(d). Factor x(l).
2*l*(l + 1)*(l + 2)/5
Suppose 4*d - 3*d = 0. Let y(q) be the first derivative of 0*q + 343/24*q**6 - 147/10*q**5 - 2/3*q**3 + d*q**2 + 1 + 21/4*q**4. Suppose y(b) = 0. Calculate b.
0, 2/7
Let y(v) be the first derivative of -42*v**5/55 + 69*v**4/22 - 12*v**3/11 - 84*v**2/11 + 48*v/11 - 4. Let y(x) = 0. What is x?
-1, 2/7, 2
Let a(k) be the first derivative of k**5/100 - k**3/10 - k**2/5 - 5*k + 3. Let q(n) be the first derivative of a(n). What is z in q(z) = 0?
-1, 2
Suppose -2/11*b**3 - 50/11 - 30/11*b + 18/11*b**2 = 0. What is b?
-1, 5
Factor 3*t**5 + 4*t**3 + 0*t**3 - 12*t**5 + t**4 + 8*t**5 - 4*t**2.
-t**2*(t - 2)*(t - 1)*(t + 2)
Let z = 1152 + -1150. Solve 1/9*g**4 + 0*g**3 - 1/9*g**z + 0*g + 0 = 0 for g.
-1, 0, 1
Let b(m) be the second derivative of -m**3/6 - 6*m. Let a be b(0). Let 1/3*u**4 + a*u**2 + 2/3*u**5 + 0*u - 1/3*u**3 + 0 = 0. Calculate u.
-1, 0, 1/2
Let y = 6 - -3. Suppose -15 + 3*n**3 + 4*n**2 + 5*n**2 - 3*n**4 - 3*n + y = 0. Calculate n.
-1, 1, 2
Let y(a) be the first derivative of a**5/20 - a**4/8 - a**3/12 + a**2/4 + 6. Factor y(q).
q*(q - 2)*(q - 1)*(q + 1)/4
Factor 0 - 1/2*j + 5/4*j**2 + 1/2*j**3 - 5/4*j**4.
-j*(j - 1)*(j + 1)*(5*j - 2)/4
Let b be 1/(-4) + (-27)/(-12). Factor -5*f + 3*f + 2*f - 4 - 2*f + b*f**2.
2*(f - 2)*(f + 1)
Suppose -n**2 - 3*n + 5*n**2 - 12 - n + 12*n = 0. Calculate n.
-3, 1
Let c(t) = t**3 + 6*t**2 - 6*t + 5. Let l be c(-7). Let z be (2 + 5/l)/(-2). Determine x, given that 1/2*x**3 + z*x**4 + 0 + 0*x + 1/4*x**2 = 0.
-1, 0
Let w(k) be the second derivative of -k**7/504 + k**6/360 + k**5/180 - k**3/6 + 9*k. Let o(p) be the second derivative of w(p). Factor o(z).
-z*(z - 1)*(5*z + 2)/3
Let t(w) be the first derivative of w**3 + 1 + 0*w**3 - 2*w**3 - 6*w**2 + 3*w**2 - 3*w. Find k, given that t(k) = 0.
-1
Solve 0*t**3 + 9*t**4 - 3*t**4 + 3*t**3 + 3*t**4 = 0 for t.
-1/3, 0
Suppose 2*k + k - 9 = 0. Find m such that -m - m + 0*m**3 - m**k + 3*m**3 = 0.
-1, 0, 1
Let h = 702/5 + -140. Factor -2/5*r**2 + 0 + h*r.
-2*r*(r - 1)/5
Factor -2/9*t**2 - 4/9 - 2/3*t.
-2*(t + 1)*(t + 2)/9
Let m(t) be the first derivative of -5/9*t**3 + 1/3*t - 2/3*t**2 - 7. Let m(y) = 0. Calculate y.
-1, 1/5
Let k = -1 + 4. Find j such that -6*j**2 + 2*j**2 - 4*j**4 - 6*j**k - j**5 + 0*j**2 - j = 0.
-1, 0
Suppose 0 = -2*k + 7*k - 10, -12 = -3*r - 3*k. Solve 6*c**2 + 7*c - 3*c**4 - c**4 - 4 - 7*c**3 + 4 - r = 0 for c.
-2, -1, 1/4, 1
Factor -2/5*s**3 - 12/5 - 2/5*s + 8/5*s**2.
-2*(s - 3)*(s - 2)*(s + 1)/5
Let c(x) be the second derivative of -x**7/2100 - x**6/450 + x**3/6 + 7*x. Let k(d) be the second derivative of c(d). Find l, given that k(l) = 0.
-2, 0
Factor -8*c**4 - 4*c**4 - 56*c**2 + 14*c - 50*c**3 - 22*c.
