 + t(i). Suppose k(b) = 0. What is b?
-6
Let r(x) be the first derivative of x**6/10 + 33*x**5/25 + 51*x**4/10 + 14*x**3/5 - 21*x**2/2 - 15*x - 4. Let r(i) = 0. What is i?
-5, -1, 1
Let u(x) = -6*x**4 - 14*x**3 + 8*x**2 + 8. Let g(y) = 4*y**4 + 9*y**3 - 5*y**2 - 5. Let m(w) = -8*g(w) - 5*u(w). Determine t, given that m(t) = 0.
-1, 0
Let w(n) be the first derivative of 0*n**4 + 1 - 1/50*n**5 + n + 0*n**2 - 1/75*n**6 + 0*n**3. Let c(s) be the first derivative of w(s). Factor c(q).
-2*q**3*(q + 1)/5
What is l in 26*l**2 + 4 - 19*l**3 + 34*l - 10*l + 2*l**4 + 31*l**3 + 4 = 0?
-2, -1
Let c(v) be the second derivative of 0 + 0*v**4 + 1/18*v**3 - 1/60*v**5 - v + 0*v**2. Solve c(j) = 0.
-1, 0, 1
Let n(y) be the first derivative of 0*y**4 + 3 + 4/21*y**3 - 1/7*y**2 - 4/35*y**5 + 0*y + 1/21*y**6. Suppose n(o) = 0. What is o?
-1, 0, 1
Let v(d) be the first derivative of d**7/3360 + d**6/720 + d**5/480 - 2*d**3/3 - 1. Let f(k) be the third derivative of v(k). Suppose f(h) = 0. What is h?
-1, 0
Let k = 0 - -4. Let c(y) = y**2 + 4*y + 1. Let w be c(-5). Factor -4*h**3 + w*h**k + 15 - 15.
2*h**3*(3*h - 2)
Let l = -142 - -142. Factor 2/5*f**4 + 0*f**3 + l - 2/5*f**2 + 0*f.
2*f**2*(f - 1)*(f + 1)/5
Let h(y) = -4*y**4 + 7*y**3 + y**2 - 5*y. Let x(l) be the first derivative of -l**5 + 2*l**4 + l**3/3 - 3*l**2 + 4. Let v(f) = -6*h(f) + 5*x(f). Factor v(r).
-r**2*(r + 1)**2
Let o be 117/(-405) + 1/3. Let c(w) be the second derivative of w - o*w**6 + 0*w**2 + 0*w**3 + 1/63*w**7 + 0 + 1/30*w**5 + 0*w**4. What is s in c(s) = 0?
0, 1
Let x(r) be the first derivative of -1/2*r - 1/4*r**2 + 1/8*r**4 - 3 + 1/6*r**3. Factor x(t).
(t - 1)*(t + 1)**2/2
Let l be (-2)/(3*(-2)/(-15)). Let a be (l - -1)*21/(-12). Factor j**2 - j**4 - a*j + 7*j.
-j**2*(j - 1)*(j + 1)
Suppose -31*q**4 - 28*q**4 + 12*q**3 + 3*q**3 + 64*q**4 = 0. Calculate q.
-3, 0
Let b be ((-3)/(-537))/((-3)/9). Let z = 379/1253 + b. Factor z*r**4 + 6/7*r**3 + 0 + 2/7*r + 6/7*r**2.
2*r*(r + 1)**3/7
Let n = -6 - -7. Let t be 10/80*2/n. Find u, given that 1/4*u**3 - 1/4*u + t*u**2 - 1/4 = 0.
-1, 1
Let y(i) be the second derivative of -i**6/480 - i**5/240 + i**2/2 - 3*i. Let a(h) be the first derivative of y(h). Factor a(t).
-t**2*(t + 1)/4
Let a(k) = -k**2 - 8*k - 1. Let z(s) = -9*s. Let y = -11 + 13. Let t(j) = y*z(j) - 3*a(j). Find h such that t(h) = 0.
-1
Let j = 8 - 4. Suppose 4*c - 8 = -5*n + j, 6 = n - c. Factor -4 + 4 - n + v + 6 - v**2.
-(v - 2)*(v + 1)
Let v(w) = -5*w**3 - 6*w**2 + 6. Let j(f) = -5*f**3 - 7*f**2 + 7. Let h(b) = -6*j(b) + 7*v(b). Factor h(t).
-5*t**3
Let u(f) be the second derivative of f**5/120 - f**3/36 - 8*f. Let u(p) = 0. What is p?
-1, 0, 1
Let t(i) be the first derivative of 4*i**5/45 + i**4/6 - i**2/9 - 16. Find g, given that t(g) = 0.
