d. Let w(x) be the first derivative of p(x). Factor w(v).
2*(v - 1)*(v + 1)
Suppose 2*t + 0*t - 19 = 5*l, -2*t = 4*l + 8. Let k(r) be the first derivative of -2/21*r**3 + 0*r + 1/7*r**t - 2. Factor k(w).
-2*w*(w - 1)/7
Let f(a) be the first derivative of -4/9*a + 1/3*a**2 - 5 - 2/27*a**3. Let f(n) = 0. Calculate n.
1, 2
Suppose -4*k - 13 = 5*j - 8, -k = 2*j - 1. Let 0 + 4/5*y**2 + 1/5*y**5 + 1/5*y + 6/5*y**j + 4/5*y**4 = 0. Calculate y.
-1, 0
Factor 2/11 + 8/11*c**3 + 2/11*c**4 + 8/11*c + 12/11*c**2.
2*(c + 1)**4/11
Let w(s) be the first derivative of -1/4*s**4 + 1/3*s**3 + 0*s**2 + 0*s + 2. Suppose w(d) = 0. Calculate d.
0, 1
Let x(h) = -2*h - 6. Let k be x(-4). Let c(i) be the first derivative of -1/6*i**k + 2/15*i**5 + 0*i + 2 + 1/4*i**4 + 0*i**3. Determine b so that c(b) = 0.
-1, 0, 1/2
Let m(x) = x + 15. Let t be m(-8). Let y be 8 - 10 - (-18)/t. Factor -6/7*z**2 + 0 + y*z.
-2*z*(3*z - 2)/7
Determine h, given that 3/4*h**2 - 1/2*h + 0 - 1/4*h**3 = 0.
0, 1, 2
Let s(g) = g**2 - g**2 + 47 + g**3 - 51 + 3*g. Let y(b) = b**3 - 1. Let z(i) = i. Let v be z(4). Let q(t) = v*y(t) - s(t). Factor q(a).
3*a*(a - 1)*(a + 1)
Let f be ((-2)/(8/(-6)))/6. Suppose 0 - f*v**2 - 1/4*v = 0. Calculate v.
-1, 0
Let v(h) be the second derivative of 0*h**2 + 2*h + 1/50*h**5 - 1/10*h**4 + 0 + 2/15*h**3. Let v(s) = 0. Calculate s.
0, 1, 2
Let o = 3/10 + 11/30. Let d(c) be the first derivative of -o*c**3 + 0*c + 1 - 1/4*c**4 - 1/2*c**2. Factor d(f).
-f*(f + 1)**2
Factor -4*j**3 - 4*j**2 + 3 + 16*j + 11 + 2.
-4*(j - 2)*(j + 1)*(j + 2)
Factor 8/23*n - 8/23 - 2/23*n**2.
-2*(n - 2)**2/23
Let v(o) be the second derivative of -o**7/1080 + o**6/432 + o**5/180 + o**4/12 - 3*o. Let f(l) be the third derivative of v(l). Let f(m) = 0. What is m?
-2/7, 1
Let x be (-165)/(-22)*12/75. Factor -2/5*f**2 - x*f - 4/5.
-2*(f + 1)*(f + 2)/5
Suppose -2 = 5*u + 13. Let n be u + 6/1 + -1. Factor 0 + 1/3*m**3 + 0*m + 0*m**n - 1/3*m**5 + 0*m**4.
-m**3*(m - 1)*(m + 1)/3
Suppose s - 3*r - 15 = -2*s, 0 = -4*s - 2*r + 2. Suppose -s*p + 8 = -0. What is o in 0*o**5 - p*o**2 - o**3 + o**5 - o**4 + 5*o**2 = 0?
-1, 0, 1
Suppose 0 = 3*p + 6. Let w(i) = 1. Let q(j) = -j**2 + j - 1. Let a(h) = p*w(h) - 2*q(h). Determine z, given that a(z) = 0.
0, 1
Let x be 1/1*6/2. Suppose f = 3*f - 5*l - 14, l = -2. Factor -4*y**f - y - 2*y + y + 4 + 2*y**x.
2*(y - 2)*(y - 1)*(y + 1)
Suppose z = 5*z - 8. Factor 1/4*y**4 - 3/4*y**z - 1/4*y + 1/4*y**3 + 1/2.
(y - 1)**2*(y + 1)*(y + 2)/4
Let c be (4/(-14))/((-360)/42 + 8). Let u(a) be the first derivative of 2/5*a**3 + 3 - 1/5*a**2 + 4/25*a**5 + c*a**4 - 2/5*a. Let u(w) = 0. Calculate w.
-1, 1/2
Suppose -3 = -2*s + 9. Let q = s + -2. Factor -w**3 - 9*w**2 + 13*w**3 + 2*w - 8*w**4 + 3*w**q.