-2*c*(c + 2)**2*(6*c + 1)
Let z(v) be the first derivative of 2*v**5/15 - v**4/6 - 2*v**3/3 + v**2/3 + 4*v/3 - 15. What is y in z(y) = 0?
-1, 1, 2
Let u be -1 + (-3)/((-15)/35). Let a be 1/(2/u) + -3. Factor -1/4 + a*b + 1/4*b**2.
(b - 1)*(b + 1)/4
Let a(j) be the first derivative of j**4/42 + 2*j**3/21 + j**2/7 + 2*j - 3. Let v(i) be the first derivative of a(i). What is d in v(d) = 0?
-1
Let o(j) be the third derivative of j**5/15 + j**4/2 + 4*j**3/3 - 4*j**2. Factor o(c).
4*(c + 1)*(c + 2)
Let o(v) be the first derivative of -v**3 - 6*v - 9/2*v**2 - 1. Factor o(j).
-3*(j + 1)*(j + 2)
Let n be (-6)/(-14) + (-2)/21. Let j(g) be the second derivative of 0*g**2 + n*g**4 + 0 + 2/15*g**6 + 1/6*g**3 + 1/42*g**7 + 3/10*g**5 + g. Factor j(y).
y*(y + 1)**4
Find i such that -2*i**3 + 4*i**3 + 3*i**2 - 5*i**3 = 0.
0, 1
Let z(m) be the second derivative of -m**5/40 + m**4/8 - m**3/6 - 21*m. Find b such that z(b) = 0.
0, 1, 2
Let w = -324 + 980/3. Factor -w - 2/3*h**2 + 8/3*h.
-2*(h - 2)**2/3
Determine h so that 103*h**2 + 90*h**2 + 18 - 177*h**2 + h**3 - 35*h = 0.
-18, 1
Let d be (-35)/(-12) + 6/(-9). Let o = 11/4 - d. Factor 1/2*h**5 + h**2 - o - 1/2*h**4 + 1/2*h - h**3.
(h - 1)**3*(h + 1)**2/2
Let j(b) be the third derivative of 1/42*b**4 + 0*b + 0 - 6*b**2 + 0*b**3 + 1/105*b**5. Factor j(t).
4*t*(t + 1)/7
Let t be (-11)/(-2) - 4 - (0 + 1). Let -t*p**3 - 3*p + 1 + 9/4*p**2 = 0. What is p?
1/2, 2
Suppose 17*x + 15 - 49 = 0. Find n, given that -2*n + 1/2*n**x + 2 = 0.
2
Let w(y) be the first derivative of y**4 + 0*y + 2 + 0*y**2 - 2/3*y**3 - 2/5*y**5. Let w(a) = 0. What is a?
0, 1
Suppose -5*w = 9*c - 10*c + 5, -3*w = 5*c - 25. Let y(b) be the first derivative of 4/27*b**3 + 4 - 2/9*b + 0*b**4 + w*b**2 - 2/45*b**5. Factor y(r).
-2*(r - 1)**2*(r + 1)**2/9
Let d(u) = 5*u. Let c be d(1). Let b(q) be the first derivative of -1/5*q**c + 0*q - 5/3*q**3 + 3 - q**2 - q**4. Factor b(s).
-s*(s + 1)**2*(s + 2)
Let l(h) be the second derivative of 0 - 1/3*h**3 - 3*h - 1/3*h**4 + 2*h**2 + 1/10*h**5. Determine g so that l(g) = 0.
-1, 1, 2
Let w(h) be the first derivative of -h**4/24 - h**3/9 + h**2/12 + h/3 - 9. Factor w(u).
-(u - 1)*(u + 1)*(u + 2)/6
Suppose 7 = 4*a - 1. Solve a*s**2 - 4*s**2 + 0 + 2 = 0.
-1, 1
Suppose 0*a = 3*a + 15, -2*a - 4 = -t. Let s be (2/2 - 5)/t. Solve 20/3*x + 50/3*x**2 + s = 0 for x.
-1/5
Find s, given that -6/5 + 2*s + 2/15*s**3 - 14/15*s**2 = 0.
1, 3
Let n(l) be the second derivative of l**7/231 - 2*l**6/55 + 6*l**5/55 - 5*l**4/33 + l**3/11 + 5*l. Let n(s) = 0. What is s?
0, 1, 3
Let t = 22/43 + -288/731. Factor 6/17*r**3 + 6/17*r**4 + 0 + 0*r + 2/17*r**2 + t*r**5.
2*r**2*(r + 1)**3/17
Let b(i) be the second derivative of 7*i**5/6 - 43*i**4/6 + 76*i**3/9 - 4*i**2 + 2*i. Determine n so that b(n) = 0.
2/7, 2/5, 3
Let r = 119 + -594/5. Factor -2/5*g**3 - r*g**2 + 1/5*g**4 + 2/5*g + 0.
g*(g - 2)*(g - 1)*(g + 1)/5
Factor -2*r + 4*r**2 + 11*r + 5*r + 14*r.