-1, 0, 1/2
Let j(f) be the second derivative of f**5/4 + 5*f**4/4 - 10*f**2 - 3*f. Find u, given that j(u) = 0.
-2, 1
Let j(x) be the third derivative of x**5/30 + x**4/6 + x**2. Let n(u) = -2*u**2 - 4*u. Let b(a) = 5*j(a) + 4*n(a). Let b(p) = 0. Calculate p.
-2, 0
Suppose 2*x - x = 4. Determine n so that -4*n**3 + x*n**3 + 2*n + n**4 - 1 - 2*n**3 = 0.
-1, 1
Let l(z) be the third derivative of z**8/2184 + z**7/455 + z**6/260 + z**5/390 - 6*z**2. Factor l(g).
2*g**2*(g + 1)**3/13
Let p(z) be the third derivative of -4*z**2 + 1/45*z**5 + 0 + 1/72*z**4 + 0*z - 1/120*z**6 - 1/9*z**3. Find o such that p(o) = 0.
-2/3, 1
Let q(f) = f**2 - 6*f + 4. Let m be q(6). Solve 39 + 64*o**3 - 39 - m*o = 0.
-1/4, 0, 1/4
What is z in -4/7*z + 0 - 2/7*z**2 + 2*z**4 + 12/7*z**3 + 4/7*z**5 = 0?
-2, -1, 0, 1/2
Let r be 3/18*-1 + (-20)/(-12). Let k(y) be the first derivative of 4 - 1/3*y**3 - r*y**2 - 2*y. Find h such that k(h) = 0.
-2, -1
Let y(o) be the first derivative of 1/15*o**6 + 0*o**4 + 0*o**5 - 1 + 0*o**3 + 0*o**2 + o. Let z(l) be the first derivative of y(l). Factor z(j).
2*j**4
Let s(x) be the third derivative of x**6/90 - x**5/45 - x**4/9 + 26*x**2. Factor s(u).
4*u*(u - 2)*(u + 1)/3
Let l(x) be the first derivative of -2*x**3/3 + 6*x**2 - 8. Find g, given that l(g) = 0.
0, 6
Suppose -6*k - k + 14 = 0. Let h(a) = a**2 - 2. Let c be h(-2). Factor 2*o**2 - o - o**k - c + 0.
(o - 2)*(o + 1)
Let d(v) be the first derivative of v**5/5 + 4*v**4/3 + 10*v**3/3 + 4*v**2 + 3*v - 3. Let c(a) be the first derivative of d(a). Factor c(p).
4*(p + 1)**2*(p + 2)
Let p(h) be the first derivative of h**4/48 - h**3/6 + 3*h**2/8 + 7*h - 1. Let n(v) be the first derivative of p(v). Solve n(j) = 0.
1, 3
Let c be ((-12)/(-27))/((-3)/(0 - 3)). Find v such that -2/9*v + c - 2/9*v**2 = 0.
-2, 1
Let m(t) be the second derivative of 7*t + 1/39*t**6 + 0*t**2 + 0 - 1/39*t**4 + 0*t**3 - 3/130*t**5. Determine v so that m(v) = 0.
-2/5, 0, 1
Let s(g) be the third derivative of -g**5/40 + 3*g**4/16 + g**3 - 5*g**2. Find t, given that s(t) = 0.
-1, 4
Let i(g) = 66*g**3 - 64*g**2 + 7. Let p(r) = -65*r**3 + 65*r**2 - 6. Suppose 3*d = 8 + 7. Suppose 1 = d*k - 9. Let f(u) = k*i(u) + 3*p(u). Factor f(h).
-(h - 1)*(7*h - 2)*(9*h + 2)
Suppose 2*i = c + 1, -3*i + 4*c = -5*i + 26. Suppose -f**3 + f**4 + i*f**2 + 5*f**3 - f**3 + f = 0. Calculate f.
-1, 0
Let d(k) be the second derivative of -2*k**7/105 - k**2/2 + 6*k. Let p(j) be the first derivative of d(j). Solve p(n) = 0 for n.
0
Find a such that 0 + 2/11*a**2 - 6/11*a = 0.
0, 3
Let f(q) be the second derivative of q**5/20 + q**4/24 - q**3/12 - 15*q. Factor f(z).
z*(z + 1)*(2*z - 1)/2
Let d(v) be the first derivative of v**5/20 - v**4/12 - 3*v + 2. Let b(s) be the first derivative of d(s). Solve b(k) = 0 for k.