-w*(w - 1)**2*(5*w - 2)
Let i be 30/(-25)*(-210)/(-9). Let k be ((-5)/(-30))/((-1)/i). Let -k*c + 4/3 + 10/3*c**2 = 0. Calculate c.
2/5, 1
Let j be -1 + 2 - 4/(3 - 7). Let w = 11 - 8. Factor -8/5*o**j - 2/5*o + 0 - 6/5*o**w.
-2*o*(o + 1)*(3*o + 1)/5
Let l be 1 + ((-16)/2)/(-4). Let i(r) be the third derivative of 1/12*r**l - 1/24*r**4 + 0*r + 1/120*r**5 + r**2 + 0. Factor i(v).
(v - 1)**2/2
Let z be 1/(3/12*1). Let j(f) be the second derivative of 4/15*f**3 - 2/25*f**5 + f - 1/10*f**z - 1/75*f**6 + 4/5*f**2 + 0. Solve j(w) = 0.
-2, -1, 1
Find u, given that 0 + 1/6*u - 1/2*u**2 = 0.
0, 1/3
Factor -36*a**2 + 28*a + 92 + 80*a + 4*a**3 - 200.
4*(a - 3)**3
What is z in 0*z - 1/5*z**3 + 0 - 1/5*z**2 = 0?
-1, 0
Factor 1/7*v**2 + 11/7 - 12/7*v.
(v - 11)*(v - 1)/7
Suppose -6*p + 135 = -5*p. Solve 72*g - 36*g**5 - 12 - 111*g**2 + p*g**4 - 39*g**5 - 12*g**2 + 3*g**3 = 0.
-1, 2/5, 1
Solve 0 + 2/11*n + 4/11*n**2 = 0.
-1/2, 0
Let g(z) be the first derivative of -z**3/7 + 3*z**2/2 - 3. Solve g(a) = 0 for a.
0, 7
Let u = 46 - 46. Let n(r) be the third derivative of u*r**3 - 3*r**2 + 1/60*r**5 + 1/36*r**4 + 1/360*r**6 + 0*r + 0. Factor n(h).
h*(h + 1)*(h + 2)/3
Let i be 3 - (8 + -15 + 6). Suppose 0*h**2 + 2/9*h**i - 2/9*h**3 + 0*h + 0 = 0. What is h?
0, 1
Let q be ((-1)/(-9))/(5/10). Suppose 2/9*x**2 - q*x**3 + 0 + 4/9*x = 0. Calculate x.
-1, 0, 2
Factor -3/4*r**3 + 21/4*r**2 - 45/4*r + 27/4.
-3*(r - 3)**2*(r - 1)/4
Let m(u) = -u**2 - 1. Let c(v) = v**2 + 2. Let k(s) = -3*c(s) - 6*m(s). Factor k(r).
3*r**2
Let d(m) = -m**3 + 5*m**2 + 5*m. Let k(w) = -6*w**2 - 6*w. Let z(c) = -4*d(c) - 6*k(c). Solve z(g) = 0 for g.
-2, 0
Let l(p) be the second derivative of -p**5/5 - 5*p**4/8 - p**3/2 - 3*p**2/2 - 5*p. Let f(m) be the first derivative of l(m). Find r such that f(r) = 0.
-1, -1/4
Suppose -20*i = -5*x - 23*i, 4*i = 0. Let d(y) be the second derivative of y - 3/80*y**5 + 1/120*y**6 + 0*y**2 + 1/16*y**4 - 1/24*y**3 + x. Factor d(v).
v*(v - 1)**3/4
Find b such that 27/2*b**2 + 3/4*b**3 + 81*b + 162 = 0.
-6
Let i(p) = 148*p**2 - 84*p - 8. Let v(n) = -21*n**2 + 12*n + 1. Let o(a) = 6*i(a) + 44*v(a). Determine r so that o(r) = 0.
1/3
Let d(f) = -4*f**2 + 2*f - 3. Let p(v) = 5*v**2 - v + 2. Let t(s) = 4*d(s) + 3*p(s). Factor t(g).
-(g - 3)*(g - 2)
Let t(o) = o**2 + 22*o + 144. Let z(r) = 2*r**2 + 43*r + 288. Let w(x) = -10*t(x) + 4*z(x). Determine v, given that w(v) = 0.
-12
Factor 13/5*s**2 - 48/5*s + 36/5 - 1/5*s**3.
-(s - 6)**2*(s - 1)/5
What is n in -8/7*n**3 - 2/7*n**4 + 0*n + 2/7*n**5 + 0 + 8/7*n**2 = 0?
