + 2)/2
Let u(h) be the third derivative of 1/3*h**3 + 7/36*h**4 - 1/63*h**7 + 1/45*h**5 + 6*h**2 + 0*h - 1/504*h**8 + 0 - 1/30*h**6. Suppose u(r) = 0. Calculate r.
-3, -1, 1
Let t(d) be the first derivative of d**6/24 - 3*d**4/16 - d**3/6 - 8. Factor t(r).
r**2*(r - 2)*(r + 1)**2/4
Let h(y) be the third derivative of y**5/15 + y**4/3 - 20*y**2. Factor h(a).
4*a*(a + 2)
Let t(v) be the third derivative of v**6/360 + v**5/180 - v**4/72 - v**3/18 - 17*v**2. Factor t(m).
(m - 1)*(m + 1)**2/3
Let x = 1069 - 1068. Solve -x - 5/6*i**2 + 17/6*i = 0.
2/5, 3
Let t(y) be the first derivative of 7*y**6 - 39*y**5/5 - 24*y**4 + y**3 + 9*y**2 - 41. Determine w, given that t(w) = 0.
-1, -1/2, 0, 3/7, 2
Factor -18*b**2 + 112*b + 9*b**3 - 2*b**2 - 87*b - 10 - 4*b**3.
5*(b - 2)*(b - 1)**2
Suppose 0*n - 3 = -3*n. Let k = n + -1. Solve k*o - o**5 - 1 - 10*o**3 + 5*o**4 + 2 + 10*o**2 - 5*o = 0.
1
Let m be (-286)/(-546) - (-2)/14. Factor 4/3*v + m*v**2 + 0.
2*v*(v + 2)/3
Let c(g) be the first derivative of 0*g + 6 + g**2 - 2/3*g**3. Find p such that c(p) = 0.
0, 1
Factor -4/17*u**2 - 2/17*u**3 + 0 + 0*u.
-2*u**2*(u + 2)/17
Let t(j) be the second derivative of -j**7/210 + j**5/50 - j**3/30 + 25*j. Factor t(i).
-i*(i - 1)**2*(i + 1)**2/5
Solve 7/4*a**4 - 4*a**3 + a**2 + 0 + 0*a = 0 for a.
0, 2/7, 2
Factor -201*h + 100*h + h**3 + 99*h - h**2.
h*(h - 2)*(h + 1)
Let t(v) be the third derivative of -v**8/10080 + v**7/840 - 