0, 1
Let f(j) = -j**2 + 5*j + 1. Let n be f(7). Let m = n - -16. Find x such that -2/9*x + 0 + 2/9*x**m + 2/9*x**2 - 2/9*x**4 = 0.
-1, 0, 1
Let n be 0 + 10 + -3 + 0 + -2. Let k(c) be the first derivative of 4/35*c**n + 0*c**3 + 1/21*c**6 + 1/14*c**4 + 0*c**2 + 0*c - 1. Factor k(h).
2*h**3*(h + 1)**2/7
Suppose 12 = 6*q - 0. Find j such that 4*j + j - 3*j**q - 12 - 17*j = 0.
-2
Let f = -5 + 7. Let 0*y + 0*y**2 - y**f - 2*y = 0. Calculate y.
-2, 0
Let n be (-24)/(-2) + 0 + 0. Let w be (-8)/n + (-6)/(-9). Find p such that w + 1/2*p**3 + 0*p - 1/4*p**4 - 1/4*p**2 = 0.
0, 1
Let x(a) = -a - 1. Let o(w) = 3*w**2 - 54*w + 90. Let r(u) = o(u) - 18*x(u). Factor r(b).
3*(b - 6)**2
Factor 4/5*f**2 + 80 - 16*f.
4*(f - 10)**2/5
Let c(v) = -7*v**3 + 13*v**2 - 5*v. Let h(w) = 10*w**3 - 20*w**2 + 8*w. Let y be (-3 - -6) + 2 + 3. Let n(j) = y*c(j) + 5*h(j). Let n(l) = 0. What is l?
0, 2/3
Let f be (-3*(-2)/(-21))/(3/(-21)). Let b(g) be the second derivative of 4*g + 0 - g**3 + 1/12*g**4 + 9/2*g**f. Factor b(u).
(u - 3)**2
Let s be (49/56*(-3)/(-7))/3. Let p(i) be the third derivative of 1/120*i**6 + 1/20*i**5 + s*i**4 + 3*i**2 + 1/6*i**3 + 0*i + 0. Factor p(n).
(n + 1)**3
Let j = 82 + -80. Let v(y) be the second derivative of -1/60*y**4 + 1/100*y**5 - 1/30*y**3 + 1/10*y**j + 3*y + 0. Factor v(u).
(u - 1)**2*(u + 1)/5
Let i(f) = 10*f**3 - 10*f. Let q(v) = -3*v**3 + 3*v. Let b(c) = 2*i(c) + 7*q(c). Factor b(l).
-l*(l - 1)*(l + 1)
Let s = 23 + -20. Let l(j) be the first derivative of -37/6*j**4 - 158/15*j**5 + 8/9*j**s + 1 + 0*j + 4/3*j**2 - 14/3*j**6. Suppose l(b) = 0. Calculate b.
-1, -2/3, -1/2, 0, 2/7
Let o be ((-1)/(-4) - (-4)/(-16))/1. Let d = 506/7 + -72. Find m such that o*m**2 + 2/7 - 4/7*m - d*m**4 + 4/7*m**3 = 0.
-1, 1
Let s(x) be the third derivative of -x**8/1848 + x**7/231 + x**6/22 + 5*x**5/33 + 35*x**4/132 + 3*x**3/11 + 4*x**2 - 2. Factor s(r).
-2*(r - 9)*(r + 1)**4/11
Suppose 4*t + 2*i = 70, -3*t - 2*t + 55 = -4*i. What is c in -c - 26*c**3 - t*c**2 + 5*c**3 + 4*c + 3*c = 0?
-1, 0, 2/7
Suppose -4*x = -2*c - 20, 3*x - c = -2*x + 19. Suppose -4*i = -0*i. Factor 2/5*t**x + 2/5*t**2 + i*t + 0.
2*t**2*(t + 1)/5
Let a(k) be the third derivative of -k**6/24 - 7*k**5/12 - 10*k**4/3 - 10*k**3 - 55*k**2. Factor a(m).
-5*(m + 2)**2*(m + 3)
Find p such that 3*p - 3/2*p**2 - 3/2 = 0.
1
Let x(w) be the third derivative of w**8/840 + 4*w**7/525 + w**6/50 + 2*w**5/75 + w**4/60 + 2*w**2. What is g in x(g) = 0?
-1, 0
Let s(i) be the third derivative of i**8/2184 - i**6/390 + i**4/156 + i**2 + i. Factor s(b).
2*b*(b - 1)**2*(b + 1)**2/13
Let x(b) = -b - 2. Let a be x(-4). Suppose c + 0*c - a = 0. Suppose 2 - s**2 + 2*s + 0*s - s**c - 2*s**3 = 0. What is s?
-1, 1
Let 