-2, 0, 1, 2
Let o(l) be the first derivative of l**7/2520 - l**6/540 + l**5/360 + 2*l**3/3 - 1. Let a(d) be the third derivative of o(d). Factor a(y).
y*(y - 1)**2/3
Let q be (2/4)/((-5)/10). Let w(f) = f + 1. Let d be w(q). Solve -2/3*y - 1/3*y**4 + 1/3 + 2/3*y**3 + d*y**2 = 0.
-1, 1
Let -2/11*n**2 + 0*n + 2/11 = 0. What is n?
-1, 1
Let v(m) be the third derivative of 1/180*m**6 + 0*m - 1/18*m**3 + 0*m**5 + 0 - m**2 - 1/36*m**4 + 1/630*m**7. Factor v(a).
(a - 1)*(a + 1)**3/3
Let u(x) be the third derivative of x**8/2688 + x**7/2520 - x**4/12 + 2*x**2. Let d(g) be the second derivative of u(g). Factor d(k).
k**2*(5*k + 2)/2
Let l(y) be the first derivative of y**4/4 + 2*y**3 - 7*y**2/2 - 35. Factor l(p).
p*(p - 1)*(p + 7)
Let s(v) be the first derivative of 4*v**3/3 + 4*v**2 + 4*v + 5. Factor s(h).
4*(h + 1)**2
Let u = -8/29 - -82/87. Factor 4/3 + 2/3*v - u*v**2.
-2*(v - 2)*(v + 1)/3
Factor 476*j - 4*j**2 + 6*j**2 - 448*j.
2*j*(j + 14)
Suppose -5*a + 15 - 5 = 0. Factor -7*g**2 - a*g + 4*g**2 + g**2 + 4*g**2.
2*g*(g - 1)
Let h be 1 + (2 - 7 - 16/(-3)). Let 0*o**2 + 2/3*o**3 - h*o**4 + 2/3*o**5 + 0 + 0*o = 0. What is o?
0, 1
Let q(h) be the third derivative of h**6/60 + h**5/30 + 20*h**2. Solve q(v) = 0 for v.
-1, 0
Factor -4/5*m + 4*m**2 + 0 - 28/5*m**3 + 12/5*m**4.
4*m*(m - 1)**2*(3*m - 1)/5
Let z(p) be the first derivative of -p**3/33 - p**2/22 + 2*p/11 - 22. Find r such that z(r) = 0.
-2, 1
Suppose 0 = -5*p + 9 + 6. Suppose -p*t - t = -q - 16, -5*t = -q - 21. Determine l, given that 7/3*l**t + 2/3 - 4/3*l**3 - l + 4*l**4 - 14/3*l**2 = 0.
-1, 2/7, 1
Solve 4/11*a**2 + 0 + 6/11*a - 2/11*a**3 = 0.
-1, 0, 3
Let m = -128 + 1156/9. Factor m - 2/9*t - 2/9*t**2.
-2*(t - 1)*(t + 2)/9
Let v = -30 - -34. Let g(t) be the second derivative of -2/7*t**2 - 1/21*t**3 + 1/42*t**v + 0 - t. Suppose g(i) = 0. What is i?
-1, 2
Let a(f) be the first derivative of f**6/1980 - f**5/220 + f**3/3 - 1. Let x(i) be the third derivative of a(i). Factor x(r).
2*r*(r - 3)/11
Let b(c) = c**2 + c - 2. Suppose -5*y - 2*q = -15, -3*y + 5*q - 16 = 6. Let o be b(y). Solve -5/2*t**2 + o - 1/2*t = 0 for t.
-1/5, 0
Let m(y) be the second derivative of y**9/12096 - y**7/1680 + y**5/480 - y**3/2 + 4*y. Let q(x) be the second derivative of m(x). Find u, given that q(u) = 0.
-1, 0, 1
Let p = 3053576/587 + -5202. Let a = p - -3508/4109. Determine w so that -6/7*w - 2/7*w**3 + 2/7 + a*w**2 = 0.
1
Let x(l) be the third derivative of l**8/1680 - l**7/1050 - l**6/600 + l**5/300 - 12*l**2. Let x(t) = 0. Calculate t.
-1, 0, 1
Let p be -2*(-4)/24*-3. Let k be p + 32/(-20) - -3. Determine l, given that k*l**3 + 6/5*l**2 + 2/5 + 6/5*l = 0.
-1
Let g(z) be the first derivative of -5*z**3/3 - 25*z**2/2 - 20*z - 51. Factor g(r).
-5*(r + 1)*(r + 4)
Let k(l) = l. Let y(u) = -3*u**2 + 7*u. Let c(j) = -4*k(j) + y(j). Factor c(a).
-3*a*(a - 1)
Let o(t) = t**2 - 9*t + 10. Suppose 28 = 4*w - n, w = n - 0*n + 4. Let y be o(w). Factor m**2 - 6*m + 2 + 2*m + m**y.
2