4*r*(r + 7)
Determine t so that 11*t**2 + 10*t**3 - 7*t**2 - 11*t**3 = 0.
0, 4
Suppose 0*s + 4*s + 22 = 3*g, 5*s + 20 = 0. Factor 3*q**4 + q**g - 2*q**4 - 2*q**4 - 3*q**2 + 3*q**3.
-q**2*(q - 2)*(q - 1)
Determine i, given that 2/9*i**5 + 2/9*i + 4/9*i**2 - 2/9 - 4/9*i**3 - 2/9*i**4 = 0.
-1, 1
Factor 52*l**5 - 12*l**4 - 15*l**3 - 57*l**5 - 8*l**4.
-5*l**3*(l + 1)*(l + 3)
Let z(w) be the second derivative of -w**4/8 - 3*w**3/4 - 3*w**2/2 + 6*w. Factor z(k).
-3*(k + 1)*(k + 2)/2
Let w be (2/(-4))/(1/(-14)). Let k = -4 + w. Factor p**5 - 4*p**2 + 9*p**k - 9*p**4 + 2*p**5 + p**2.
3*p**2*(p - 1)**3
Let n(j) = -j**5 + 16*j**4 - 3*j**3 - 8*j**2 - 4*j. Let r(l) = -3*l**5 + 33*l**4 - 6*l**3 - 15*l**2 - 9*l. Let i(y) = 9*n(y) - 4*r(y). Factor i(w).
3*w**2*(w - 1)*(w + 1)*(w + 4)
Let k be 5 - (-7 - -3) - 3. Factor 4*y**4 - k*y - 12*y**3 + 12*y**2 + 9*y - 7*y.
4*y*(y - 1)**3
Let w(o) = -7*o**3 - 9*o**2 - 2*o + 9. Let v(b) = -3*b**3 - 4*b**2 - b + 4. Let r(d) = 9*v(d) - 4*w(d). Factor r(l).
l*(l - 1)*(l + 1)
Let h(n) be the second derivative of n**4/27 - n**3/27 + 3*n. Factor h(a).
2*a*(2*a - 1)/9
Factor 2*p**2 + 4*p - 3*p - 7*p.
2*p*(p - 3)
Solve 2*q**2 + 3 - 13 - 2 + 73*q**2 + 27*q**3 + 36*q = 0 for q.
-2, -1, 2/9
Suppose 0 + 28/3*m**2 + 2/3*m**3 + 98/3*m = 0. Calculate m.
-7, 0
Let i(n) be the third derivative of -n**8/23520 + n**6/2520 - n**4/4 + n**2. Let v(y) be the second derivative of i(y). Suppose v(j) = 0. What is j?
-1, 0, 1
Suppose -h - 9*h = -4*h. Determine g so that 0*g**4 + 0*g**2 - 2/9*g + 4/9*g**3 + h - 2/9*g**5 = 0.
-1, 0, 1
Let q be (-1)/((-5)/(-15)) + 52/15. Let t(b) be the first derivative of -2/9*b**3 - 3 + 3/4*b**4 + 0*b - q*b**5 + 0*b**2. Suppose t(y) = 0. What is y?
0, 2/7, 1
Let u(z) be the third derivative of 3*z**7/70 + z**6/8 - 11*z**5/20 + 3*z**4/8 + z**2. Determine w, given that u(w) = 0.
-3, 0, 1/3, 1
Suppose -4*s = -0*j - 3*j + 4, -24 = -4*s - 4*j. Factor 1/3*m**5 + 0 + 0*m**4 + 0*m + 0*m**s - 1/3*m**3.
m**3*(m - 1)*(m + 1)/3
Let g(r) be the third derivative of 1/12*r**4 + 0*r**3 - 1/30*r**5 + 0*r + 0 - 2*r**2. Let g(p) = 0. What is p?
0, 1
Suppose 0 = 4*t - 5*j - 3, 4*j + 5 = 9*j. Let 2/7*r - 2/7*r**t + 0 = 0. What is r?
0, 1
Solve -4/5*k + 0 - 1/5*k**3 + 4/5*k**2 = 0.
0, 2
Let i(t) be the second derivative of -t**6/150 + t**4/20 + t**3/15 - 33*t. Determine f so that i(f) = 0.
-1, 0, 2
Let s(p) be the third derivative of -p**6/420 + 12*p**2. Find o, given that s(o) = 0.
0
Let q = 28 + -25. Let z(l) be the third derivative of 1/30*l**5 + 0 - 1/105*l**7 + 0*l**q - 1/60*l**6 + 3*l**2 + 0*l + 1/12*l**4. Factor z(a).
-2*a*(a - 1)*(a + 1)